Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 2 / e / Solution

Under frequency-dependent mass-action kinetics, if $I(t)$ of the $N(t)$ individuals are infectious, the force of infection isOne newly infectious person in an otherwise susceptible population transmits at total rate approximately $\beta$ for mean infectious duration $1/\gamma$. Hence the basic reproduction number iswhere $d_I$ is the infectious, rather than latent-plus-infectious, duration.