A Bistable Reaction-Diffusion Analysis of Tumour to Determine Oncolytic Virotherapy Outcome

Abstract

Oncolytic viruses selectively replicate inside cancer cells and spread through tumour tissue as an infection front, so that the therapeutic outcome is set not only by how strongly the virus replicates but by whether and where that front advances, stalls, or collapses. We cast spatial oncolytic virotherapy as a bistable reaction–diffusion problem in which uninfected and infected tumour populations are coupled through infection and lysis, and we map the outcomes across geometry and parameter space. Linear analysis of the local kinetics shows that the tumour-free state is stable while the fully established tumour is unstable to viral invasion, so an infection front can be launched from a localized inoculation. Simulations in one dimension, on a planar disc, and in a radially symmetric spheroid reveal three sharply distinct outcomes: complete eradication, in which the front traverses the whole tumour; partial remission by wave pinning, in which the front stalls at a finite position and leaves a viable residual rim; and treatment failure, in which the infection dies out. A two-parameter regime map identifies the infection rate as the decisive control, with a finite window separating pinning at lower values from failure at higher values, whereas the bistability threshold of the tumour kinetics has almost no influence. The infected-cell spread rate behaves similarly, with eradication confined to an intermediate band. These results frame eradication as a tuned, geometry-dependent property of a travelling front and provide a compact map from measurable kinetic parameters to therapeutic outcome.