Dynamics of a tumor model governed by a coupled reaction-diffusion and telegraph equations

This paper focuses on the study of the properties and dynamic behaviors of a novel oncolytic virus-cancer cell interaction model governed by a set of reaction-diffusion and telegraph equations. Initially, the original model is simplified by neglecting spatial diffusion, leading to a temporal model that is subsequently examined in detail to explore the dynamic behaviors of various equilibrium points. Secondly, we employ the theory and methods of functional analysis to establish the existence and uniqueness of a local classical solution for the original spatiotemporal model. Furthermore, an analytical solution to the model is derived when cancer cells attain equilibrium. Finally, numerical simulations further verify the validity of the theoretical results.