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Modelovanie dynamiky vírusu Ebola celulárnym automatom - HackMD
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<div id="doc" class="markdown-body container-fluid" style="position: relative;"><h1 id="modelovanie-dynamiky-vírusu-ebola-celulárnym-automatom"><a class="anchor hidden-xs" href="#modelovanie-dynamiky-vírusu-ebola-celulárnym-automatom" title="modelovanie-dynamiky-vírusu-ebola-celulárnym-automatom"><span class="octicon octicon-link"></span></a>Modelovanie dynamiky vírusu Ebola celulárnym automatom</h1><h1 id="1-úvod"><a class="anchor hidden-xs" href="#1-úvod" title="1-úvod"><span class="octicon octicon-link"></span></a>1. Úvod</h1><p>Vírus Ebola je filovírus spôsobujúci vážne ochorenia väčšine ľudí, ktorí s ním prídu do kontaktu.<br>
Úmrtnosť pacientov je podľa správy[2] Svetovej zdravotníckej organizácie (WHO) z roku 2014 približne 70.8%.</p><p>Vzhľadom na extrémnu virulenciu Eboly sú možnosti pitiev a skúmania telesných tekutín pacientov značne obmedzené[3]. Počítačový model správania vírusu sa tak stáva cenným nástrojom pri skúmaní priebehu ochorenia, reakcie imunitného systému a potencionálneho nasadenia liekov. Model celulárneho automatu je založený na predchádzajúcom výskume vírusu HIV, ktorého negatívny dopad na imunitný systém je Ebole značne podobný[4].</p><p>V tomto článku predstavíme tri celulárne automaty, ktoré modelujú správanie sa vírusu pri rôznych reakciách imunitného systému. Na základe týchto troch celulárnych automatov zostavíme stochastický celulárny automat (SCA), modelujúci priebeh ochorenia pri variabilnej reakcii imunitného systému danej vstupnými parametrami.</p><p>Pomocou experimentov na zostavenom SCA budeme sledovať závislosť šírenia sa infekcie na pravdepodobnostiach druhov reakcií imunitného sytému. Zmyslom experimentov je zistiť vplyv spôsobu reakcie imunitného systému na úmrtnosť pacientov nakazených vírusom Ebola. Koncepcia bude overená porovnaním s údajmi o dobe liečby a miere úmrtnosti pacientov.</p><h2 id="11-zdroje-faktov"><a class="anchor hidden-xs" href="#11-zdroje-faktov" title="11-zdroje-faktov"><span class="octicon octicon-link"></span></a>1.1 Zdroje faktov</h2><h3 id="111-autori"><a class="anchor hidden-xs" href="#111-autori" title="111-autori"><span class="octicon octicon-link"></span></a>1.1.1 Autori</h3><ul>
<li>Eduard Čuba <a href="mailto:xcubae00@stud.fit.vutbr.cz" target="_blank">xcubae00@stud.fit.vutbr.cz</a></li>
<li>Jakub Kulich <a href="mailto:xkulic03@stud.fit.vutbr.cz" target="_blank">xkulic03@stud.fit.vutbr.cz</a></li>
</ul><h3 id="112-literatúra"><a class="anchor hidden-xs" href="#112-literatúra" title="112-literatúra"><span class="octicon octicon-link"></span></a>1.1.2 Literatúra</h3><p>Hlavným zdrojom, z ktorého táto štúdia vychádza je:</p><p><a href="https://doi.org/10.1016/j.physa.2015.06.049" target="_blank">Emily Burkhead, Jane Hawkins, A cellular automata model of Ebola virus dynamics, In Physica A: Statistical Mechanics and its Applications, Volume 438, 2015, Pages 424-435, ISSN 0378-4371</a></p><p>Ako ďalšie zdroje boli použité zdroje, ktoré hlavný článok cituje. Ich zoznam je uvedený v sekcii <a href="#bibliografia">Bibliografia</a>.</p><h2 id="12-overenie-validity"><a class="anchor hidden-xs" href="#12-overenie-validity" title="12-overenie-validity"><span class="octicon octicon-link"></span></a>1.2 Overenie validity</h2><p>O víruse Ebola so toho stále vie pomerne málo. Rôzne zdroje hovoria o mortalite v rozmedzí 25 až 90%[1]. Takto význačná odchýlka môže spôsobiť signifikantný rozdiel medzi výsledkami experimentov a realitou. Dáta o mortalite sú v rozvojových krajinách skreslené problematickou identifikáciou a nahlásením ochorenia[8]. V štúdii sa budeme odvíjať od údajov, ktoré publikovala Svetová zdravotnícka organizácia (WHO). Okrem údajov o mortalite je pre modelovanie šírenia vírusu dôležité správne interpretovať spôsob replikácie vírusu, ktorá vychádza z podobnosti s vírusom HIV. Validita modelu Eboly spolieha na validitu modelov používaných pre vírus HIV a správne predpoklady o podobnostiach a rozdieloch v replikácii týchto vírusov.</p><h1 id="2-rozbor-tématu-a-použitých-metodtechnologií"><a class="anchor hidden-xs" href="#2-rozbor-tématu-a-použitých-metodtechnologií" title="2-rozbor-tématu-a-použitých-metodtechnologií"><span class="octicon octicon-link"></span></a>2. Rozbor tématu a použitých metod/technologií</h1><p>Šírenie HIV, jeho efekt na organizmus a odozva na užívanie liekov bolo niekoľko krát skúmané a modelované pomocou stochastických celulárnych automatov([5, 6, 7]). Časové okno vírusu Ebola je kratšie[1], ako pri víruse HIV. U pacientov, ktorí nákazu vírusom Ebola prežili neboli pozorované vážne chronické následky[8].</p><p>V tejto štúdii sa preto zameriame na adaptáciu počiatočných fáz dynamiky modelu HIV z článku [5]. Pomocou celulárneho automatu budeme modelovať šírenie infekcie Eboly v jednom orgáne. Originálny model upravíme tak, aby jeho parametre a pravidlá pre šírenie infekcie zodpovedali dynamike vírusu Ebola. Z doposiaľ získaných poznatkov sa predpokladá[1], že miera mutácia vírusu Ebola je podstatne nižšia, ako pri víruse HIV. Preto je jednou z významných úprav pôvodného modelu nahradenie pravidla predstavujúceho mutáciu vírusu pravidlom, ktoré reflektuje oneskorenú, alebo spomalenú reakciu imunitného systému. Zvyšné pravidlá zostanú rovnaké. Táto malá zmena však spôsobí urýchlenie priebehu infekcie, čo vedie k pomerne rýchlemu vyzdraveniu, alebo smrti. Doba trvania príznakov je zvyčajne 2 až 21 dní[8]. Pacienti, ktorých stav sa nezlepší zvyčajne umierajú na šok, vykrvácanie, alebo zlyhanie orgánov[8]. Terminálna podmienka zastúpenia zdravých buniek sa pohybuje približne na úrovni jednej tretiny[1] - ak pomer zdravých buniek ku všetkým bunkám klesne pod jednu tretinu, človek zomrie.</p><p>Dáta o počiatočnej miere infekcie v orgáne v súčastnej dobe nie sú presne dostupné[1], budeme preto vychádzať z údajov používaných pre modelovanie infekcie HIV[5], ktoré sú na úrovni <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mo>&#x2212;</mo><mn>2</mn></mrow></msup><mo>+</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mo>&#x2212;</mo><mn>3</mn></mrow></msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn><mo>=</mo><mn>0.0055</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-16" style="width: 13.476em; display: inline-block;"><span style="display: inline-block; position: relative; width: 11.017em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1010.97em 2.666em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-17"><span class="mo" id="MathJax-Span-18" style="font-family: MathJax_Main;">(</span><span class="msubsup" id="MathJax-Span-19"><span style="display: inline-block; position: relative; width: 2.001em; height: 0px;"><span style="position: absolute; clip: rect(3.179em 1000.98em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mn" id="MathJax-Span-20" style="font-family: MathJax_Main;">10</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -4.403em; left: 1.027em;"><span class="texatom" id="MathJax-Span-21"><span class="mrow" id="MathJax-Span-22"><span class="mo" id="MathJax-Span-23" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-24" style="font-size: 70.7%; font-family: MathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-25" style="font-family: MathJax_Main; padding-left: 0.207em;">+</span><span class="msubsup" id="MathJax-Span-26" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 2.001em; height: 0px;"><span style="position: absolute; clip: rect(3.179em 1000.98em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mn" id="MathJax-Span-27" style="font-family: MathJax_Main;">10</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -4.403em; left: 1.027em;"><span class="texatom" id="MathJax-Span-28"><span class="mrow" id="MathJax-Span-29"><span class="mo" id="MathJax-Span-30" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-31" style="font-size: 70.7%; font-family: MathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-32" style="font-family: MathJax_Main;">)</span><span class="texatom" id="MathJax-Span-33"><span class="mrow" id="MathJax-Span-34"><span class="mo" id="MathJax-Span-35" style="font-family: MathJax_Main;">/</span></span></span><span class="mn" id="MathJax-Span-36" style="font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-37" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-38" style="font-family: MathJax_Main; padding-left: 0.259em;">0.0055</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.372em; border-left: 0px solid; width: 0px; height: 1.503em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>3</mn></mrow></msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn><mo>=</mo><mn>0.0055</mn></math></span></span><script type="math/tex" id="MathJax-Element-4">(10^{-2} + 10^{-3})/2 = 0.0055</script></span>.</p><h2 id="21-celulárny-automat"><a class="anchor hidden-xs" href="#21-celulárny-automat" title="21-celulárny-automat"><span class="octicon octicon-link"></span></a>2.1 Celulárny automat</h2><p>V experimentoch chceme sledovať šírenie infekcie medzi bunkami pomocou predom definovaných krokov. Využijeme na to model celulárneho automatu. Ten je typicky definovaný nasledujúcimi prvkami[IMS 317]:</p><ul>
<li>bunka (Cell) - základný element, ktorý môže byť v jednom z konečného počtu stavov</li>
<li>pole buniek (Lattice) - n-rozmerné, rovnomerné rozdelenie priestoru</li>
<li>okolie (Neighbourhood) - počet a pozícia okolitých buniek, s ktorými sa pracuje</li>
<li>pravidlá - funkcia stavu bunky a jej okolia definujúca nový stav bunky</li>
</ul><p>Použitie celulárneho automatu nám umožní modelovať šírenie vírusu medzi bunkami naprieč generáciami buniek.</p><h1 id="3-koncepcia"><a class="anchor hidden-xs" href="#3-koncepcia" title="3-koncepcia"><span class="octicon octicon-link"></span></a>3. Koncepcia</h1><p>V tejto kapitole uvedieme modely celulárnych automatov, ktoré sme využívali na simuláciu šírenia vírusu. Pre začiatok si uvedieme jednoduchý základný model, ktorý predstavuje šírenie vírusu pri správnom fungovaní imunitného systému. Následne uvedieme dve obmeny tohoto modelu, ktoré modelujú šírenie vírusu pri spomalenej, alebo vyčerpanej imunitnej reakcii. S využitím týchto troch modelov zostavíme stochastický celulárny automat, ktorého krok pre každú generáciu bude krokom jedného z predstavených automatov. Konkrétny na krok sa určí na základe vstupných pravdepodobností.</p><h2 id="31-základný-model-šírenia-vírusu"><a class="anchor hidden-xs" href="#31-základný-model-šírenia-vírusu" title="31-základný-model-šírenia-vírusu"><span class="octicon octicon-link"></span></a>3.1 Základný model šírenia vírusu</h2><p>V nasledujúcich podkapitolách bližšie špecifikujeme základný model celulárneho automatu, z ktorého budú ďalšie modely vychádzať.</p><h3 id="311-bunka"><a class="anchor hidden-xs" href="#311-bunka" title="311-bunka"><span class="octicon octicon-link"></span></a>3.1.1 Bunka</h3><p>V našom celulárnom automate môže bunka byť v jednom zo stavov <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-39" style="width: 6.406em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.228em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.335em 1005.18em 2.666em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-40"><span class="mo" id="MathJax-Span-41" style="font-family: MathJax_Main;">{</span><span class="mn" id="MathJax-Span-42" style="font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-43" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-44" style="font-family: MathJax_Main; padding-left: 0.156em;">1</span><span class="mo" id="MathJax-Span-45" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-46" style="font-family: MathJax_Main; padding-left: 0.156em;">2</span><span class="mo" id="MathJax-Span-47" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-48" style="font-family: MathJax_Main; padding-left: 0.156em;">3</span><span class="mo" id="MathJax-Span-49" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-50" style="font-family: MathJax_Main; padding-left: 0.156em;">4</span><span class="mo" id="MathJax-Span-51" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.372em; border-left: 0px solid; width: 0px; height: 1.378em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-5">\{0 ,1, 2, 3, 4\}</script></span>.</p><ul>
<li><span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-52" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-53"><span class="mn" id="MathJax-Span-54" style="font-family: MathJax_Main;">0</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-6">0</script></span> reprezentuje zdravú bunku (v simulácii značená ako <em>HEALTHY</em>)</li>
<li><span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-55" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-56"><span class="mn" id="MathJax-Span-57" style="font-family: MathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-7">1</script></span> reprezentuje infikovanú bunku (v simulácii značená ako <em>INFECTED</em>)
<ul>
<li>infikovaná bunka môže infikovať okolité bunky</li>
</ul>
</li>
<li><span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-58" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-59"><span class="mn" id="MathJax-Span-60" style="font-family: MathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span></span><script type="math/tex" id="MathJax-Element-8">2</script></span> reprezentuje infikovanú bunku, ktorá kvôli spomalenej reakcii imunitného systému nebola zabitá (v simulácii značená ako <em>SPOILED</em>)</li>
<li><span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-61" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-62"><span class="mn" id="MathJax-Span-63" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span></span><script type="math/tex" id="MathJax-Element-9">3</script></span> reprezentuje mŕtvu bunku (v simulácii značená ako <em>DEAD</em>)</li>
