A Nonlinear Mathematical Model of Virus-Tumor-Immune System Interaction: Deterministic and Stochastic Analysis

Ongoing research on cancer has indicated that viruses which specifically infect and destroy tumor cells could be used as a therapeutic agent to arrest tumors. Some of these oncolytic viruses had already been tested clinically with success. However, the interaction dynamics between the tumor host, the invading virus and the immune system response is highly nonlinear and complex and, hence, a proper understanding of such dynamics requires involvement of mathematical models. In the present research, we consider a mathematical model of tumor-virus-immune system dynamics. We analyze the basic deterministic model to find out the importance of different host, viral and immune system parameters in controlling the system dynamics. Next we incorporate random noise inherent in any physiological process by extending the deterministic model into a stochastic one. The resulting stochastic model is studied using the mean square stability approach and criteria for stochastic stability is derived in terms of important system parameters. Numerical simulations are performed in support of analytical findings.