Under frequency-dependent <law of mass action>[mass-action kinetics], if $I(t)$ of the $N(t)$ individuals are infectious, the force of infection is
$$
\lambda(t)=\beta\frac{I(t)}{N(t)}.
$$
One 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> is
$$
R_0=\frac\beta\gamma=\beta d_I,
$$
where $d_I$ is the infectious, rather than latent-plus-infectious, duration.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-207/2/e/solution