</ul><h3 id="312-pole-buniek"><a class="anchor hidden-xs" href="#312-pole-buniek" title="312-pole-buniek"><span class="octicon octicon-link"></span></a>3.1.2 Pole buniek</h3><p>Infekcia sa môže šíriť v orgánoch rôznych tvarov ako cievy (prevažne v jednej dimenzii), koža (prevažne v dvoch dimenziách), alebo pečeň (v troch dimenziách). Pole celulárneho automatu však nezobrazuje priestorovú štruktúru orgánu ako takého, ale relatívne usporiadanie a pozície buniek medzi sebou. Pre názornejšie ukázanie konceptu je tak vhodné použiť dvoj-rozmerné pole. Veľkosť poľa, ktorú budeme v experimente používať je 700 krát 700 buniek. Závislosť výsledkov na veľkosti ukážeme v experimentoch. Okraje poľa buniek sú prepojené (pole je periodické [IMS 320]).</p><h3 id="312-okolie"><a class="anchor hidden-xs" href="#312-okolie" title="312-okolie"><span class="octicon octicon-link"></span></a>3.1.2 Okolie</h3><p>Model používa Moorove okolie [IMS 318]. Bunka sa teda môže nakaziť od ľubovoľnej inej bunky v matici <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>&#x2217;</mo><mn>3</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-64" style="width: 2.308em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.898em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1001.85em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-65"><span class="mn" id="MathJax-Span-66" style="font-family: MathJax_Main;">3</span><span class="mo" id="MathJax-Span-67" style="font-family: MathJax_Main; padding-left: 0.207em;">∗</span><span class="mn" id="MathJax-Span-68" style="font-family: MathJax_Main; padding-left: 0.207em;">3</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>∗</mo><mn>3</mn></math></span></span><script type="math/tex" id="MathJax-Element-10">3*3</script></span>, ktorej je stredom.</p><h3 id="313-základné-pravidlá"><a class="anchor hidden-xs" href="#313-základné-pravidlá" title="313-základné-pravidlá"><span class="octicon octicon-link"></span></a>3.1.3 Základné pravidlá</h3><p>Pravidlá základného celulárneho automatu <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-69" style="width: 0.873em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.72em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.283em 1000.72em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-70"><span class="mi" id="MathJax-Span-71" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi></math></span></span><script type="math/tex" id="MathJax-Element-11">Z</script></span> pre prechod bunky <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-72" style="width: 0.515em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.41em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-73"><span class="mi" id="MathJax-Span-74" style="font-family: MathJax_Math-italic;">c</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></span></span><script type="math/tex" id="MathJax-Element-12">c</script></span> v čase <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-75" style="width: 0.771em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.617em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.62em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-76"><span class="mi" id="MathJax-Span-77" style="font-family: MathJax_Math-italic;">n</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></span></span><script type="math/tex" id="MathJax-Element-13">n</script></span> s okolím <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-78" style="width: 0.976em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.771em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.77em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-79"><span class="mi" id="MathJax-Span-80" style="font-family: MathJax_Math-italic;">O</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math></span></span><script type="math/tex" id="MathJax-Element-14">O</script></span> medzi stavmi z množiny <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo fence="false" stretchy="false">{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-81" style="width: 7.789em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.355em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.335em 1006.3em 2.666em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-82"><span class="mi" id="MathJax-Span-83" style="font-family: MathJax_Math-italic;">A</span><span class="mo" id="MathJax-Span-84" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mo" id="MathJax-Span-85" style="font-family: MathJax_Main; padding-left: 0.259em;">{</span><span class="mn" id="MathJax-Span-86" style="font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-87" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-88" style="font-family: MathJax_Main; padding-left: 0.156em;">1</span><span class="mo" id="MathJax-Span-89" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-90" style="font-family: MathJax_Main; padding-left: 0.156em;">2</span><span class="mo" id="MathJax-Span-91" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-92" style="font-family: MathJax_Main; padding-left: 0.156em;">3</span><span class="mo" id="MathJax-Span-93" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.372em; border-left: 0px solid; width: 0px; height: 1.378em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo fence="false" stretchy="false">{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-15">A = \{0, 1, 2, 3 \}</script></span> definujeme ako:</p><p><span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>c</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mn>1</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn><mo>&#x2227;</mo><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2208;</mo><mi>O</mi><mo>&#x2228;</mo><mn>2</mn><mo>&#x2208;</mo><mi>O</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>1</mn><mo>&#x2228;</mo><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>i</mi><mi>n</mi><mi>a</mi><mi>k</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math>" role="presentation" style="text-align: center; position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-94" style="width: 23.619em; display: inline-block;"><span style="display: inline-block; position: relative; width: 19.367em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.949em 1019.37em 5.74em -999.997em); top: -4.096em; left: 0em;"><span class="mrow" id="MathJax-Span-95"><span class="msubsup" id="MathJax-Span-96"><span style="display: inline-block; position: relative; width: 1.847em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-97" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="texatom" id="MathJax-Span-98"><span class="mrow" id="MathJax-Span-99"><span class="mi" id="MathJax-Span-100" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span class="mo" id="MathJax-Span-101" style="font-size: 70.7%; font-family: MathJax_Main;">+</span><span class="mn" id="MathJax-Span-102" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-103" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mrow" id="MathJax-Span-104" style="padding-left: 0.259em;"><span class="mo" id="MathJax-Span-105" style="vertical-align: 2.001em;"><span style="display: inline-block; position: relative; width: 0.873em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -3.071em; left: 0em;">⎧<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -1.432em; left: 0em;">⎩<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -1.995em; left: 0em;">⎨<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mtable" id="MathJax-Span-106" style="padding-right: 0.156em; padding-left: 0.156em;"><span style="display: inline-block; position: relative; width: 15.064em; height: 0px;"><span style="position: absolute; clip: rect(2.154em 1000.46em 5.587em -999.997em); top: -4.147em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px;"><span style="position: absolute; clip: rect(3.179em 1000.41em 4.152em -999.997em); top: -5.172em; left: 0em;"><span class="mtd" id="MathJax-Span-107"><span class="mrow" id="MathJax-Span-108"><span class="mn" id="MathJax-Span-109" style="font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1000.46em 4.152em -999.997em); top: -3.942em; left: 0em;"><span class="mtd" id="MathJax-Span-131"><span class="mrow" id="MathJax-Span-132"><span class="mn" id="MathJax-Span-133" style="font-family: MathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1000.46em 4.152em -999.997em); top: -2.713em; left: 0em;"><span class="mtd" id="MathJax-Span-151"><span class="mrow" id="MathJax-Span-152"><span class="mn" id="MathJax-Span-153" style="font-family: MathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.152em;"></span></span><span style="position: absolute; clip: rect(2.154em 1002em 5.587em -999.997em); top: -4.147em; left: 1.488em;"><span style="display: inline-block; position: relative; width: 2.001em; height: 0px;"><span style="position: absolute; clip: rect(3.128em 1001.03em 4.152em -999.997em); top: -5.172em; left: 0em;"><span class="mtd" id="MathJax-Span-110"><span class="mrow" id="MathJax-Span-111"><span class="mi" id="MathJax-Span-112" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-113" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.128em 1001.03em 4.152em -999.997em); top: -3.942em; left: 0em;"><span class="mtd" id="MathJax-Span-134"><span class="mrow" id="MathJax-Span-135"><span class="mi" id="MathJax-Span-136" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-137" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.128em 1002em 4.152em -999.997em); top: -2.713em; left: 0em;"><span class="mtd" id="MathJax-Span-154"><span class="mrow" id="MathJax-Span-155"><span class="mi" id="MathJax-Span-156" style="font-family: MathJax_Math-italic;">i</span><span class="mi" id="MathJax-Span-157" style="font-family: MathJax_Math-italic;">n</span><span class="mi" id="MathJax-Span-158" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-159" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.152em;"></span></span><span style="position: absolute; clip: rect(1.898em 1010.45em 4.408em -999.997em); top: -3.993em; left: 4.511em;"><span style="display: inline-block; position: relative; width: 10.556em; height: 0px;"><span style="position: absolute; clip: rect(3.076em 1010.45em 4.408em -999.997em); top: -5.172em; left: 0em;"><span class="mtd" id="MathJax-Span-114"><span class="mrow" id="MathJax-Span-115"><span class="msubsup" id="MathJax-Span-116"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-117" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-118" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-119" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-120" style="font-family: MathJax_Main; padding-left: 0.259em;">0</span><span class="mo" id="MathJax-Span-121" style="font-family: MathJax_Main; padding-left: 0.207em;">∧</span><span class="mo" id="MathJax-Span-122" style="font-family: MathJax_Main; padding-left: 0.207em;">(</span><span class="mn" id="MathJax-Span-123" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-124" style="font-family: MathJax_Main; padding-left: 0.259em;">∈</span><span class="mi" id="MathJax-Span-125" style="font-family: MathJax_Math-italic; padding-left: 0.259em;">O</span><span class="mo" id="MathJax-Span-126" style="font-family: MathJax_Main; padding-left: 0.207em;">∨</span><span class="mn" id="MathJax-Span-127" style="font-family: MathJax_Main; padding-left: 0.207em;">2</span><span class="mo" id="MathJax-Span-128" style="font-family: MathJax_Main; padding-left: 0.259em;">∈</span><span class="mi" id="MathJax-Span-129" style="font-family: MathJax_Math-italic; padding-left: 0.259em;">O</span><span class="mo" id="MathJax-Span-130" style="font-family: MathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1006.51em 4.306em -999.997em); top: -3.942em; left: 0em;"><span class="mtd" id="MathJax-Span-138"><span class="mrow" id="MathJax-Span-139"><span class="msubsup" id="MathJax-Span-140"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-141" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-142" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-143" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-144" style="font-family: MathJax_Main; padding-left: 0.259em;">1</span><span class="mo" id="MathJax-Span-145" style="font-family: MathJax_Main; padding-left: 0.207em;">∨</span><span class="msubsup" id="MathJax-Span-146" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-147" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-148" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-149" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-150" style="font-family: MathJax_Main; padding-left: 0.259em;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-160"></span></span></span><span style="display: inline-block; width: 0px; height: 4.101em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.872em; border-left: 0px solid; width: 0px; height: 4.316em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>c</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mn>1</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn><mo>∧</mo><mo stretchy="false">(</mo><mn>1</mn><mo>∈</mo><mi>O</mi><mo>∨</mo><mn>2</mn><mo>∈</mo><mi>O</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>1</mn><mo>∨</mo><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>i</mi><mi>n</mi><mi>a</mi><mi>k</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-16">\begin{equation}
c_{n+1} =
\begin{cases}
1 & ak & c_n = 0 \land (1 \in O \lor 2 \in O) \\
3 & ak & c_n = 1 \lor c_n = 2 \\
0 & inak
\end{cases}
