Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 6A / b / Solution

In a homogeneous population,An infected fox remains infectious for mean time $1/\mu$ and creates new infections at initial rate $S_0$, so the basic reproductive ratio isInitially $I$ grows exactly when $S_0-\mu >0$, equivalently ${\mathcal{R}}_0>1$. Below that threshold each infective produces fewer than one replacement on average and the infection decays.