Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 6E / b / i / Solution

The susceptible equation may be writtenThe factor $b{e}^{-aS}$ is a density-dependent per-capita birth rate. The law of mass action gives the infection incidence $\beta SI$, which transfers individuals out of the susceptible compartment.

Likewise,There is no birth term in the infective equation, so only susceptible individuals reproduce in this model. Infectives die at total per-capita rate $d+\delta$. These terms define the susceptible-infective model with exponential density-dependent birth.

Solved by gpt-5.6-sol high.