\end{equation}</script></span></p><p>Teda zdravá bunka zostáva zdravou, kým sa v jej okolí neobjaví infikovaná bunka. Infikovaná bunka po jednom kroku zomiera. Mŕtva bunka po jednom kroku ožíva.</p><pre class="graphviz"><!--?xml version="1.0" encoding="UTF-8" standalone="no"?-->
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</pre><p>Odozva imunitného systému sa môže počas priebehu ochorenia meniť. Definujeme si pre to ďalšie dve obdoby základného celulárneho automatu.</p><h2 id="32-model-pre-oneskorenú-imunitnú-reakciu"><a class="anchor hidden-xs" href="#32-model-pre-oneskorenú-imunitnú-reakciu" title="32-model-pre-oneskorenú-imunitnú-reakciu"><span class="octicon octicon-link"></span></a>3.2 Model pre oneskorenú imunitnú reakciu</h2><p>Pri napadnutí imunitného systému vírusom dochádza k pomalej, či oneskorenej reakcii imunitného systému[8]. Infikovaná bunka zostáva nažive o generáciu dlhšie a naďalej infikuje ostatné bunky. Celulárny automat modelujúci oneskornú reakciu si označme <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-161" style="width: 0.822em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.669em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.283em 1000.62em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-162"><span class="mi" id="MathJax-Span-163" style="font-family: MathJax_Math-italic;">L</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></span></span><script type="math/tex" id="MathJax-Element-17">L</script></span>. Jeho pravidlá pre prechod bunky <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-164" style="width: 0.515em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.41em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-165"><span class="mi" id="MathJax-Span-166" style="font-family: MathJax_Math-italic;">c</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></span></span><script type="math/tex" id="MathJax-Element-18">c</script></span> v čase <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-167" style="width: 0.771em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.617em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.62em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-168"><span class="mi" id="MathJax-Span-169" style="font-family: MathJax_Math-italic;">n</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></span></span><script type="math/tex" id="MathJax-Element-19">n</script></span> a okolím <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-170" style="width: 0.976em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.771em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.77em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-171"><span class="mi" id="MathJax-Span-172" style="font-family: MathJax_Math-italic;">O</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math></span></span><script type="math/tex" id="MathJax-Element-20">O</script></span> do ďalšieho stavu vyzerajú následovne.</p><p><span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>c</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mn>1</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn><mo>&#x2227;</mo><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2208;</mo><mi>O</mi><mo>&#x2228;</mo><mn>2</mn><mo>&#x2208;</mo><mi>O</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>i</mi><mi>n</mi><mi>a</mi><mi>k</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math>" role="presentation" style="text-align: center; position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-173" style="width: 23.619em; display: inline-block;"><span style="display: inline-block; position: relative; width: 19.367em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.949em 1019.37em 6.919em -999.997em); top: -4.659em; left: 0em;"><span class="mrow" id="MathJax-Span-174"><span class="msubsup" id="MathJax-Span-175"><span style="display: inline-block; position: relative; width: 1.847em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-176" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="texatom" id="MathJax-Span-177"><span class="mrow" id="MathJax-Span-178"><span class="mi" id="MathJax-Span-179" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span class="mo" id="MathJax-Span-180" style="font-size: 70.7%; font-family: MathJax_Main;">+</span><span class="mn" id="MathJax-Span-181" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-182" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mrow" id="MathJax-Span-183" style="padding-left: 0.259em;"><span class="mo" id="MathJax-Span-184" style="vertical-align: 2.564em;"><span style="display: inline-block; position: relative; width: 0.873em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -3.071em; left: 0em;">⎧<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -0.254em; left: 0em;">⎩<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -1.432em; left: 0em;">⎨<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -2.815em; left: 0em;">⎪<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -2.559em; left: 0em;">⎪<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -0.51em; left: 0em;">⎪<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -0.202em; left: 0em;">⎪<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mtable" id="MathJax-Span-185" style="padding-right: 0.156em; padding-left: 0.156em;"><span style="display: inline-block; position: relative; width: 15.064em; height: 0px;"><span style="position: absolute; clip: rect(2.718em 1000.46em 7.38em -999.997em); top: -5.325em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px;"><span style="position: absolute; clip: rect(3.179em 1000.41em 4.152em -999.997em); top: -5.786em; left: 0em;"><span class="mtd" id="MathJax-Span-186"><span class="mrow" id="MathJax-Span-187"><span class="mn" id="MathJax-Span-188" style="font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1000.46em 4.152em -999.997em); top: -4.506em; left: 0em;"><span class="mtd" id="MathJax-Span-210"><span class="mrow" id="MathJax-Span-211"><span class="mn" id="MathJax-Span-212" style="font-family: MathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1000.46em 4.152em -999.997em); top: -3.327em; left: 0em;"><span class="mtd" id="MathJax-Span-224"><span class="mrow" id="MathJax-Span-225"><span class="mn" id="MathJax-Span-226" style="font-family: MathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1000.46em 4.152em -999.997em); top: -2.098em; left: 0em;"><span class="mtd" id="MathJax-Span-238"><span class="mrow" id="MathJax-Span-239"><span class="mn" id="MathJax-Span-240" style="font-family: MathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.33em;"></span></span><span style="position: absolute; clip: rect(2.769em 1002em 7.431em -999.997em); top: -5.377em; left: 1.488em;"><span style="display: inline-block; position: relative; width: 2.001em; height: 0px;"><span style="position: absolute; clip: rect(3.128em 1001.03em 4.152em -999.997em); top: -5.786em; left: 0em;"><span class="mtd" id="MathJax-Span-189"><span class="mrow" id="MathJax-Span-190"><span class="mi" id="MathJax-Span-191" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-192" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.128em 1001.03em 4.152em -999.997em); top: -4.506em; left: 0em;"><span class="mtd" id="MathJax-Span-213"><span class="mrow" id="MathJax-Span-214"><span class="mi" id="MathJax-Span-215" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-216" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.128em 1001.03em 4.152em -999.997em); top: -3.327em; left: 0em;"><span class="mtd" id="MathJax-Span-227"><span class="mrow" id="MathJax-Span-228"><span class="mi" id="MathJax-Span-229" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-230" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.128em 1002em 4.152em -999.997em); top: -2.098em; left: 0em;"><span class="mtd" id="MathJax-Span-241"><span class="mrow" id="MathJax-Span-242"><span class="mi" id="MathJax-Span-243" style="font-family: MathJax_Math-italic;">i</span><span class="mi" id="MathJax-Span-244" style="font-family: MathJax_Math-italic;">n</span><span class="mi" id="MathJax-Span-245" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-246" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.382em;"></span></span><span style="position: absolute; clip: rect(1.693em 1010.45em 5.33em -999.997em); top: -4.352em; left: 4.511em;"><span style="display: inline-block; position: relative; width: 10.556em; height: 0px;"><span style="position: absolute; clip: rect(3.076em 1010.45em 4.408em -999.997em); top: -5.786em; left: 0em;"><span class="mtd" id="MathJax-Span-193"><span class="mrow" id="MathJax-Span-194"><span class="msubsup" id="MathJax-Span-195"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-196" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-197" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-198" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-199" style="font-family: MathJax_Main; padding-left: 0.259em;">0</span><span class="mo" id="MathJax-Span-200" style="font-family: MathJax_Main; padding-left: 0.207em;">∧</span><span class="mo" id="MathJax-Span-201" style="font-family: MathJax_Main; padding-left: 0.207em;">(</span><span class="mn" id="MathJax-Span-202" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-203" style="font-family: MathJax_Main; padding-left: 0.259em;">∈</span><span class="mi" id="MathJax-Span-204" style="font-family: MathJax_Math-italic; padding-left: 0.259em;">O</span><span class="mo" id="MathJax-Span-205" style="font-family: MathJax_Main; padding-left: 0.207em;">∨</span><span class="mn" id="MathJax-Span-206" style="font-family: MathJax_Main; padding-left: 0.207em;">2</span><span class="mo" id="MathJax-Span-207" style="font-family: MathJax_Main; padding-left: 0.259em;">∈</span><span class="mi" id="MathJax-Span-208" style="font-family: MathJax_Math-italic; padding-left: 0.259em;">O</span><span class="mo" id="MathJax-Span-209" style="font-family: MathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1002.67em 4.306em -999.997em); top: -4.506em; left: 0em;"><span class="mtd" id="MathJax-Span-217"><span class="mrow" id="MathJax-Span-218"><span class="msubsup" id="MathJax-Span-219"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-220" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-221" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-222" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-223" style="font-family: MathJax_Main; padding-left: 0.259em;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1002.67em 4.306em -999.997em); top: -3.327em; left: 0em;"><span class="mtd" id="MathJax-Span-231"><span class="mrow" id="MathJax-Span-232"><span class="msubsup" id="MathJax-Span-233"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-234" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-235" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-236" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-237" style="font-family: MathJax_Main; padding-left: 0.259em;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.357em;"></span></span></span></span><span class="mo" id="MathJax-Span-247"></span></span></span><span style="display: inline-block; width: 0px; height: 4.664em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.622em; border-left: 0px solid; width: 0px; height: 5.816em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>c</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mn>1</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn><mo>∧</mo><mo stretchy="false">(</mo><mn>1</mn><mo>∈</mo><mi>O</mi><mo>∨</mo><mn>2</mn><mo>∈</mo><mi>O</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>i</mi><mi>n</mi><mi>a</mi><mi>k</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-21">\begin{equation}
c_{n+1} =
\begin{cases}
1 & ak & c_n = 0 \land (1 \in O \lor 2 \in O) \\
2 & ak & c_n = 1 \\
3 & ak & c_n = 2 \\
0 & inak
\end{cases}
\end{equation}</script></span></p><p>Medzi stavy <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-248" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-249"><span class="mn" id="MathJax-Span-250" style="font-family: MathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-22">1</script></span> a <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-251" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-252"><span class="mn" id="MathJax-Span-253" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span></span><script type="math/tex" id="MathJax-Element-23">3</script></span> vložíme stav <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-254" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-255"><span class="mn" id="MathJax-Span-256" style="font-family: MathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span></span><script type="math/tex" id="MathJax-Element-24">2</script></span>, ktorý nám spôsobí oneskorenie o jeden časový krok.</p><pre class="graphviz"><!--?xml version="1.0" encoding="UTF-8" standalone="no"?-->
