Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 207 / 2 / f / Solution

While $I>0$, divide the susceptible equation by the recovered equation:Taking $R(0)=0$ and integrating givesAt the end of the epidemic $E_{\infty }=I_{\infty }=0$, so conservation gives $R_{\infty }=N-S_{\infty }$. Definingwe obtain the final size relation for an epidemic