Dynamic analysis and optimal control of cancer oncolytic virotherapy model with chemotherapy and immune response

Abstract Oncolytic virotherapy is another therapeutic treatment for cancer and has been greatly interested recently by many researchers. In this study, a mathematical model of treating cancer by a combination of oncolytic virotherapy and chemotherapy is proposed. This model involves both immune response to cancer and virus. We derive three equilibrium points which are cancer-free, virus-free and cancer endemic. The stability of each equilibrium point is performed and we show that these equilibrium points are conditionally stable. Further, parameter analysis is established to explore which parameters playing role in cancer treatment overall. The results show that although chemotherapy is a successful treatment, with an addition of oncolytic virotherapy, it can help treatment more successful. Finally, optimal control problem is applied into the model by adding three controls which are immunotherapy control, virotherapy control and chemotherapy control to seek the best strategy in reducing cancer cells as much as possible. Numerical results of each strategy are carried out and they demonstrate that a combination of all three controls gives the best result in reducing cancer cells eventually. 2000 Mathematics Subject Classification: 34D20; 34D23; 34H05; 37N25