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</pre><h2 id="33-model-pre-vyčerpanú-imunitnú-reakciu"><a class="anchor hidden-xs" href="#33-model-pre-vyčerpanú-imunitnú-reakciu" title="33-model-pre-vyčerpanú-imunitnú-reakciu"><span class="octicon octicon-link"></span></a>3.3 Model pre vyčerpanú imunitnú reakciu</h2><p>Vírus môže narušiť schopnosť organizmu nahradzovať mŕtve bunky[8]. V taktomto bunky nebudú prechádzať zo stavu <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-257" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-258"><span class="mn" id="MathJax-Span-259" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span></span><script type="math/tex" id="MathJax-Element-25">3</script></span> späť do stavu <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-260" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-261"><span class="mn" id="MathJax-Span-262" style="font-family: MathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-26">1</script></span> (organizmus bude vymierať). Celulárny automat modelujúci túto situáciu si označme <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-263" style="width: 1.027em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.822em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.283em 1000.82em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-264"><span class="mi" id="MathJax-Span-265" style="font-family: MathJax_Math-italic;">D</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-27">D</script></span>. Pravidlá pre prechod bunky <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-266" style="width: 0.515em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.41em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-267"><span class="mi" id="MathJax-Span-268" style="font-family: MathJax_Math-italic;">c</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></span></span><script type="math/tex" id="MathJax-Element-28">c</script></span> v generácii <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-269" style="width: 0.771em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.617em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.62em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-270"><span class="mi" id="MathJax-Span-271" style="font-family: MathJax_Math-italic;">n</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></span></span><script type="math/tex" id="MathJax-Element-29">n</script></span> a okolím <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-272" style="width: 0.976em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.771em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.77em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-273"><span class="mi" id="MathJax-Span-274" style="font-family: MathJax_Math-italic;">O</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math></span></span><script type="math/tex" id="MathJax-Element-30">O</script></span> sú definované následovne.</p><p><span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>c</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mn>1</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn><mo>&#x2227;</mo><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2208;</mo><mi>O</mi><mo>&#x2228;</mo><mn>2</mn><mo>&#x2208;</mo><mi>O</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>1</mn><mo>&#x2228;</mo><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>2</mn><mo>&#x2228;</mo><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>i</mi><mi>n</mi><mi>a</mi><mi>k</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math>" role="presentation" style="text-align: center; position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-275" style="width: 23.619em; display: inline-block;"><span style="display: inline-block; position: relative; width: 19.367em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.949em 1019.37em 5.74em -999.997em); top: -4.096em; left: 0em;"><span class="mrow" id="MathJax-Span-276"><span class="msubsup" id="MathJax-Span-277"><span style="display: inline-block; position: relative; width: 1.847em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-278" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="texatom" id="MathJax-Span-279"><span class="mrow" id="MathJax-Span-280"><span class="mi" id="MathJax-Span-281" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span class="mo" id="MathJax-Span-282" style="font-size: 70.7%; font-family: MathJax_Main;">+</span><span class="mn" id="MathJax-Span-283" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-284" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mrow" id="MathJax-Span-285" style="padding-left: 0.259em;"><span class="mo" id="MathJax-Span-286" style="vertical-align: 2.001em;"><span style="display: inline-block; position: relative; width: 0.873em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -3.071em; left: 0em;">⎧<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -1.432em; left: 0em;">⎩<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -1.995em; left: 0em;">⎨<span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mtable" id="MathJax-Span-287" style="padding-right: 0.156em; padding-left: 0.156em;"><span style="display: inline-block; position: relative; width: 15.064em; height: 0px;"><span style="position: absolute; clip: rect(2.154em 1000.46em 5.587em -999.997em); top: -4.147em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px;"><span style="position: absolute; clip: rect(3.179em 1000.41em 4.152em -999.997em); top: -5.172em; left: 0em;"><span class="mtd" id="MathJax-Span-288"><span class="mrow" id="MathJax-Span-289"><span class="mn" id="MathJax-Span-290" style="font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1000.46em 4.152em -999.997em); top: -3.942em; left: 0em;"><span class="mtd" id="MathJax-Span-312"><span class="mrow" id="MathJax-Span-313"><span class="mn" id="MathJax-Span-314" style="font-family: MathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1000.46em 4.152em -999.997em); top: -2.713em; left: 0em;"><span class="mtd" id="MathJax-Span-338"><span class="mrow" id="MathJax-Span-339"><span class="mn" id="MathJax-Span-340" style="font-family: MathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.152em;"></span></span><span style="position: absolute; clip: rect(2.154em 1002em 5.587em -999.997em); top: -4.147em; left: 1.488em;"><span style="display: inline-block; position: relative; width: 2.001em; height: 0px;"><span style="position: absolute; clip: rect(3.128em 1001.03em 4.152em -999.997em); top: -5.172em; left: 0em;"><span class="mtd" id="MathJax-Span-291"><span class="mrow" id="MathJax-Span-292"><span class="mi" id="MathJax-Span-293" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-294" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.128em 1001.03em 4.152em -999.997em); top: -3.942em; left: 0em;"><span class="mtd" id="MathJax-Span-315"><span class="mrow" id="MathJax-Span-316"><span class="mi" id="MathJax-Span-317" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-318" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.128em 1002em 4.152em -999.997em); top: -2.713em; left: 0em;"><span class="mtd" id="MathJax-Span-341"><span class="mrow" id="MathJax-Span-342"><span class="mi" id="MathJax-Span-343" style="font-family: MathJax_Math-italic;">i</span><span class="mi" id="MathJax-Span-344" style="font-family: MathJax_Math-italic;">n</span><span class="mi" id="MathJax-Span-345" style="font-family: MathJax_Math-italic;">a</span><span class="mi" id="MathJax-Span-346" style="font-family: MathJax_Math-italic;">k</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.152em;"></span></span><span style="position: absolute; clip: rect(1.898em 1010.45em 4.408em -999.997em); top: -3.993em; left: 4.511em;"><span style="display: inline-block; position: relative; width: 10.556em; height: 0px;"><span style="position: absolute; clip: rect(3.076em 1010.45em 4.408em -999.997em); top: -5.172em; left: 0em;"><span class="mtd" id="MathJax-Span-295"><span class="mrow" id="MathJax-Span-296"><span class="msubsup" id="MathJax-Span-297"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-298" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-299" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-300" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-301" style="font-family: MathJax_Main; padding-left: 0.259em;">0</span><span class="mo" id="MathJax-Span-302" style="font-family: MathJax_Main; padding-left: 0.207em;">∧</span><span class="mo" id="MathJax-Span-303" style="font-family: MathJax_Main; padding-left: 0.207em;">(</span><span class="mn" id="MathJax-Span-304" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-305" style="font-family: MathJax_Main; padding-left: 0.259em;">∈</span><span class="mi" id="MathJax-Span-306" style="font-family: MathJax_Math-italic; padding-left: 0.259em;">O</span><span class="mo" id="MathJax-Span-307" style="font-family: MathJax_Main; padding-left: 0.207em;">∨</span><span class="mn" id="MathJax-Span-308" style="font-family: MathJax_Main; padding-left: 0.207em;">2</span><span class="mo" id="MathJax-Span-309" style="font-family: MathJax_Main; padding-left: 0.259em;">∈</span><span class="mi" id="MathJax-Span-310" style="font-family: MathJax_Math-italic; padding-left: 0.259em;">O</span><span class="mo" id="MathJax-Span-311" style="font-family: MathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.179em 1010.3em 4.306em -999.997em); top: -3.942em; left: 0em;"><span class="mtd" id="MathJax-Span-319"><span class="mrow" id="MathJax-Span-320"><span class="msubsup" id="MathJax-Span-321"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-322" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-323" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-324" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-325" style="font-family: MathJax_Main; padding-left: 0.259em;">1</span><span class="mo" id="MathJax-Span-326" style="font-family: MathJax_Main; padding-left: 0.207em;">∨</span><span class="msubsup" id="MathJax-Span-327" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-328" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-329" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-330" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-331" style="font-family: MathJax_Main; padding-left: 0.259em;">2</span><span class="mo" id="MathJax-Span-332" style="font-family: MathJax_Main; padding-left: 0.207em;">∨</span><span class="msubsup" id="MathJax-Span-333" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.925em; height: 0px;"><span style="position: absolute; clip: rect(3.384em 1000.41em 4.152em -999.997em); top: -3.993em; left: 0em;"><span class="mi" id="MathJax-Span-334" style="font-family: MathJax_Math-italic;">c</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; top: -3.84em; left: 0.412em;"><span class="mi" id="MathJax-Span-335" style="font-size: 70.7%; font-family: MathJax_Math-italic;">n</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-336" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-337" style="font-family: MathJax_Main; padding-left: 0.259em;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span></span></span><span class="mo" id="MathJax-Span-347"></span></span></span><span style="display: inline-block; width: 0px; height: 4.101em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.872em; border-left: 0px solid; width: 0px; height: 4.316em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>c</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mn>1</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn><mo>∧</mo><mo stretchy="false">(</mo><mn>1</mn><mo>∈</mo><mi>O</mi><mo>∨</mo><mn>2</mn><mo>∈</mo><mi>O</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mi>a</mi><mi>k</mi></mtd><mtd><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>1</mn><mo>∨</mo><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>2</mn><mo>∨</mo><msub><mi>c</mi><mi>n</mi></msub><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>i</mi><mi>n</mi><mi>a</mi><mi>k</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-31">\begin{equation}
c_{n+1} =
\begin{cases}
1 & ak & c_n = 0 \land (1 \in O \lor 2 \in O) \\
3 & ak & c_n = 1 \lor c_n = 2 \lor c_n = 3 \\
0 & inak
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</pre><h2 id="34-stochastický-model-priebehu-ochorenia"><a class="anchor hidden-xs" href="#34-stochastický-model-priebehu-ochorenia" title="34-stochastický-model-priebehu-ochorenia"><span class="octicon octicon-link"></span></a>3.4 Stochastický model priebehu ochorenia</h2><p>Priebeh ochorenia silne závisí od imunitného systému konkrétneho jedinca, ale v každom prípade je odpoveď imunitného systému premenlivá. Túto premenlivosť budeme modelovať použitím stochastického celulárneho automatu. Zavedieme si paramtere <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-354" style="width: 0.566em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.464em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.46em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-355"><span class="mi" id="MathJax-Span-356" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></span></span><script type="math/tex" id="MathJax-Element-34">z</script></span>, <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-357" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.51em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-358"><span class="mi" id="MathJax-Span-359" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-35">d</script></span> a <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-360" style="width: 0.412em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.31em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.26em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-361"><span class="mi" id="MathJax-Span-362" style="font-family: MathJax_Math-italic;">l</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></span></span><script type="math/tex" id="MathJax-Element-36">l</script></span>, ktoré budú určovať pravdepdobnosť výberu kroku pre vytvorenie ďalšej generácie, obecne musí platiť <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>l</mi><mo>=</mo><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-363" style="width: 6.662em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.433em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1005.38em 2.513em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-364"><span class="mi" id="MathJax-Span-365" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-366" style="font-family: MathJax_Main; padding-left: 0.207em;">+</span><span class="mi" id="MathJax-Span-367" style="font-family: MathJax_Math-italic; padding-left: 0.207em;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-368" style="font-family: MathJax_Main; padding-left: 0.207em;">+</span><span class="mi" id="MathJax-Span-369" style="font-family: MathJax_Math-italic; padding-left: 0.207em;">l</span><span class="mo" id="MathJax-Span-370" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-371" style="font-family: MathJax_Main; padding-left: 0.259em;">1</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.184em; border-left: 0px solid; width: 0px; height: 1.066em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>l</mi><mo>=</mo><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-37">z + d + l = 1</script></span>.