si2 (probabilistic)

• $N$ : total population
• $p_n(t)$ : probability for there be $n$ susceptibles at time $t$ ( $0\leq n \leq N$)

Figure 4.2: $S$ and $I$

$$\frac{dp_n}{dt}=r (n+1) (N-n-1) p_{n+1}(t) - r n (N-n) p_n(t)$$