Bayesian Inference and Model Selection for Partially-Observed, Continuous-Time, Stochastic Epidemic Models

Abstract

Emerging infectious diseases are an ongoing threat to the health of populations around the world. In response, countries such as the USA, UK and Australia, have outlined data collection protocols to surveil these novel diseases. One of the aims of these data collection protocols is to characterise the disease in terms of transmissibility and clinical severity in order to inform an appropriate public health response. This kind of data collection protocol is yet to be enacted in Australia, but such a protocol is likely to be tested during a seasonal in uenza ( u) outbreak in the next few years. However, it is important that methods for characterising these diseases are ready and well understood for when an epidemic disease emerges. The epidemic may only be characterised well if its dynamics are well described (by a model) and are accurately quanti ed (by precisely inferred model parameters). This thesis models epidemics and the data collection process as partially-observed continuous-time Markov chains and aims to choose between models and infer parameters using early outbreak data. It develops Bayesian methods to infer epidemic parameters from data on multiple small outbreaks, and outbreaks in a population of households. An exploratory analysis is conducted to assess the accuracy and precision of parameter estimates under di erent epidemic surveillance schemes, di erent models and di erent kinds of model misspeci cation. It describes a novel Bayesian model selection method and employs it to infer two important characteristics for understanding emerging epidemics: the shape of the infectious period distribution; and, the time of infectiousness relative to symptom onset. Lastly, this thesis outlines a method for jointly inferring model parameters and selecting between epidemic models. This new method is compared with an existing method on two epidemic models and is applied to a di cult model selection problem.