Hopf bifurcation analysis of a tumor virotherapy model with two time delays

Abstract Oncolytic virotherapy is gradually applied in clinical trial, which provides a new potential approach to cancer treatment. Tumor volume doubling time (TVDT) is so short that the infection delay caused by oncolytic virus should be considered in the modeling of virotherapy. A DDE model is constructed by adding two infection delays based on an ODE model that describes the dynamics of cancer cells, tumor cells, immune cells and oncolytic viruses. According to the different values of two delays, three cases of the model are discussed to investigate the stability and bifurcation of both the virus-free equilibrium and the positive equilibrium. Finally, some numerical simulations are performed to verify the obtained theoretical conclusions based on clinical trial data.