Integrated modelling and Bayesian inference applied to population and disease dynamics in wildlife: M.Bovis in badgers in Woodchester Park

Abstract

Understanding demographic and disease processes in wildlife populations tends to be hampered by incomplete observations which can include significant errors. Models provide useful insights into the potential impacts of key processes and the value of such models greatly improves through integration with available data in a way that includes all sources of stochasticity and error. To date, the impact on disease of spatial and social structures observed in wildlife populations has not been widely addressed in modelling. I model the joint effects of differential fecundity and spatial heterogeneity on demography and disease dynamics, using a stochastic description of births, deaths, social-geographic migration, and disease transmission. A small set of rules governs the rates of births and movements in an environment where individuals compete for improved fecundity. This results in realistic population structures which, depending on the mode of disease transmission can have a profound effect on disease persistence and therefore has an impact on disease control strategies in wildlife populations. I also apply a simple model with births, deaths and disease events to the long-term observations of TB (Mycobacterium bovis) in badgers in Woodchester Park. The model is a continuous time, discrete state space Markov chain and is fitted to the data using an implementation of Bayesian parameter inference with an event-based likelihood. This provides a flexible framework to combine data with expert knowledge (in terms of model structure and prior distributions of parameters) and allows us to quantify the model parameters and their uncertainties. Ecological observations tend to be restricted in terms of scope and spatial temporal coverage and estimates are also affected by trapping efficiency and disease test sensitivity. My method accounts for such limitations as well as the stochastic nature of the processes. I extend the likelihood function by including an error term that depends on the difference between observed and inferred state space variables. I also demonstrate that the estimates improve by increasing observation frequency, combining the likelihood of more than one group and including variation of parameter values through the application of hierarchical priors.