</p><p>Parameter <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-372" style="width: 0.566em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.464em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.46em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-373"><span class="mi" id="MathJax-Span-374" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></span></span><script type="math/tex" id="MathJax-Element-38">z</script></span> určuje pravdepodobnosť správnej imunitnej reakcie. Určíme ho ako <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mi>d</mi><mo>&#x2212;</mo><mi>l</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-375" style="width: 6.662em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.433em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1005.38em 2.513em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-376"><span class="mi" id="MathJax-Span-377" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-378" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-379" style="font-family: MathJax_Main; padding-left: 0.259em;">1</span><span class="mo" id="MathJax-Span-380" style="font-family: MathJax_Main; padding-left: 0.207em;">−</span><span class="mi" id="MathJax-Span-381" style="font-family: MathJax_Math-italic; padding-left: 0.207em;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-382" style="font-family: MathJax_Main; padding-left: 0.207em;">−</span><span class="mi" id="MathJax-Span-383" style="font-family: MathJax_Math-italic; padding-left: 0.207em;">l</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.184em; border-left: 0px solid; width: 0px; height: 1.066em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>1</mn><mo>−</mo><mi>d</mi><mo>−</mo><mi>l</mi></math></span></span><script type="math/tex" id="MathJax-Element-39">z = 1 - d - l</script></span>. Parametrom <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-384" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.51em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-385"><span class="mi" id="MathJax-Span-386" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-40">d</script></span> určíme pravdepodobnosť výberu kroku s vyčerpanou imunitnou reakciu, pri ktorej neprebehne obnova mŕtvych buniek, čo spôsobuje šírenie nekrózy. Podľa článku [1] ja jeho hodnota pohybuje na úrovni <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.35</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-387" style="width: 4.408em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.589em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.54em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-388"><span class="mi" id="MathJax-Span-389" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-390" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-391" style="font-family: MathJax_Main; padding-left: 0.259em;">0.35</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.35</mn></math></span></span><script type="math/tex" id="MathJax-Element-41">d=0.35</script></span>. Parameter <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-392" style="width: 0.412em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.31em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.26em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-393"><span class="mi" id="MathJax-Span-394" style="font-family: MathJax_Math-italic;">l</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></span></span><script type="math/tex" id="MathJax-Element-42">l</script></span> určuje pravdepodobnosť kroku s oneskorenou imunitnou reakciou, jeho hodnota sa podľa [1] pohybuje okolo <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.05</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-395" style="width: 4.152em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.384em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.33em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-396"><span class="mi" id="MathJax-Span-397" style="font-family: MathJax_Math-italic;">l</span><span class="mo" id="MathJax-Span-398" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-399" style="font-family: MathJax_Main; padding-left: 0.259em;">0.05</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.05</mn></math></span></span><script type="math/tex" id="MathJax-Element-43">l=0.05</script></span>. Neskôr si ukážeme, že aj malé zvýšenie parametra <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-400" style="width: 0.412em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.31em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.26em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-401"><span class="mi" id="MathJax-Span-402" style="font-family: MathJax_Math-italic;">l</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></span></span><script type="math/tex" id="MathJax-Element-44">l</script></span> má význačný vplyv na šírenie vírusu.</p><pre class="graphviz"><!--?xml version="1.0" encoding="UTF-8" standalone="no"?-->
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<text text-anchor="middle" x="118.7008" y="-264.4" font-family="Times,serif" font-size="14.00" fill="#000000">HEALTHY</text>
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<g id="node2" class="node">
<title>INFECTED</title>
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<title>INFECTED->DEAD</title>
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</pre><pre><code>Pozn.: Z, L alebo D znamená, že bol zvolený daný krok
</code></pre><p>Na nasledujúcich obrázkoch je možno vidieť ukážkový priebeh infekcie pri parametroch <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-916-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.35</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4645" style="width: 4.408em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.589em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.54em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-4646"><span class="mi" id="MathJax-Span-4647" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-4648" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-4649" style="font-family: MathJax_Main; padding-left: 0.259em;">0.35</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.35</mn></math></span></span><script type="math/tex" id="MathJax-Element-916">d=0.35</script></span> a <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-917-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.05</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4650" style="width: 4.152em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.384em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.33em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-4651"><span class="mi" id="MathJax-Span-4652" style="font-family: MathJax_Math-italic;">l</span><span class="mo" id="MathJax-Span-4653" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-4654" style="font-family: MathJax_Main; padding-left: 0.259em;">0.05</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.05</mn></math></span></span><script type="math/tex" id="MathJax-Element-917">l=0.05</script></span>. Infikované bunky sú zobrazené červenou farbou. Mŕtve bunky sú zobrazené čiernou farbou. Zdravé bunky sú ponechané biele.</p><p><img src="https://i.imgur.com/qgBekdf.png" alt=""></p><h2 id="35-podmienka-ukončenia-simulácie"><a class="anchor hidden-xs" href="#35-podmienka-ukončenia-simulácie" title="35-podmienka-ukončenia-simulácie"><span class="octicon octicon-link"></span></a>3.5 Podmienka ukončenia simulácie</h2><p>Pre určenie okamihu, kedy je vhodné simuláciu ukončiť si musíme definovať konečné stavy automatu.</p><h3 id="351-úplné-vyzdravenie"><a class="anchor hidden-xs" href="#351-úplné-vyzdravenie" title="351-úplné-vyzdravenie"><span class="octicon octicon-link"></span></a>3.5.1 Úplné vyzdravenie</h3><p>Ako podmienku pre ukončenie simulácie úplným vyzdravením budem považovať stav, v ktorom žiadne bunka modelu nie je v infikovanom stave a zároveň je pomer zdravých buniek väčší, ako určuje terminálna podmienka. Bunky sa teda môžu nachádzať v stave <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-403" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-404"><span class="mn" id="MathJax-Span-405" style="font-family: MathJax_Main;">0</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-45">0</script></span> (<em>HEALTHY</em>) alebo <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-406" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1000.46em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-407"><span class="mn" id="MathJax-Span-408" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span></span><script type="math/tex" id="MathJax-Element-46">3</script></span> (<em>DEAD</em>), pričom štúdium nekrózy nemôže byť smrtelné. V takejto situácii pre každý parameter <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>&lt;</mo><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-409" style="width: 2.82em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.308em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1002.26em 2.462em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-410"><span class="mi" id="MathJax-Span-411" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-412" style="font-family: MathJax_Main; padding-left: 0.259em;"><</span><span class="mn" id="MathJax-Span-413" style="font-family: MathJax_Main; padding-left: 0.259em;">1</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.122em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo><</mo><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-47">d < 1</script></span> dôjde po určitom počte krokov k úplnému vyzdraveniu.</p><h3 id="352-smrť-prekročením-terminálnej-podmienky"><a class="anchor hidden-xs" href="#352-smrť-prekročením-terminálnej-podmienky" title="352-smrť-prekročením-terminálnej-podmienky"><span class="octicon octicon-link"></span></a>3.5.2 Smrť prekročením terminálnej podmienky</h3><p>Podmienka pre ukončenie simulácie prekročením terminálnej podmienky je platná, ak je pomer zdravých buniek voči všetkým bunkám poľa menší, ako pomer určený terminálnou podmienkou (v základe <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-414" style="width: 0.822em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.669em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.078em 1000.67em 2.666em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-415"><span class="mfrac" id="MathJax-Span-416"><span style="display: inline-block; position: relative; width: 0.464em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.384em 1000.31em 4.152em -999.997em); top: -4.403em; left: 50%; margin-left: -0.151em;"><span class="mn" id="MathJax-Span-417" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.384em 1000.31em 4.152em -999.997em); top: -3.635em; left: 50%; margin-left: -0.151em;"><span class="mn" id="MathJax-Span-418" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(0.873em 1000.46em 1.232em -999.997em); top: -1.278em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.464em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.078em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-48">\frac{1}{3}</script></span>). Takýto stav môže vypovedať napríklad smrť spôsobenú zlyhaním orgánov.</p><h3 id="353-smrť-prekročením-maximálneho-počtu-dní"><a class="anchor hidden-xs" href="#353-smrť-prekročením-maximálneho-počtu-dní" title="353-smrť-prekročením-maximálneho-počtu-dní"><span class="octicon octicon-link"></span></a>3.5.3 Smrť prekročením maximálneho počtu dní</h3><p>Experimentálne sme zistili, že pomery počtu buniek v jednotlivých štádiách jedincov, ktorí sa nevyliečia v priebehu prvých 31 dní zostávajú vo veľkej miere oscilovať medzi stavom vyzdravenia sa a smrti prekročením terminálnej podmienky po dlhú dobu. Z článku [8] vieme, že bežná doba trvania príznakov je 2-21 dní, pričom odozva imunitného systému vytvorením protilátok nastáva medzi 6. až 18. dňom. Ďalej je uvedené, že protilátkový profil jedincov ktorí prežili, sa značne líši od tých, ktorí neprežili a protilátková odozva je jeden z rozhodujúcich faktorov medzi prežitím a smrťou. Môžeme teda predpokladať, že jedinci, ktorých protilátky sa včas nevyvinuli nemajú vzhľadom na fatálnosť symptómov Eboly v dlhšom časovom okne šancu na prežitie. Hranicu (36 dní), za ktorou budeme považovať jedinca za mŕtveho sme určili v experimente <a href="#51-doba-uzdravenia">5.1</a>.</p><h1 id="4-architektura-simulačního-modelu"><a class="anchor hidden-xs" href="#4-architektura-simulačního-modelu" title="4-architektura-simulačního-modelu"><span class="octicon octicon-link"></span></a>4. Architektura simulačního modelu</h1><p>Vstupom do simulácie sú argumenty na príkazovom riadku. Zadať je možné následujúce parametre (v zátvorkách je uvedená predvolená hodnota):</p><ul>
