Structure of optimal therapy protocols for a simple compartmental model of chemoresistance

Chemoresistance poses a major obstacle in effective chemotherapy protocol planning. Chemotherapy schedules which prevent or delay the onset of drug resistance are of interest from clinical point of view. This motivated us to formulate an optimal control problem with an objective functional explicitely penalising chemoresistant phenotype. By analising a simple dynamical model of tumour growth we investigate the structure of theoretically optimal chemotherapy protocols. We show how this new objective funtional may give rise to singular optimal controls and we attempt to conduct a full optimal control synthesis