Optimal control of a delayed breast cancer stem cells nonlinear model

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