Optimal control applied to drug administration in cancer chemotherapy: the case of several toxicity constraints

Cancer chemotherapy for the case of one drug is studied. The negative and inhibiting effect of the tumor on normal cells is taken into account. Under certain assumptions, we determine the optimal regimen that minimizes the tumor burden at the end of a fixed period of therapy, while maintaining certain normal cell populations above prescribed levels. More precisely, it is demonstrated that the optimal strategy corresponds to injection of the drug at the maximal rate