<li><code>-l LPROB</code> - kde <code>LPROB</code> je pravdepodobnosť použitia kroku modelu <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-419" style="width: 0.822em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.669em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.283em 1000.62em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-420"><span class="mi" id="MathJax-Span-421" style="font-family: MathJax_Math-italic;">L</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></span></span><script type="math/tex" id="MathJax-Element-49">L</script></span> (<span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.05</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-422" style="width: 2.205em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.796em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1001.74em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-423"><span class="mn" id="MathJax-Span-424" style="font-family: MathJax_Main;">0.05</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.05</mn></math></span></span><script type="math/tex" id="MathJax-Element-50">0.05</script></span>)</li>
<li><code>-d DPROB</code> - kde <code>DPROB</code> je pravdepodobnosť použitia kroku modelu <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-425" style="width: 1.027em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.822em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.283em 1000.82em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-426"><span class="mi" id="MathJax-Span-427" style="font-family: MathJax_Math-italic;">D</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-51">D</script></span> (<span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.35</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-428" style="width: 2.205em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.796em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1001.74em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-429"><span class="mn" id="MathJax-Span-430" style="font-family: MathJax_Main;">0.35</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.35</mn></math></span></span><script type="math/tex" id="MathJax-Element-52">0.35</script></span>)</li>
<li><code>-r ROWS</code> - kde <code>ROWS</code> je počet riadkov matice (<span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-431" style="width: 1.847em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.488em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1001.44em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-432"><span class="mn" id="MathJax-Span-433" style="font-family: MathJax_Main;">700</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn></math></span></span><script type="math/tex" id="MathJax-Element-53">700</script></span>)</li>
<li><code>-c COLS</code> - kde <code>COLS</code> je počet stĺpcov matice (<span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-434" style="width: 1.847em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.488em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1001.44em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-435"><span class="mn" id="MathJax-Span-436" style="font-family: MathJax_Main;">700</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn></math></span></span><script type="math/tex" id="MathJax-Element-54">700</script></span>)</li>
<li><code>-s SEED</code> - kde <code>SEED</code> je počiatočná zastúpenie infikovaných buniek v tvare indexu (<span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.0055</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-437" style="width: 3.384em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.769em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1002.72em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-438"><span class="mn" id="MathJax-Span-439" style="font-family: MathJax_Main;">0.0055</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.0055</mn></math></span></span><script type="math/tex" id="MathJax-Element-55">0.0055</script></span>)</li>
<li><code>-t TERM</code> - kde <code>TERM</code> je úroveň terminálnej podmienky (<span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-440" style="width: 0.822em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.669em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.078em 1000.67em 2.666em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-441"><span class="mfrac" id="MathJax-Span-442"><span style="display: inline-block; position: relative; width: 0.464em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.384em 1000.31em 4.152em -999.997em); top: -4.403em; left: 50%; margin-left: -0.151em;"><span class="mn" id="MathJax-Span-443" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(3.384em 1000.31em 4.152em -999.997em); top: -3.635em; left: 50%; margin-left: -0.151em;"><span class="mn" id="MathJax-Span-444" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 3.998em;"></span></span><span style="position: absolute; clip: rect(0.873em 1000.46em 1.232em -999.997em); top: -1.278em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.464em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.078em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-56">\frac{1}{3}</script></span>)</li>
<li><code>-o</code> - generovaie CSV súboru s dátami o počte buniek v jednotlivých stavoch pre každú generáciu</li>
<li><code>-f</code> - spočíta priemernú mieru mortality (v 100 pokusoch)</li>
</ul><p>Simulátor na základe vstupných parametrov inicializuje celulárny automat triedy <code>CA</code> a zavedie do poľa <code>ROWS*COLS*SEED</code> infikovaných buniek. Následne volá metódu <code>CA::randomStep()</code>, ktorá na základne pravdepodobností nastavených pri inicializácii objektu vykoná jeden náhodný krok. Týmto krokom sa na základe zvoleného pravidla vygeneruje nová generácia buniek a zvýši počítadlo dní. Metódu volá až do chvíle, kým sa celulárny automat nedostane do konečného stavu.</p><p>Na stav modelu sa simulátor dotazuje pomocou metódy <code>CA::status()</code>. Jedna bunka je reprezentovaná celým číslom z číselníku (0: <em>HEALTHY</em>, 1: <em>INFECTED</em>, 2: <em>SPOILED</em>, 3: <em>DEAD</em>). Bunky sú uložené v matici s prepojenými okrajmi, ktorá je implementovaná pomocou C++ triedy <code>std::vector</code>.</p><h2 id="41-zbieranie-údajov"><a class="anchor hidden-xs" href="#41-zbieranie-údajov" title="41-zbieranie-údajov"><span class="octicon octicon-link"></span></a>4.1 Zbieranie údajov</h2><p>Pomocou prepínača <code>-o</code> vieme pre simuláciu zapnúť zbieranie dát o každom kroku celulárneho automatu - zastúpenie jednotlivých buniek v kroku. Výstup je zapísaný do súboru <code>simulation.csv</code> typu CSV.</p><h1 id="5-podstata-simulačních-experimentů-a-jejich-průběh"><a class="anchor hidden-xs" href="#5-podstata-simulačních-experimentů-a-jejich-průběh" title="5-podstata-simulačních-experimentů-a-jejich-průběh"><span class="octicon octicon-link"></span></a>5. Podstata simulačních experimentů a jejich průběh</h1><p>Podstatou simulačných experimentov je ukázanie závislosti medzi reakciou imunitného systému a mierou fatality vírusu. Zároveň využijeme experimenty na overenie a doladenie simulačného modelu.</p><h2 id="51-doba-uzdravenia"><a class="anchor hidden-xs" href="#51-doba-uzdravenia" title="51-doba-uzdravenia"><span class="octicon octicon-link"></span></a>5.1 Doba uzdravenia</h2><p>Tento experiment ukazuje dobu liečby v dňoch ľudí, ktorí sa dokázali vyliečiť z nakazenia Ebolou. Vstupom simulácie boli základné parametre stochastického modelu, ktoré by mali predstavovať bežnú reakciu imunitného systému <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.35</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-445" style="width: 4.408em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.589em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.54em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-446"><span class="mi" id="MathJax-Span-447" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-448" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-449" style="font-family: MathJax_Main; padding-left: 0.259em;">0.35</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.35</mn></math></span></span><script type="math/tex" id="MathJax-Element-57">d=0.35</script></span>, <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.05</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-450" style="width: 4.152em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.384em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.33em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-451"><span class="mi" id="MathJax-Span-452" style="font-family: MathJax_Math-italic;">l</span><span class="mo" id="MathJax-Span-453" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-454" style="font-family: MathJax_Main; padding-left: 0.259em;">0.05</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.05</mn></math></span></span><script type="math/tex" id="MathJax-Element-58">l=0.05</script></span> a <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>0.6</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-455" style="width: 3.691em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.025em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1002.97em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-456"><span class="mi" id="MathJax-Span-457" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-458" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-459" style="font-family: MathJax_Main; padding-left: 0.259em;">0.6</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>0.6</mn></math></span></span><script type="math/tex" id="MathJax-Element-59">z=0.6</script></span>. Ako bolo spomenuté v kapitole <a href="#353-smr%C5%A5-prekro%C4%8Den%C3%ADm-maxim%C3%A1lneho-po%C4%8Dtu-dn%C3%AD">3.5.3</a>, šanca, že sa človek nakazený Ebolou vylieči sa postupom času znižuje. Experiment pozostáva z spustením simulácie 1000 krát čo predstavuje 1000 jedincov, pričom za živého sa považuje človek, ktorý sa vyliečil do 120 dní.</p><p><img src="https://i.imgur.com/hbT9ZNs.png" alt=""><br>
Graf č. 1: Doba uzdravenia</p><p>Z grafu je vidieť, že najvyššia šance vyliečiť sa je medzi 20 - 26. dňom. Pre ďalšie výpočty budeme predpokladať, že ak sa človek nevylieči do 36 dní, tak zomrie. Do 36 dní sa vyliečilo 84,59% z vyliečených ľudí. Pre zvyšných ľudí sa dá predpokladať, že zomreli účinkom symptómov Eboly(vykrvácanie, šok, vyčerpanie), nie samotným odumretím buniek.</p><h2 id="52-závislosť-úmrtnosti-na-veľkosti-celulárneho-automatu"><a class="anchor hidden-xs" href="#52-závislosť-úmrtnosti-na-veľkosti-celulárneho-automatu" title="52-závislosť-úmrtnosti-na-veľkosti-celulárneho-automatu"><span class="octicon octicon-link"></span></a>5.2 Závislosť úmrtnosti na veľkosti celulárneho automatu</h2><p>Experiment zisťuje, či veľkosť celulárneho automatu zvolená autormi pôvodného článku 700x700 má vplyv na výsledky. Experiment bol vykonaný tak, že sa opakovane (1000 krát) spúšťala simulácia so základnými parametrami modelu a do grafu sme zaznamenali mieru úmrtnosti.</p><p><img src="https://i.imgur.com/S52FvZp.png" alt=""><br>
Graf č. 2: Závislosť úmrtnosti na veľkosti celulárneho automatu</p><p>Zistili sme že výsledky sú závislé na veľkosti celulárneho automatu. Z uvedeného grafu je vidieť, že od veľkosti 700x700 sa už hodnoty ustáľujú v rozmedzí ±5 %, čo je vzhľadom na povahu stochastického celulárneho automatu prijateľná odchýlka. Zároveň sa výsledky približujú k údajnej miere úmrtnosti 50 % publikovanej v článku [8], takže ju môžeme považujeme za správnu. Veľkosť matice 700x700 nám ponúka rýchlejší beh simulácie ako pri väčších rozmeroch, nakoľko nárnočnosť simulácie stúpa kvadraticky s veľkosťou celulárneho automatu.</p><h2 id="53-závislosť-úmrtnosti-na-oneskorenej-imunitnej-reakcii"><a class="anchor hidden-xs" href="#53-závislosť-úmrtnosti-na-oneskorenej-imunitnej-reakcii" title="53-závislosť-úmrtnosti-na-oneskorenej-imunitnej-reakcii"><span class="octicon octicon-link"></span></a>5.3 Závislosť úmrtnosti na oneskorenej imunitnej reakcii</h2><p>Experimentom sme chceli zistiť, aký veľký vplyv má oneskorená reakcia imunitného systému na úmrtnosť ľudí. Parameter <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1216-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5936" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.51em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-5937"><span class="mi" id="MathJax-Span-5938" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-1216">d</script></span> zostal počas experimentu nemenný na základnej úrovni <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1217-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.35</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5939" style="width: 4.408em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.589em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.54em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-5940"><span class="mi" id="MathJax-Span-5941" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; 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display: inline-block;"><span style="display: inline-block; position: relative; width: 0.464em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.46em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-5945"><span class="mi" id="MathJax-Span-5946" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></span></span><script type="math/tex" id="MathJax-Element-1218">z</script></span> sa dopočítaval ako <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1219-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mi>d</mi><mo>&#x2212;</mo><mi>l</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5947" style="width: 6.662em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.433em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1005.38em 2.513em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-5948"><span class="mi" id="MathJax-Span-5949" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-5950" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-5951" style="font-family: MathJax_Main; padding-left: 0.259em;">1</span><span class="mo" id="MathJax-Span-5952" style="font-family: MathJax_Main; padding-left: 0.207em;">−</span><span class="mi" id="MathJax-Span-5953" style="font-family: MathJax_Math-italic; padding-left: 0.207em;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-5954" style="font-family: MathJax_Main; padding-left: 0.207em;">−</span><span class="mi" id="MathJax-Span-5955" style="font-family: MathJax_Math-italic; padding-left: 0.207em;">l</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.184em; border-left: 0px solid; width: 0px; height: 1.066em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>1</mn><mo>−</mo><mi>d</mi><mo>−</mo><mi>l</mi></math></span></span><script type="math/tex" id="MathJax-Element-1219">z=1-d-l</script></span>.