Modelling the evolutionary epidemiology of chronic viral infections: Incorporating host heterogeneity into nested models of virus evolution (360G-Wellcome-202168_Z_16_Z)

One of the principal challenges in epidemiology is using mathematical models to plan disease control. This is made more challenging by pathogen evolution, which increases the complexity of disease dynamics, acting as a barrier to effective control. Chronic viruses such as HIV exhibit evolution over significantly shorter timescales than the long duration of infection. Understanding pathogen evolution and including it in models is therefore a key challenge for mathematical biologists. This project will explore how heterogeneity between hosts affects evolutionary dynamics at the population scale, building on a model in an existing paper that assumes that all hosts are identical. In this project, the model will be extended to include the heterogeneous immune responses to infection observed in different individuals. The dynamics of this new model will then be compared with the model in which all individuals are identical. Mathematical techniques required for this project include analysis of integro-differential equations (such as calculation of equilibria) and examination of the behaviour of integro-differential equations via numerical solution. The key goal is to develop a model of virus evolution that includes heterogeneous host types, and to investigate the evolutionary behaviour predicted by the model with different extents of host heterogeneity.