Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2025 / Paper 1 / 5 / c

This is the Nicholson-Bailey model for a host-parasitoid interaction with discrete generations. The factor $r$ is the host multiplication factor in the absence of parasitism; $a$ measures effective attack or searching intensity per parasitoid; and $b$ is the number of next-generation parasitoids produced per attacked host, with any survival or unit conversion absorbed into it.

If the number of attacks on a host has a Poisson distribution with expected value $a{P}_t$, then the probability of no attack is $e^{-a{P}_t}$. Consequently $e^{-a{P}_t}$ is the surviving, unparasitized host fraction, and $1-e^{-a{P}_t}$ is the attacked fraction. The two update equations count host descendants from surviving hosts and parasitoid descendants from attacked hosts, respectively.