Optimal control in reducing side effects during and after chemotherapy of solid tumors

Abstract

In this paper, we discuss the effect of optimal chemotherapy doses on solid tumor during treatment and cancer recurrence after the end of treatment. First, an optimal control problem is designed. Then, by changing the control range, the objective function, and adding a control to the previous problem, three new optimal control problems are constructed. We pursue two critical ideas for the success of the drug delivery system to the patient: minimizing the normalized global population density of cancer cells during treatment and at the end of treatment and minimizing side effects during treatment. The optimal control problem is considered with two linear and quadratic objective functions. These models are solved by a well‐established numerical method with high accuracy and a low discretization cost. The numerical results have confirmed that reducing the total dose of the cytotoxic drugs during the treatment period leads to a rapid recurrence of cancer shortly after the end of the treatment period.