From 37b0a323644bd9697ca2251d5ea529fdc83b3b18 Mon Sep 17 00:00:00 2001 From: Sebastian Funk Date: Fri, 1 Sep 2023 10:21:53 +0100 Subject: [PATCH] Update vignettes/theoretical_background.Rmd Co-authored-by: James Azam --- vignettes/theoretical_background.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/vignettes/theoretical_background.Rmd b/vignettes/theoretical_background.Rmd index 5a44565..fe040a8 100644 --- a/vignettes/theoretical_background.Rmd +++ b/vignettes/theoretical_background.Rmd @@ -41,7 +41,7 @@ Below we will call these infected individuals _cases_ but the methods could be a To simulate from a branching process, we start with a single case and proceed in discrete steps or generations, drawing from the offspring distribution $p(Z=z | \theta)$ to generate new cases from each case. -If we additionally define the distribution of times $T$ as a random variable with distribution $f(T = t; \theta)$ we can assign each case $j$ a time $t_{j}$ which, if case $j$ has been affected by case $i$ is given by $f(t_{j} - t_{i} | \theta)$. +Given an infector $i$ and infectee $j$, we can additionally assign them a distribution of times $T$ that approximates when the infection event occurred. If we define $T$ as a random variable with distribution $f(T = t; \theta)$ we can assign each case $j$ a time $t_{j}$ which, if case $j$ has been affected by case $i$ is given by $f(t_{j} - t_{i} | \theta)$. If we identify the timing cases by the time of their symptom onset this is the [serial interval](https://en.wikipedia.org/wiki/Serial_interval), but depending on case definitions this could be another interval. ## Summary statistics