Cancer is a devastating disease that touches almost everyone and finding effective treatments presents a highly complex problem, requiring extensive multidisciplinary research. Mathematical modelling can provide insight into both cancer formation and treatment. A range of techniques are developed in this thesis to investigate two promising therapies: oncolytic virotherapy, and combined oncolytic virotherapy and immunotherapy. Oncolytic virotherapy endeavours to eradicate cancer cells by exploiting the aptitude of virus-induced cell death. Building on this premise, combined oncolytic virotherapy and immunotherapy aims to harness and stimulate the immune system's inherent ability to recognise and destroy cancerous cells.
Using deterministic and agent-based mathematical modelling, perturbations of treatment characteristics are investigated and optimal treatment protocols are suggested. An integro differential equation with distributed parameters is developed to characterise the function of the E1B genes in an oncolytic adenovirus. Subsequently, by using a bifurcation analysis of a coupled-system of ordinary differential equations for oncolytic virotherapy, regions of bistability are discovered, where increased injections can result in either tumour eradication or tumour stabilisation. Through an extensive hierarchical optimisation to multiple data sets, drawn from in vitro and in vivo modelling, gel-release of a combined oncolytic virotherapy and immunotherapy treatment is optimised. Additionally, using an agent-based modelling approach, delayed-infection of an intratumourally administered virus is shown to be able to reduce tumour burden.
This thesis develops new mathematical models that can be applied to a range of cancer therapies and suggests engineered treatment designs that can significantly advance current therapies and improve treatments.