Statistical modeling and analyses of partially observed infectious diseases

This thesis is concerned with the development of Bayesian inference approach for the analysis of infectious disease models. Stochastic SIS household-based epidemic models were considered with individuals allowed to be contracted locally at a given rate and there also exists a global force of infection. The study covers both when the population of interest is assumed to be constant and when the population is allowed to vary over time. It also covers when the global force of infection is constant and when it is spatially varying as a function of some unobserved Gaussian random fields realizations. In addition, we also considered diseases coinfection models allowing multiple strains transmission and recovery. For each model, Bayesian inference approach was developed and implemented via MCMC framework using extensive data augmentation schema. Throughout, we consider two most prevalent forms of endemic disease data- the individual-based data and the aggregate-based data. The models and Bayesian approach were tested with simulated data sets and successfully applied to real-life data sets of tick-borne diseases among Tanzania cattle.