From b23ae7ce79bebcefa39f8a4a1e0fca308c013072 Mon Sep 17 00:00:00 2001 From: Romain Ragonnet Date: Thu, 14 Sep 2023 14:12:42 +1000 Subject: [PATCH] Incorporate Michael's suggestions in appendix --- .../models/sm_covid/model_description.tex | 3 ++- .../tex_descriptions/models/sm_covid/odes.tex | 2 +- .../sm_covid/stratifications/immunity.tex | 4 ++-- docs/tex/user/rragonnet/sm_covid.pdf | Bin 1732300 -> 1732372 bytes 4 files changed, 5 insertions(+), 4 deletions(-) diff --git a/docs/tex/tex_descriptions/models/sm_covid/model_description.tex b/docs/tex/tex_descriptions/models/sm_covid/model_description.tex index 18e7973ab..c3b0f277f 100644 --- a/docs/tex/tex_descriptions/models/sm_covid/model_description.tex +++ b/docs/tex/tex_descriptions/models/sm_covid/model_description.tex @@ -5,7 +5,8 @@ \section{Model description} \subsection{General approach} -We use a semi-mechanistic compartmental model of COVID-19 transmission governed by ordinary differential equations (ODEs). +We use a semi-mechanistic compartmental model of COVID-19 transmission governed by ordinary differential equations (ODEs) to +simulate country-specific COVID-19 epidemics during the first three years of the pandemic (2020-2022). Our model captures important factors of COVID-19 transmission and disease such as age-specific characteristics, heterogeneous mixing, vaccination and the emergence of different variants of concern. The ODE-based model is used to capture only states relevant to transmission, whereas hospitalisations and deaths are diff --git a/docs/tex/tex_descriptions/models/sm_covid/odes.tex b/docs/tex/tex_descriptions/models/sm_covid/odes.tex index 4083c5a34..bffd4c96e 100644 --- a/docs/tex/tex_descriptions/models/sm_covid/odes.tex +++ b/docs/tex/tex_descriptions/models/sm_covid/odes.tex @@ -5,7 +5,7 @@ the average duration of active disease is denoted $w$. The relative susceptibility to infection with strain $s$ of individuals aged $a$ with vaccination status $v$ is denoted $\rho_{a,v,s}$. The term $b_{a,v,s}(t)$ designates the introduction of individuals of age $a$ and with vaccination status $v$ that are infected with strain $s$ (infection seeding). Vaccination is characterised by the age-specific -and time-variant per-capita vaccination rate $w_a$. Finally, $\chi_{s,\sigma}$ represents the relative susceptibility to infection +and time-variant per-capita vaccination rate $\omega_a$. Finally, $\chi_{s,\sigma}$ represents the relative susceptibility to infection with strain $\sigma$ for individuals whose most recent infection episode was with strain $s$. Using this new notation combined with those previously introduced, we can describe the model with the following set of ordinary differential equations: diff --git a/docs/tex/tex_descriptions/models/sm_covid/stratifications/immunity.tex b/docs/tex/tex_descriptions/models/sm_covid/stratifications/immunity.tex index 7a04623f4..ed13da340 100644 --- a/docs/tex/tex_descriptions/models/sm_covid/stratifications/immunity.tex +++ b/docs/tex/tex_descriptions/models/sm_covid/stratifications/immunity.tex @@ -10,7 +10,7 @@ are allocated. Note that in the event that the population-level vaccine coverage exceeds 80\%, the saturation coverage was set equal to the population-level coverage. Let us consider two successive time points $t_i$ and $t_{i+1}$ for which vaccination data are available. Let us denote $r_{a, i}$ and $r_{a, i+1}$ the associated vaccine -coverage for age group $a$. The time-variant and age-specific vaccination rate per capita $w_a(t)$ verifies: +coverage for age group $a$. The time-variant and age-specific vaccination rate per capita $\omega_a(t)$ verifies: \begin{equation} 1 - r_{a, i+1} = (1 - r_{a, i})e^{-w_a(t)(t_{i+1} - t_i)} \quad, \forall t \in [t_i, t_{i+1}) . @@ -19,7 +19,7 @@ Then, \begin{equation} \label{eq:vacc} - w_a(t) = \frac{\ln(1 - r_{a, i}) - \ln(1 - r_{a, i+1})}{t_{i+1} - t_i} \quad, \forall t \in [t_i, t_{i+1}) , + \omega_a(t) = \frac{\ln(1 - r_{a, i}) - \ln(1 - r_{a, i+1})}{t_{i+1} - t_i} \quad, \forall t \in [t_i, t_{i+1}) , \end{equation} where $\ln(x)$ represents the natural logarithm of $x$. diff --git a/docs/tex/user/rragonnet/sm_covid.pdf b/docs/tex/user/rragonnet/sm_covid.pdf index 1ced2957b6c8929aa43d52d0434abd40be84ebb5..bbaf41655af14254dd2ad0380a85b1c5fcbbe2a6 100644 GIT binary patch delta 25558 zcmai52{cyS*EfYsnKDHo6p3dZh>)Q|B!!eQ5k;k>#A8;5%n3!(JSuY`AyOh5j7iCm zLNY|8Z$C|M&i$|TS?^tMYu|nD*=L_U{PsTQse8REsdHD(N)9iTX@!*D6P$T@X3>UC&EPFj($7G^_pW%V-nMSU$3b&oz&XEMOSb; 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