Section 4 of the vignette

[choisy]

As explained here, here we are facing 2 different situations.

In the first case, we are dealing with concurrent events. By definition, concurrent events occurs exactly at the same time, which is impossible to compute in practice (although we approach this more and more as the time step decreases in duration). To deal with that, you need to decompose the problem into 2 successive steps (within each time step). First you compute how many people are getting out of S (here, it's \beta SI/N + 5) and, second, you compute the proportions of these people who go in each direction (here, it's gonna be \beta SI/N / (\beta SI/N + 5) going to I and 5 / (\beta SI/N + 5) going to V.

The second case is then very similar, except that the proportion of people going in each direction are known in advance. Here, as explained here, you first split I -> I_R and I -> I_D with proportions 0.9 and 0.1 respectively, and then you apply the gamma distribution on I_R and the lognormal distribution on I_D.

[choisy]

For the diagramme, instead of drawing it this way:

You should draw it this way instead:

where the convention would that numbers on arrows getting out of a black circle refer to proportions.