Modeling oncolytic virus therapy with distributed delay and non-local diffusion

Abstract

In the field of modeling the dynamics of oncolytic viruses, researchers often face the challenge of using specialized mathematical terms to explain uncertain biological phenomena. This paper introduces a basic framework for an oncolytic virus dynamics model with a general growth rate $\mathcal{F}$ and a general nonlinear incidence term $\mathcal{G}$. The construction and derivation of the model explain in detail the generation process and practical significance of the distributed time delays and non-local infection terms. The paper provides the existence and uniqueness of solutions to the model, as well as the existence of a global attractor. Furthermore, through two auxiliary linear partial differential equations, the threshold parameters $\sigma_1$ are determined for sustained tumor growth and $\lambda_1$ for successful viral invasion of tumor cells to analyze the global dynamic behavior of the model. Finally, we illustrate and analyze our abstract theoretical results through a specific example.