Mathematical Analysis for Oncolytic Virotherapy, Considering the Role of the Lytic Cycle in the Presence of Immune System Response

Abstract

Abstract. The immune system of the cancer patient’s body and viral lytic cycle play important roles in the cancer virotherapy. Most mathematical models for virotherapy do not include these two agents simultaneously. The viral lytic cycle depends on the time of the viral lytic cycle and the viral burst size. In this paper, we propose a mathematical model including the time of the viral lytic cycle, the viral burst size and the immune system response. The proposed model is a nonlinear system of delay differential equations in which the period of the viral lytic cycle is modeled as a delay parameter. We study the stability of equilibrium points and the existence of Hopf bifurcation. We use the delay parameter as the bifurcation parameter and obtain some conditions for stability of equilibrium points in terms of the burst size and delay parameter.