The first thing that comes to mind when algorithm 1 no longer suffices is the SIR approach. We look at the entire population and divide it into three compartments: who can be infected (**S** for susceptible), who are infected (**I** for infected) and who are resistant (**R** for resistant). To keep things simple for the time being, we start with a fixed number (**N**). The population does not increase or decrease during the time the model works. This means that we can assume that N = S + I + R . But the mutual relationships do change during that period. If we divide the time that the model works into periods, we can translate that assumption into:

N=S_t+I_t+R_t

so we can express S, I and R in percentages.

The SIR approach has a second assumption in the form of an associated transition model: S individuals can only change into I individuals and I individuals can only change into R individuals. We can try to capture the rate of the transitions from S_ {t} to I_ {t} in an infection rate per period, say \beta_ {t} and the rate of the transitions from I_ {t} to R_ {t} in a recovery rate per period, say \mu_ {t}.

We made algorithm 2 to get an impression of how this approach works out.