Stability and Hopf Bifurcation Analysis of an Oncolytic Virus Infection Model with Two Time Delays and Saturation Incidence

Abstract

In this paper, we study a model of oncolytic virus infection with two time delays, one of which is the time from the entry of viruses into tumor cells to start gene replication, and the other is the time from the entry of viruses into tumor cells to release new virus particles by infected tumor cells. In previous studies on oncolytic virus infection models, the infection rate was linear. Combined with the virus infection models, the saturated infection rate, $\beta TV/1+qV$ is further considered to describe the dynamic evolution between viruses and tumor cells more objectively so as to further study the therapeutic effect of oncolytic viruses. This paper discusses the dynamics of the system under three conditions: (1) ${\tau }_1={\tau }_2=0$ , (2) ${\tau }_1=0$ and ${\tau }_2>0$ , and (3) ${\tau }_1>0$ and ${\tau }_2>0$ , and proves the global stability and local stability of the virusfree equilibrium, the stability of the infection equilibrium, and the existence of Hopf bifurcation. Finally, the conclusions of the paper are verified by MATLAB numerical simulations.