Modeling oncolytic virus therapy with distributed delay and nonlocal diffusion

The study of oncolytic virus dynamics encounters a significant challenge in accurately describing uncertain biological phenomena using specific mathematical terms. To overcome this problem, we introduce 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 nonlocal infection terms. Our results provide 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 are determined for sustained tumor growth $\sigma _{1}$ 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.