Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy

A mathematical model for the depletion of bone marrow under cancer chemotherapy is analyzed as an optimal control problem. The control represents the drug dosage of a single chemotherapeutic agent and pharmacokinetic equations which model its plasma concentration are included. The drug dosages enter the objective linearly. It is shown that optimal controls are bang–bang, i.e. alternate the drug dosages at full dose with rest-periods in between, and that singular controls which correspond to treatment schedules with varying dosages at less than maximum rate are not optimal. Numerical simulations are given to illustrate the effect of the pharmacokinetic equations on the dosages.