Improving the effectiveness of oncolytic virotherapy: insights from mathematical modelling

Oncolytic viruses are viral particles that specifically infect cancer cells, while mostly preserving healthy tissues. Their use as cancer treatment has received considerable attention in recent years, but their clinical use still faces many challenges. Some of the main obstacles to the propagation of oncolytic viruses inside a tumour include clearance by the immune system, physical obstacles (such as the extracellular matrix) and inhibition of the infection in hypoxic areas. Furthermore, stochastic events may play a central role in blocking viral infection. All these dynamics are still poorly understood from the biological point of view and the use of mathematical models could help to reach a more comprehensive understanding. The main aim of this thesis is to develop mathematical models to study spatial dynamics of infections by oncolytic viruses and obstacles to its diffusion, with a special emphasis on the role of stochastic events. Furthermore, in the last Chapter, we describe a hybrid mathematical framework whose application is not exclusive to oncolytic virotherapy. This framework adopts either a pointwise or a density-based description for the cells, according to their phenotype: transitions between the two descriptions are assumed to happen stochastically and are affected by environmental conditions and gene expression; thus, the model is hybrid, but not necessarily multiscale. This modelling framework could help reproduce phenomena such as epithelial-to-mesenchymal transitions, metastasis and, in the future, evaluate the effect of an oncolytic viral infection on these phenomena.