Inertia induced oscillations in an oncolytic virotherapy model

This is the authors' abstract. We don't add key points for this paper.

In this paper, we apply the hyperbolic reaction-diffusion equation to establish an oncolytic virotherapy model. Firstly, we analyze the existence of solutions, the stability and wave instability of the constant equilibrium. Meanwhile, we have provided the conditions of the oncolytic virotherapy model for generating wave instability. Secondly, we explore the wave solutions of the model and analyze the existence and stability of the wave solutions via the method of the multiple time scales (MTS) and provide a theorem for the model to generate wave solutions. Finally, we carry out numerical simulations and the effect of hyperbolic term is considered. The results demonstrate that the inertial effect can significantly alter the stability structure of the system and may contribute to the emergence of oscillatory dynamics.