</p><p><img src="https://i.imgur.com/44No62Q.png" alt=""></p><p>Graf č. 3: Závislosť úmrtnosti na oneskorenej imunitnej reakcii</p><p>Z grafu môžeme vidieť, že miera úmrtnosti stúpa veľmi rýchlo v prípade malého oneskorenia imunitného systému, čo potvrdzduje informáciu z článku [1]. Pri malej pravdepodobnosti <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-947-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.05</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4805" style="width: 4.152em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.384em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.33em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-4806"><span class="mi" id="MathJax-Span-4807" style="font-family: MathJax_Math-italic;">l</span><span class="mo" id="MathJax-Span-4808" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-4809" style="font-family: MathJax_Main; padding-left: 0.259em;">0.05</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.05</mn></math></span></span><script type="math/tex" id="MathJax-Element-947">l = 0.05</script></span> je miera úmrtnosti 50,86 %.</p><p>V prípade že imunitná reakcia ľudského tela nie je oneskorená, teda <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-948-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4810" style="width: 2.564em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.103em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1002.05em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-4811"><span class="mi" id="MathJax-Span-4812" style="font-family: MathJax_Math-italic;">l</span><span class="mo" id="MathJax-Span-4813" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-4814" style="font-family: MathJax_Main; padding-left: 0.259em;">0</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-948">l = 0</script></span>, ľudské telo sa zbaví infekcie takmer vždy. Priebeh takejto regenerácie je vidieť na nasledovnom grafe.</p><p><img src="https://i.imgur.com/m5kisA3.png" alt=""><br>
Graf č. 4: Priebeh regenerácie</p><h2 id="54-závislosť-úmrtnosti-na-vyčerpanej-imunitnej-reakcii"><a class="anchor hidden-xs" href="#54-závislosť-úmrtnosti-na-vyčerpanej-imunitnej-reakcii" title="54-závislosť-úmrtnosti-na-vyčerpanej-imunitnej-reakcii"><span class="octicon octicon-link"></span></a>5.4 Závislosť úmrtnosti na vyčerpanej imunitnej reakcii</h2><p>Experimentom skúmame, aký veľký vplyv má vyčerpaná imunitná reakcia na úmrtnosť ľudí. Počas tohto experimentu mal parameter <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-949-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4815" style="width: 0.412em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.31em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.26em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-4816"><span class="mi" id="MathJax-Span-4817" style="font-family: MathJax_Math-italic;">l</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></span></span><script type="math/tex" id="MathJax-Element-949">l</script></span> hodnotu <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-950-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.0</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4818" style="width: 3.537em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.871em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1002.82em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-4819"><span class="mi" id="MathJax-Span-4820" style="font-family: MathJax_Math-italic;">l</span><span class="mo" id="MathJax-Span-4821" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-4822" style="font-family: MathJax_Main; padding-left: 0.259em;">0.0</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.0</mn></math></span></span><script type="math/tex" id="MathJax-Element-950">l = 0.0</script></span>, a <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-951-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4823" style="width: 0.566em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.464em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.488em 1000.46em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-4824"><span class="mi" id="MathJax-Span-4825" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.691em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></span></span><script type="math/tex" id="MathJax-Element-951">z</script></span> bol počítaný ako <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-952-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mi>d</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4826" style="width: 4.818em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.947em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.95em 2.513em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-4827"><span class="mi" id="MathJax-Span-4828" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-4829" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-4830" style="font-family: MathJax_Main; padding-left: 0.259em;">1</span><span class="mo" id="MathJax-Span-4831" style="font-family: MathJax_Main; padding-left: 0.207em;">−</span><span class="mi" id="MathJax-Span-4832" style="font-family: MathJax_Math-italic; padding-left: 0.207em;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.184em; border-left: 0px solid; width: 0px; height: 1.066em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>1</mn><mo>−</mo><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-952">z=1-d</script></span>.</p><p><img src="https://i.imgur.com/tA96NRj.png" alt=""><br>
Graf č. 5: Závislosť úmrtnosti na vyčerpanej imunitnej reakcii</p><p>Z grafu môžeme vidieť, že miera úmrtnosti sa začína zvyšovať až v prípade, že pravdepodobnosť vyčerpanej imunitnej reakcie je približne <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-953-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.4</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4833" style="width: 3.794em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.076em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1003.02em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-4834"><span class="mi" id="MathJax-Span-4835" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-4836" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-4837" style="font-family: MathJax_Main; padding-left: 0.259em;">0.4</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0.4</mn></math></span></span><script type="math/tex" id="MathJax-Element-953">d = 0.4</script></span>. Výsledok bol predpokladaný a vieme ho obhájiť tým, že vírus sa nemôže preniesť na mŕtve bunky a teda mŕtve bunky môžu izolovať zdravé bunky od tých infikovaných.</p><h2 id="55-závislosť-úmrtnosti-pri-rôznych-kombináciach-imunitných-reakcií"><a class="anchor hidden-xs" href="#55-závislosť-úmrtnosti-pri-rôznych-kombináciach-imunitných-reakcií" title="55-závislosť-úmrtnosti-pri-rôznych-kombináciach-imunitných-reakcií"><span class="octicon octicon-link"></span></a>5.5 Závislosť úmrtnosti pri rôznych kombináciach imunitných reakcií</h2><p>V tomto experimente sme hýbali s oboma parametrami v rozmedzí <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1011-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>&#x2208;</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>0.4</mn><mo stretchy="false">]</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5281" style="width: 5.228em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.255em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.335em 1004.15em 2.666em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-5282"><span class="mi" id="MathJax-Span-5283" style="font-family: MathJax_Math-italic;">l</span><span class="mo" id="MathJax-Span-5284" style="font-family: MathJax_Main; padding-left: 0.259em;">∈</span><span class="mo" id="MathJax-Span-5285" style="font-family: MathJax_Main; padding-left: 0.259em;">[</span><span class="mn" id="MathJax-Span-5286" style="font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-5287" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-5288" style="font-family: MathJax_Main; padding-left: 0.156em;">0.4</span><span class="mo" id="MathJax-Span-5289" style="font-family: MathJax_Main;">]</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.372em; border-left: 0px solid; width: 0px; height: 1.378em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>0.4</mn><mo stretchy="false">]</mo></math></span></span><script type="math/tex" id="MathJax-Element-1011">l \in [0, 0.4]</script></span> a <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1012-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>&#x2208;</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>0.6</mn><mo stretchy="false">]</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5290" style="width: 5.433em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.46em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.335em 1004.36em 2.666em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-5291"><span class="mi" id="MathJax-Span-5292" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-5293" style="font-family: MathJax_Main; padding-left: 0.259em;">∈</span><span class="mo" id="MathJax-Span-5294" style="font-family: MathJax_Main; padding-left: 0.259em;">[</span><span class="mn" id="MathJax-Span-5295" style="font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-5296" style="font-family: MathJax_Main;">,</span><span class="mn" id="MathJax-Span-5297" style="font-family: MathJax_Main; padding-left: 0.156em;">0.6</span><span class="mo" id="MathJax-Span-5298" style="font-family: MathJax_Main;">]</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.372em; border-left: 0px solid; width: 0px; height: 1.378em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>0.6</mn><mo stretchy="false">]</mo></math></span></span><script type="math/tex" id="MathJax-Element-1012">d \in [0, 0.6]</script></span> s krokom <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1013-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.05</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5299" style="width: 2.205em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.796em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.437em 1001.74em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-5300"><span class="mn" id="MathJax-Span-5301" style="font-family: MathJax_Main;">0.05</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 0.941em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.05</mn></math></span></span><script type="math/tex" id="MathJax-Element-1013">0.05</script></span>.</p><p><img src="https://i.imgur.com/y26nmwT.png" alt=""><br>
Graf č. 6: Závislosť úmrtnosti pri rôznych kombináciach imunitných reakcií</p><p>V uvedenom grafe je jasne vidieť, že úmrtnosť je ovplyvnená v podstatne vyššej miere parametrom <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1212-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5922" style="width: 0.412em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.31em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.26em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-5923"><span class="mi" id="MathJax-Span-5924" style="font-family: MathJax_Math-italic;">l</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></span></span><script type="math/tex" id="MathJax-Element-1212">l</script></span> ako parametrom <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1213-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5925" style="width: 0.669em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.515em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.51em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-5926"><span class="mi" id="MathJax-Span-5927" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-1213">d</script></span>. Taktiež je vidieť, že pravdepodobnosť oneskoreného kroku <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1214-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.4</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5928" style="width: 3.537em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.871em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.386em 1002.82em 2.41em -999.997em); top: -2.252em; left: 0em;"><span class="mrow" id="MathJax-Span-5929"><span class="mi" id="MathJax-Span-5930" style="font-family: MathJax_Math-italic;">l</span><span class="mo" id="MathJax-Span-5931" style="font-family: MathJax_Main; padding-left: 0.259em;">=</span><span class="mn" id="MathJax-Span-5932" style="font-family: MathJax_Main; padding-left: 0.259em;">0.4</span></span><span style="display: inline-block; width: 0px; height: 2.257em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0.4</mn></math></span></span><script type="math/tex" id="MathJax-Element-1214">l=0.4</script></span> je miera úmrtnosti takmer 100%.