“School of Mathematics”
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Paper IPM / M / 15948  


Abstract:  
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 twotime delays Ï1 and Ï2. The time delay Ï1 shows the lag of transmission of infection from the 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 Ï2 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.
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