Optimal control for a combination of cancer therapies in a model of cell competition*

We present a simple mathematical model of ordinary differential equations that describes the interaction between a healthy cell population and cancerous cell population. This model includes the effects on cell populations of chemotherapy and targeted therapy, which are two bounded control variables. We study this model and seek to optimize the fraction of healthy cells within the total cell population over a given therapy period. We apply the Pontryagin Maximum Principle (PMP) and establish the expressions of singular solutions in different interaction cases between healthy and cancer cells. Then, we use a direct optimization method to validate and illustrate our theoretical results.