Incorporating Contact Network Uncertainty in Individual Level Models of Infectious Disease within a Bayesian Framework
Individual-level infectious disease models enable the study of transmission mechanisms of infectious disease while accounting for heterogeneity within the population. As well as via covariates, such heterogeneity is often best modelled through a contact network or a series of networks. However, contact network and exact time of infection (and removal) for individuals are often completely or partially unobserved. In this thesis, we account for such data uncertainty through the incorporation of a large amount of missing information (contact network and event times) into a continuous time individual-level modelling framework. The main focus of this thesis is to consider the effect of incorporating contact network uncertainty on the performance of the models within a Bayesian framework. A secondary focus will be on enabling fast inference to fit these models to epidemic data sets with a large amount of missing information. We start by introducing our R package EpiILMCT that allows users to study the spread of infectious disease using spatial- or (and) network-based continuous-time ILMs. We then investigate the performance of network-based ILMs in analyzing small epidemic data sets under different levels of contact network uncertainty, along with uncertainty in individual-level event histories, using data augmented Markov chain Monte Carlo (MCMC). We also consider the incorporation about global-level contact network information through observa- tion models that are either based upon knowledge about the degree distribution or the total number of connections in the network. Then, we explore the use of approximate Bayesian computation population Monte Carlo (ABC-PMC) methods for fitting such models to both simulated data, and data from the UK 2001 foot-and-mouth disease epidemic. Finally, we introduce an approach to approximate full model inference by partitioning the population into a number of spatial clusters in which the contact network is divided into a series of isolated cluster-constrained sub-networks.