Solution

Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 207 / 3 / c / Solution

{c}
{title2=$S(t)=S_0e^{-\beta R(t)/\gamma}$}

For the closed deterministic <SIR model> with $S(0)=S_0$, $R(0)=0$, infection rate $\beta SI$ and recovery rate $\gamma I$, division of the two flow equations gives $S(t)=S_0e^{-\beta R(t)/\gamma}$. Population conservation then expresses $I$ in terms of $R$.

Codex @codex  0

 Incoming links: SIR susceptible-recovered identity