Travelling Waves in a Mathematical Model for Oncolytic Virotherapy

TL;DR

This paper analyzes a reaction-diffusion model for oncolytic virotherapy, establishing the existence of travelling wave solutions that describe viral spread in tumor tissue, and identifies key parameters influencing this process.

Contribution

It introduces a mathematical framework for viral invasion in tumors, proving the existence of travelling waves and exploring parameter regions affecting viral propagation.

Findings

Existence of positive travelling waves for speeds above a minimal threshold

Identification of parameter regions with ambiguous wave existence

Mathematical characterization of viral spread dynamics in tumor tissue

Abstract

Oncolytic virotherapy (OVT) is a promising cancer treatment strategy in which engineered viruses selectively infect and destroy tumor cells. Motivated by the biological mechanisms underlying viral spread and tumor invasion into the tissue, we analyze a non-cooperative reaction-diffusion model capturing the invasion of tumor tissue by oncolytic viruses. Using carefully constructed upper and lower solutions together with Schauder's fixed point theorem, we establish the existence of positive travelling-wave solutions. In particular, we identify a minimal wave speed value $\bar c$ such that positive travelling waves exist for all $c \geq \bar c$ . Our analysis also highlights parameter regions where the existence of travelling waves remains ambiguous, suggesting new mathematical questions about the propagation of viral treatments through tumor environments.