Intracellular Viral Life-cycle Induced Rich Dynamics in Tumor Virotherapy

The intracellular viral life-cycle is an important process in tumor virotherapy. Most mathematical models for tumor virotherapy do not incorporate the intracellular viral life-cycle. In this article, a model for tumor virotherapy with the intracellular viral life-cycle is presented and studied. The period of the intracellular viral life-cycle is modeled as a delay parameter. The model is a nonlinear system of delay differential equations. It displays interesting and rich dynamic behaviors. There exists two sets of stability switches as the period of the intracellular viral life-cycle increases. One is around the infection free equilibrium solution, and the other is the positive equilibrium solution. This intracellular viral life-cycle may explain the oscillation phenomena observed in many studies. An important clinic implication is that the period of the intracellular viral life-cycle should also be modified when a type of a virus is modified for virotherapy, so that the period of the intracellular viral life-cycle is in a suitable range which can break away the stability of the interior equilibrium solution.