TWO OPTIMAL CONTROL PROBLEMS IN CANCER CHEMOTHERAPY WITH DRUG RESISTANCE

We investigate two well-known basic optimal control problems forchemotherapeutic cancer treatment modified by introducing a timedependent “resistance factor”. This factor should be responsible for the effect of the drug resistance of tumor cells on the dynamical growth for the tumor. Both optimal control problems have common pointwise but different integral constraints on the control. We show that in both models the usually practised bang-bang control is optimal if the resistance is sufficiently strong. Further, we discuss different optimal strategies in both models for general resistance.