Stability and Hopf Bifurcation Analysis of a Tumor Immune Model of virus infection with Time-delay

Abstract

In this article, a mathematical model of the interaction between the immune system and a tumor cell employing an oncolytic viral therapy with time delay is discussed where the immune system has a dual function in the fight against cancer cells. Tumor cells that are sensitive to this sort of infection may become infected by viral infections that are developed to kill cancer cells but not healthy cells. Following oncolysis, the infected cancer cells release fresh viral infection particles to further destroy neighboring cancer cells. The boundedness of solutions of the model is derived. The time-delay differential equation theory is used to check whether the model’s equilibrium points are stable, moreover, the conditions that lead to a Hopf bifurcation are established. The results of the theoretical analysis are supported by numerical simulation.