Mathematical model of optimal chemotherapy and oncolytic virotherapy

In this paper, a mathematical model of fighting against cancer tumor growth by a combination of oncolytic virotherapy and chemotherapy is introduced. In this model, we considered two time delays ?1 and ?2. The time delay ?1 shows the lag of transmission of infection from oncolytic virus to tumor cells. A lot of kind of cancers, symptoms are diagnosed at a late stage and as a consequence the chemotherapy approach start with a lag. Thus, we take this delay into account by presenting the time delay ?2 in the control variable. Therefore, in this study, delay parameters are used for both state and control variables. The Pontryagin minimum principle with delays in both state and control is used to obtain an optimal model for the treatment to minimize the side effect as well as the cost of the treatment.