Mathematical Models in Oncolytic Virotherapy and Immunology

Abstract

In this thesis we build mathematical models to address fundamental questions in immunology and virotherapy. We begin with a study of T cell response to pathogens. Although the clonal expansion of T cells is well defined as a tightly regulated process, the mechanisms responsible for this control are not well understood. Guided by experimental data, we design a delay differential model to see if the CD4+ T cell response to infection is directly linked to antigen concentration. Our model successfully captures a series of experimental results, linking T cell expansion to antigen availability. Next, we turn our attention to virotherapy, a relatively novel form of cancer treatment. Introducing a spatial model, we investigate how enhancements in virus design could alter treatment outcome. Using bifurcation theory, we find that certain enhancements may cause undesirable effects in tumour dynamics, such as large oscillations. We then extend our virotherapy model to study a major barrier in the treatment of solid tumours: excess collagen, which is responsible for the lack of diffusion of oncolytic therapies. This investigation leads to a novel virus diffusion term that captures experimental observations. Importantly, we show that the classic diffusion equation, used in many virotherapy models, does not accurately capture the dispersion of virus in collagen-dense tumours, and this may ultimately result in inaccurate predictions of treatment outcome. Finally, we use our new virotherapy model to understand how different collagen-tumour configurations affect treatment outcome. We show that cell-collagen ratio, and gaps in the collagen surface need to be considered to better understand tumour response to treatment. The models developed in this thesis provide sound explanations to fundamental questions in immunology and virotherapy, highlighting key interactions that could significantly advance current therapies.