Optimal control of therapies on a tumor growth model with brain lactate kinetics

We prove the existence of an optimal treatment combining chemotherapy and a lactate targeting drug for a mathematical model for high grade gliomas and lactate kinetics. A necessary condition for a treatment to be optimal is also devised, allowing to design numerically the proper therapy. The analytical results are validated by the numerical simulations; as clinical experience proves, the simulations show that the effect of chemotherapy is enhanced by the other drug whose sole administration is, in turn, almost irrelevant.