Stacked Waves and Qualitative Analysis of an Oncolytic Virus-Immune Model

Oncolytic virotherapy (OVT) represents an innovative and promising therapeutic method for cancer treatment. This approach involves the introduction of oncolytic viruses into the patient, which are engineered to selectively target and lyse tumor cells. Based on previous mathematical modelling of oncolytic viruses, we consider a mathematical model that describes the intricate interactions between the oncolytic virus, cancer cell populations, and the immune system. Our study includes a detailed qualitative and quantitative analysis of the model to explain why, despite their promise, oncolytic viruses alone rarely lead to complete and lasting regression of established tumors in vivo. We use parameter sensitivity analysis to support our findings. Furthermore, we consider the spatial version of the model in the form of a system of reaction-diffusion equations. A travelling wave analysis shows an unexpected phenomenon. The solution components do not necessarily evolve into a single traveling front; rather, they develop into stacked fronts, where each front propagates at a different speed. We give explicit formulas for these different invasion speeds, confirm those through numerical simulations, and discuss their significance for OVT.