Modelling disease spread through populations of territorial animals and the effect of culling

The culling of animals in an attempt to slow or halt disease spread is a controversial method, yet frequently adopted by government agencies in the UK and beyond. In particular, the recent badger culls in the UK have generated significant controversy and attention. The central argument is that, by removing a proportion of the wild animals (e.g. badgers) that transmit a disease, this disease will be less likely to spread to humans and/or livestock. However, scientific evidence typically points towards it being an ineffective strategy.

Indeed, it has been hypothesised that culling of territorial animals can make disease spread worse, by something called a `perturbation effect’, whereby culling causes territorial and social structures to break down. This may result in animals moving longer distances and therefore having a greater probability of encountering other animals. Although this is unlikely to happen if the culling is extreme (the mathematical limit being extinction), it suggests that moderate culling efforts may result in increased disease spread.

The aim of this project is to test this hypothesis from a mathematical modelling perspective. The candidate will build upon recent models of territory formation, constructed by the supervisor and collaborators, to (a) incorporate first the effect of disease spread under different classical disease-model scenario, then (b) examine the effect of culling strategies on the spreading speed. The initial approach will be to use a stochastic individual-based modelling approach to examine these questions. Then the candidate will construct partial differential equation approximations of this model, making use of travelling wave theory to gain an analytic understanding of the effect of culling. The paradigmatic system will be European badgers (Meles meles), but we will aim to make the models as general, and generalisable, as possible.