In this thesis, mathematical models for the in vitro and in vivo dynamics of the bacterium Bacillus anthracis, the causative agent of the disease anthrax, are considered in Chapters 3 and 4. Additionally, the dynamics of infection transmission for a pathogenic wild-type strain of a given virus and defective interfering strain of the same virus within a closed population are also considered in Chapter 5.
In Chapter 3, a two-compartment stochastic model is presented which describes the behaviour of toxin-producing bacteria and the corresponding dynamics are analysed. Using a continuous-time Markov chain to describe the model allows several summary statistics to be considered, such as the number of toxin molecules produced during the lifespan of a bacterium. This two-compartment model is applied to Bacillus anthracis and antibiotic treatment. An attempt is made to quantify, for the first time, bacterial toxin production by making use of data from an in vitro assay for a particular strain of B. anthracis.
Then, in Chapter 4, the stochastic analog of a previously published model of within-host anthrax infection is considered, allowing the computation of the dose-response probabilities of this model. Furthermore, we then propose a single model, in terms of delay differential equations, to explain the in vitro dynamics of published experimental data of two strains of B. anthracis, making use of a Bayesian approach for parameter calibration.
Within the last chapter of this thesis, Chapter 5, a compartmental epidemic model of viral infection is introduced. This model explores the protection afforded by the presence of a strain of virus composed of defective interfering particles (DIPs) on an outbreak of the wild-type virus in a closed population. A number of summary statistics are introduced and described for this model, followed by an investigation into their distributions and expectations for a range of parameter regimes.
