Bayesian nonparametric inference for spatial transmission models of infectious diseases

A Bayesian Nonparametric Analysis of the 2003 Outbreak of Highly Pathogenic Avian Influenza in the Netherlands

Understanding how infectious diseases spread between farms is crucial for developing disease control strategies to prevent future outbreaks.Making nonparametric inference in this context is challenging since the likelihood function of the observed data is intractable because the underlying transmission process is unobserved.We develop novel bayesian nonparametric methodology to fit spatial stochastic transmission models in which the infection rate between any two farms is a function that depends on the distance between them, but without assuming a specified parametric form.We adopt a fully bayesian approach by assigning a transformed gaussian process prior distribution to the infectionrate function, and then develop an efficient data augmentation markov chain monte carlo algorithm to perform bayesian inference.We analyse a large outbreak of avianinfluenza in the netherlands and infer the between-farm infection rate, as well as the unknown infection status of farms which were pre-emptively culled.We use our results to analyse ring-culling strategies, and conclude that although effective, ring-culling has limited impact in high density areas.