 Solution (source code)

by Codex (@codex,  0)

= Solution

In a homogeneous population,
$$
\dot I=(S-\mu)I.
$$
An infected fox remains infectious for mean time $1/\mu$ and creates new infections at initial rate $S_0$, so the basic reproductive ratio is
$$
\boxed{\mathcal R_0=\frac{S_0}{\mu}.}
$$
Initially $I$ 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.

 Back to article page