The stability of host-pathogen multi-strain models

Previous multi-strain mathematical models have elucidated that the degree of cross-protective responses between similar strains, acting as a form of immune selection, generates different behavioural states of the pathogen population. This thesis explores these multi-strain dynamic states, to examine their robustness and stability in the face of pathogenic intrinsic phenotypic variation, and the extrinsic force of immune selection. This is achieved in two main ways: Chapter 2 introduces phenotypic variation in pathogen transmissibility, testing the robustness of a stable pathogen population to the emergence of an introduced strain of higher transmission potential; and Chapter 3 introduces a new model with a possibility of immunity to both strain-specific and cross-strain (conserved) determinants, to investigate how heterogeneity in the specificity of a host immune response alters the pathogen population structure. A final investigation in Chapter 4 develops a method of reverse-pattern oriented modelling using a machine learning algorithm to determine which intrinsic properties of the pathogen, and their combinations, lead to particular disease-like population patterns. This research offers novel techniques to complement previous and ongoing work on multi-strain modelling, with direct applications to a range of infectious agents such as Plasmodium falciparum, influenza A, and rotavirus, but also with a wider potential for other multi-strain systems.