</p><h2 id="56-závery-experimentov"><a class="anchor hidden-xs" href="#56-závery-experimentov" title="56-závery-experimentov"><span class="octicon octicon-link"></span></a>5.6 Závery experimentov</h2><p>V priebehu experimentov sme našli niekoľko nedostatkov v modeli, ktoré sme upravili. Prvým bolo nastavenie okrajovej podmienky pre pole celulárneho automatu - ktorým sa náš zdrojový článok nezaoberá. Zistili sme, že model sa správa plynulejšie, ake sa použijú periodické okraje namiesto fixnej hodnoty.</p><p>Počas experimentovania sme zistili, že model sa vo väčšine situácií chová obdobne ako v zdrojovom článku. Našli sa avšak aj nedostatky. Graf č. 4 v kapitole <a href="#53-z%C3%A1vislos%C5%A5-%C3%BAmrtnosti-na-oneskorenej-imunitnej-reakcii">5.3</a> má veľké rozdiely počtov buniek medzi krokmi simulácie čo sa v grafe javí ako zubatosť. V zdrojovom článku bol priebeh plynulejší a jednotlivé počty buniek nemali príliš odlišné hodnoty medzi krokmi simulácie. Ladením modelu sa nám však nepodarilo dosiahnuť rovnaký výsledok.</p><h1 id="6-shrnutí-simulačních-experimentů-a-závěr"><a class="anchor hidden-xs" href="#6-shrnutí-simulačních-experimentů-a-závěr" title="6-shrnutí-simulačních-experimentů-a-závěr"><span class="octicon octicon-link"></span></a>6. Shrnutí simulačních experimentů a závěr</h1><p>Na základe experimentov sme zistili citlivosť modelu na nastavenie vstupných parametrov a ich vplyv na mieru úmrtnosti. Ukázali sme, že model je najviac ovplyňovaný parametrom <span class="mathjax"><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-1215-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5933" style="width: 0.412em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.31em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.232em 1000.26em 2.257em -999.997em); top: -2.098em; left: 0em;"><span class="mrow" id="MathJax-Span-5934"><span class="mi" id="MathJax-Span-5935" style="font-family: MathJax_Math-italic;">l</span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.059em; border-left: 0px solid; width: 0px; height: 1.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></span></span><script type="math/tex" id="MathJax-Element-1215">l</script></span>, ktorý značí oneskorenú reakciu imunitného systému. Prínosom tohoto zistenia a simulácie ako takej môže byť modelovanie nasadenia liekov, ktoré by dokázali tento faktor v ľudskom tele ovplyvňovať. Ďalej sme zistili, že nekróza, či vyčerpaná reakcia imunitného systému v menšom rozsahu výrazne neprispieva k smrti pacienta. Mŕtve bunky ďalej nešíria infekciu a vo vhodnom rozostavení vedia pôsobiť ako hranica, ktorá jej šírenie zastaví.</p><p>Vzhľadom na nedostatok dát o miere úmrtnosti a obmedzených poznatkoch o samotnom víruse sa nedá s istotou povedať, či je model presný. Zdroje sa v údajoch o úmrtnosti pacientov značne líšia. Zlepšenie výsledkov je možné dosiahnuť doladením vstupných parametrov simulátoru na základe vyzbieraných údajov v budúcnosti. Pri správnom nastavení vstupných parametrov vie byť tento model užitočným nástrojom, ktorý môže potencionálne nahradiť testy na zvieratách a urýchliť vývoj liekov.</p><h1 id="bibliografia"><a class="anchor hidden-xs" href="#bibliografia" title="bibliografia"><span class="octicon octicon-link"></span></a>Bibliografia</h1><p>[1] <a href="https://doi.org/10.1016/j.physa.2015.06.049" target="_blank">Emily Burkhead, Jane Hawkins, A cellular automata model of Ebola virus dynamics, In Physica A: Statistical Mechanics and its Applications, Volume 438, 2015, Pages 424-435, ISSN 0378-4371</a><br>
[2] <a href="http://doi.org/10.1056/NEJMoa1411100" target="_blank">WHO Ebola Response Team. (2014). Ebola Virus Disease in West Africa — The First 9 Months of the Epidemic and Forward Projections. The New England Journal of Medicine, 371(16), 1481–1495.</a><br>
[3] <a href="https://doi.org/10.1002/path.4456" target="_blank">Martines, R. B., Ng, D. L., Greer, P. W., Rollin, P. E. and Zaki, S. R. (2015), Tissue and cellular tropism, pathology and pathogenesis of Ebola and Marburg viruses. J. Pathol., 235: 153–174.</a><br>
[4] <a href="https://doi.org/10.1007/BF01728658" target="_blank">Becker, Y. Virus Genes (1995) 11: 191. </a><br>
[5] <a href="https://doi.org/10.1007/s11538-008-9351-0" target="_blank">Burkhead, E.G., Hawkins, J.M. & Molinek, D.K. Bull. Math. Biol. (2009) 71: 25.</a><br>
[6] <a href="https://doi.org/10.1016/j.physa.2013.05.056" target="_blank">Ramón E.R. González, Sérgio Coutinho, Rita Maria Zorzenon dos Santos, Pedro Hugo de Figueirêdo, Dynamics of the HIV infection under antiretroviral therapy: A cellular automata approach, In Physica A: Statistical Mechanics and its Applications, Volume 392, Issue 19, 2013, Pages 4701-4716, ISSN 0378-4371</a><br>
[7] <a href="https://doi.org/10.1016/j.physa.2012.10.036" target="_blank">Ramón E.R. González, Pedro Hugo de Figueirêdo, Sérgio Coutinho, Cellular automata approach for the dynamics of HIV infection under antiretroviral therapies: The role of the virus diffusion, In Physica A: Statistical Mechanics and its Applications, Volume 392, Issue 19, 2013, Pages 4717-4725, ISSN 0378-4371</a><br>
[8] <a href="https://www.ncbi.nlm.nih.gov/pubmed/25387613" target="_blank">Goeijenbier, M, J J A van Kampen, C B E M Reusken, M P G Koopmans, and E C M van Gorp. 2014. “Ebola Virus Disease: A Review On Epidemiology, Symptoms, Treatment And Pathogenesis”. Online. The Netherlands Journal Of Medicine 72 (9): 442.</a></p></div>
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<div class="toc"><ul class="nav"><li class=""><a href="#modelovanie-dynamiky-vírusu-ebola-celulárnym-automatom">Modelovanie dynamiky vírusu Ebola celulárnym automatom</a></li><li><a href="#1-úvod">1. Úvod</a><ul class="nav"><li><a href="#11-zdroje-faktov">1.1 Zdroje faktov</a><ul class="nav"><li><a href="#111-autori">1.1.1 Autori</a></li><li><a href="#112-literatúra">1.1.2 Literatúra</a></li></ul></li><li><a href="#12-overenie-validity">1.2 Overenie validity</a></li></ul></li><li><a href="#2-rozbor-tématu-a-použitých-metodtechnologií">2. Rozbor tématu a použitých metod/technologií</a><ul class="nav"><li><a href="#21-celulárny-automat">2.1 Celulárny automat</a></li></ul></li><li><a href="#3-koncepcia">3. Koncepcia</a><ul class="nav"><li><a href="#31-základný-model-šírenia-vírusu">3.1 Základný model šírenia vírusu</a><ul class="nav"><li><a href="#311-bunka">3.1.1 Bunka</a></li><li><a href="#312-pole-buniek">3.1.2 Pole buniek</a></li><li><a href="#312-okolie">3.1.2 Okolie</a></li><li><a href="#313-základné-pravidlá">3.1.3 Základné pravidlá</a></li></ul></li><li><a href="#32-model-pre-oneskorenú-imunitnú-reakciu">3.2 Model pre oneskorenú imunitnú reakciu</a></li><li><a href="#33-model-pre-vyčerpanú-imunitnú-reakciu">3.3 Model pre vyčerpanú imunitnú reakciu</a></li><li><a href="#34-stochastický-model-priebehu-ochorenia">3.4 Stochastický model priebehu ochorenia</a></li><li><a href="#35-podmienka-ukončenia-simulácie">3.5 Podmienka ukončenia simulácie</a><ul class="nav"><li><a href="#351-úplné-vyzdravenie">3.5.1 Úplné vyzdravenie</a></li><li><a href="#352-smrť-prekročením-terminálnej-podmienky">3.5.2 Smrť prekročením terminálnej podmienky</a></li><li><a href="#353-smrť-prekročením-maximálneho-počtu-dní">3.5.3 Smrť prekročením maximálneho počtu dní</a></li></ul></li></ul></li><li><a href="#4-architektura-simulačního-modelu">4. Architektura simulačního modelu</a><ul class="nav"><li><a href="#41-zbieranie-údajov">4.1 Zbieranie údajov</a></li></ul></li><li><a href="#5-podstata-simulačních-experimentů-a-jejich-průběh">5. Podstata simulačních experimentů a jejich průběh</a><ul class="nav"><li><a href="#51-doba-uzdravenia">5.1 Doba uzdravenia</a></li><li><a href="#52-závislosť-úmrtnosti-na-veľkosti-celulárneho-automatu">5.2 Závislosť úmrtnosti na veľkosti celulárneho automatu</a></li><li><a href="#53-závislosť-úmrtnosti-na-oneskorenej-imunitnej-reakcii">5.3 Závislosť úmrtnosti na oneskorenej imunitnej reakcii</a></li><li><a href="#54-závislosť-úmrtnosti-na-vyčerpanej-imunitnej-reakcii">5.4 Závislosť úmrtnosti na vyčerpanej imunitnej reakcii</a></li><li><a href="#55-závislosť-úmrtnosti-pri-rôznych-kombináciach-imunitných-reakcií">5.5 Závislosť úmrtnosti pri rôznych kombináciach imunitných reakcií</a></li><li><a href="#56-závery-experimentov">5.6 Závery experimentov</a></li></ul></li><li><a href="#6-shrnutí-simulačních-experimentů-a-závěr">6. Shrnutí simulačních experimentů a závěr</a></li><li><a href="#bibliografia">Bibliografia</a></li></ul></div><div class="toc-menu"><a class="expand-toggle" href="#">Expand all</a><a class="back-to-top" href="#">Back to top</a><a class="go-to-bottom" href="#">Go to bottom</a></div>
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<div class="toc"><ul class="nav"><li><a href="#modelovanie-dynamiky-vírusu-ebola-celulárnym-automatom">Modelovanie dynamiky vírusu Ebola celulárnym automatom</a></li><li><a href="#1-úvod">1. Úvod</a><ul class="nav"><li><a href="#11-zdroje-faktov">1.1 Zdroje faktov</a><ul class="nav"><li><a href="#111-autori">1.1.1 Autori</a></li><li><a href="#112-literatúra">1.1.2 Literatúra</a></li></ul></li><li><a href="#12-overenie-validity">1.2 Overenie validity</a></li></ul></li><li><a href="#2-rozbor-tématu-a-použitých-metodtechnologií">2. Rozbor tématu a použitých metod/technologií</a><ul class="nav"><li><a href="#21-celulárny-automat">2.1 Celulárny automat</a></li></ul></li><li><a href="#3-koncepcia">3. Koncepcia</a><ul class="nav"><li><a href="#31-základný-model-šírenia-vírusu">3.1 Základný model šírenia vírusu</a><ul class="nav"><li><a href="#311-bunka">3.1.1 Bunka</a></li><li><a href="#312-pole-buniek">3.1.2 Pole buniek</a></li><li><a href="#312-okolie">3.1.2 Okolie</a></li><li><a href="#313-základné-pravidlá">3.1.3 Základné pravidlá</a></li></ul></li><li><a href="#32-model-pre-oneskorenú-imunitnú-reakciu">3.2 Model pre oneskorenú imunitnú reakciu</a></li><li><a href="#33-model-pre-vyčerpanú-imunitnú-reakciu">3.3 Model pre vyčerpanú imunitnú reakciu</a></li><li><a href="#34-stochastický-model-priebehu-ochorenia">3.4 Stochastický model priebehu ochorenia</a></li><li><a href="#35-podmienka-ukončenia-simulácie">3.5 Podmienka ukončenia simulácie</a><ul class="nav"><li><a href="#351-úplné-vyzdravenie">3.5.1 Úplné vyzdravenie</a></li><li><a href="#352-smrť-prekročením-terminálnej-podmienky">3.5.2 Smrť prekročením terminálnej podmienky</a></li><li><a href="#353-smrť-prekročením-maximálneho-počtu-dní">3.5.3 Smrť prekročením maximálneho počtu dní</a></li></ul></li></ul></li><li><a href="#4-architektura-simulačního-modelu">4. Architektura simulačního modelu</a><ul class="nav"><li><a href="#41-zbieranie-údajov">4.1 Zbieranie údajov</a></li></ul></li><li class=""><a href="#5-podstata-simulačních-experimentů-a-jejich-průběh">5. Podstata simulačních experimentů a jejich průběh</a><ul class="nav"><li><a href="#51-doba-uzdravenia">5.1 Doba uzdravenia</a></li><li><a href="#52-závislosť-úmrtnosti-na-veľkosti-celulárneho-automatu">5.2 Závislosť úmrtnosti na veľkosti celulárneho automatu</a></li><li><a href="#53-závislosť-úmrtnosti-na-oneskorenej-imunitnej-reakcii">5.3 Závislosť úmrtnosti na oneskorenej imunitnej reakcii</a></li><li><a href="#54-závislosť-úmrtnosti-na-vyčerpanej-imunitnej-reakcii">5.4 Závislosť úmrtnosti na vyčerpanej imunitnej reakcii</a></li><li><a href="#55-závislosť-úmrtnosti-pri-rôznych-kombináciach-imunitných-reakcií">5.5 Závislosť úmrtnosti pri rôznych kombináciach imunitných reakcií</a></li><li class=""><a href="#56-závery-experimentov">5.6 Závery experimentov</a></li></ul></li><li><a href="#6-shrnutí-simulačních-experimentů-a-závěr">6. Shrnutí simulačních experimentů a závěr</a></li><li><a href="#bibliografia">Bibliografia</a></li></ul></div><div class="toc-menu"><a class="expand-toggle" href="#">Expand all</a><a class="back-to-top" href="#">Back to top</a><a class="go-to-bottom" href="#">Go to bottom</a></div>
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toc.show();
}
$(document.body).scroll();
}
function windowResize() {
//toc right
var paddingRight = parseFloat(markdown.css('padding-right'));
var right = ($(window).width() - (markdown.offset().left + markdown.outerWidth() - paddingRight));
toc.css('right', right + 'px');
//affix toc left
var newbool;
var rightMargin = (markdown.parent().outerWidth() - markdown.outerWidth()) / 2;
//for ipad or wider device
if (rightMargin >= 133) {
newbool = true;
var affixLeftMargin = (tocAffix.outerWidth() - tocAffix.width()) / 2;
var left = markdown.offset().left + markdown.outerWidth() - affixLeftMargin;
tocAffix.css('left', left + 'px');
} else {
newbool = false;
}
if (newbool != enoughForAffixToc) {
enoughForAffixToc = newbool;
generateScrollspy();
}
}
$(window).resize(function () {
windowResize();
});
$(document).ready(function () {
windowResize();
generateScrollspy();
});
//remove hash
function removeHash() {
window.location.hash = '';
}
var backtotop = $('.back-to-top');
var gotobottom = $('.go-to-bottom');
backtotop.click(function (e) {
e.preventDefault();
e.stopPropagation();
if (scrollToTop)
scrollToTop();
removeHash();
});
gotobottom.click(function (e) {
e.preventDefault();
e.stopPropagation();
if (scrollToBottom)
scrollToBottom();
removeHash();
});
var toggle = $('.expand-toggle');
var tocExpand = false;
checkExpandToggle();
toggle.click(function (e) {
e.preventDefault();
e.stopPropagation();
tocExpand = !tocExpand;
checkExpandToggle();
})
function checkExpandToggle () {
var toc = $('.ui-toc-dropdown .toc');
var toggle = $('.expand-toggle');
if (!tocExpand) {
toc.removeClass('expand');
toggle.text('Expand all');
} else {
toc.addClass('expand');
toggle.text('Collapse all');
}
}
function scrollToTop() {
$('body, html').stop(true, true).animate({
scrollTop: 0
}, 100, "linear");
}
function scrollToBottom() {
$('body, html').stop(true, true).animate({
scrollTop: $(document.body)[0].scrollHeight
}, 100, "linear");
}
</script>
</body>
</html>