Bayesian Non-Parametric Methodology for Stochastic Epidemic Models

Simulating from and making inference for stochastic epidemic models are key strategies for understanding and controlling the spread of infectious diseases. Despite the enormous attention given to methods for parameter estimation, there has been relatively little activity in the area of nonparametric inference. That is, drawing inference for the infection rate without making specific modelling assumptions about its functional form. In this project we are concerned with heterogeneously mixing models in which the infection rate between two individuals is a function of their characteristics, for example location or type. We develop a novel method for inferring the function nonparametrically, removing the need to make questionable parametric assumptions. We adopt a Bayesian approach by assigning a Gaussian Process prior distribution to the infection rate function and then develop an efficient data augmentation Markov Chain Monte Carlo methodology to estimate the infection rate function, the GP hyperparameters and the unobserved infection times. We will illustrate our methodology using simulated data and as well as data on an Avian Influenza outbreak from the Netherlands.