Structure of optimal controls for a cancer chemotherapy model with PK/PD

A mathematical model for cancer chemotherapy treatment with a single G₂/M specific killing agent is considered as an optimal control problem. The control represents the drug dosage of a single chemotherapeutic agent and the drug dosage enters the objective linearly. In this paper, pharmacokinetic equations (PK) which model the drug´s plasma concentration and various pharmacodynamic models (PD) in terms of functions representing the concentration effects are included. It is shown that geometric properties of the PK and PD equations determine the qualitative properties of the optimal solution. Here for various models we analyze the local optimality of singular controls which correspond to treatment schedules with varying dosages at less than maximum rate.