Optimal control strategy for optimizing cancer cell growth model

In this paper, a deterministic mathematical model of cancer cell dynamics is considered. We propose a new method to simulate and control the growth of tumor cells, as well as immunotherapy and chemotherapy for patients. The model is a coupled Ordinary Differential Equation (ODEs) that describes the growth of cancer at a cellular population level in the presence of a combination of immunotherapy and chemotherapy called biochemotherapy. The model is formulated as an optimal control problem with the objective of obtaining the optimum levels of each of the treatments that must be used to decrease the rate of growth of cancer cells, and to minimize the use of chemotherapeutic agents and immunotherapy drugs while maximizing the performance of the immune system. Based on Pontryagin's Maximum Principle, the optimal control system is deduced, and the solution is obtained. The results of the simulation show that biological chemotherapy can significantly reduce the cancer cell growth in a reasonably short time.