Stochastic modelling and statistical inference for epidemics in structured populations

The aim of the proposed research is to develop stochastic epidemic models that incorporate important population heterogeneities, together with techniques for their analysis and statistical inference. Two broad classes of such models will be considered.The first class is concerned with models for infectious diseases in which the degree of severity of infected individuals and their potential for future spread are determined by the size of the infecting dose. More specifically, various models with two severities of infection, mild and severe, will be investigated, first for a homogeneously mixing population and then for a community of households. For each model, a threshold parameter that determines whether or not an outbreak can become established will be determined, together with other properties, such as the probability that an outbreak does become established and the final outcome if it does. Implications for vaccination strategies will be explored, using a variety of models for how vaccination affects a vaccinee's susceptibility to the disease in question and their ability to spread the disease if they become infected.The second class of models is that in which the spread of infection can occur at three different levels within the at-risk population. An example would be a model in which infection is permitted to occur within households, within schools, and also in the population at large, with different risks of infection in each place. Such models are relatively underexplored in the literature, but are of increasing importance in real-life epidemic and pandemic planning. In particular, the efficacy of control strategies such as school closure or travel restrictions relies crucially on the kind of population-level mixing that such models describe. The proposed research aims to explore fundamental issues of statistical inference and data collection for such models, addressing such questions as what can be inferred from different sorts of data, and the extent to which three-level-mixing models are more useful than simpler, but less realistic, models.