add clarification

Co-authored-by: James Azam <james.m.azam@gmail.com>

vignettes/theoretical_background.Rmd

@@ -39,7 +39,7 @@ Below we will call these infected individuals _cases_ but the methods could be a
 
 # Simulation
 
-To simulate from a branching process, we start with a single case and proceed in discrete steps or generations, drawing from $p(Z=z | \theta)$ to generate new cases from each case.
+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 $f(t_{j} - t_{i} | \theta)$.
 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.