Optimal control of a delayed breast cancer stem cells nonlinear model

Abstract

In this article, we consider a nonlinear model, which is governed by an ordinary differential equations systemwith time delays in state and control. The model is used in order to describe the growth of breast cancer cellsunder therapy. We seek optimal therapies to minimize the number of cancer cells as well as the total quantityof drug used in the treatment. In this way, we formulate an optimal control problem. We prove the existenceof an optimal therapy and use Pontryagin’s maximum principle in order to find optimality conditions, whichcharacterize such optimal therapy. At last, both numerical results and conclusion are presented.