Mathematical modelling of bacterial and viral infections

In this thesis, I present a series of mathematical models for describing the infection dynamics of two lethal intracellular pathogens, namely Francisella tularensis and Ebola virus. Through the construction of both stochastic and deterministic models, a multi-disciplinary approach is used to account for the key processes that dictate disease progression. Each model describes the dynamics of a population of host cells, with the analysis of interactions between individual cells and single bacteria or virus particles allowing for greater detail to be included. Throughout this thesis, the theory of birth-and-death processes, matrix analytic methods and numerical simulation algorithms are used to study the stochastic processes. In addition to these techniques, a Bayesian approach to statistical inference is applied in order to parametrise each of the models with relevant infection data.