Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 6A / a / Solution

In the SIR model with demography and permanent immunity, $\mu$ is the common per-capita death rate and, through the term $\mu N$, the replacement birth rate. The coefficient $\beta$ is the mass-action transmission rate per susceptible-infective pair, and $\nu$ is the per-capita recovery rate from infection into permanent immunity.