Mechanistic intracellular and within-host models of bacterial and viral infections

This thesis explores mathematical models for the infection dynamics of two types of pathogens, namely the specific bacterium Bacillus anthracis, which is the causative agent of anthrax, and viruses more generally. I present a stochastic multi-scale model for describing B. anthracis infection at the intracellular and within-host levels. The intracellular model uses a Markov chain to describe the key interaction between B. anthracis spores and host cells, and to predict the distribution of outcomes from this interaction. Key outputs are then used to connect this intracellular model to a within-host model of inhalational anthrax, which aims to offer a realistic mechanistic description of the infection dynamics, as well the probability of infection for a given inhaled dose. The multi-scale model is calibrated via a Bayesian approach, using various experimental in vitro and in vivo data. Stochastic models of virus kinetics are also studied, with a focus on finding probability distributions for the burst size and cellular reproduction number. It is shown how these distributions are affected by modelling choices, and how these distributions in turn affect the probability that the virus and infected cells will be eliminated before an established infection can occur.