Ensemble Optimal Control for Managing Drug Resistance in Cancer Therapies

In this paper, we explore the application of ensemble optimal control to derive enhanced strategies for pharmacological cancer treatment, and we tackle the problem of the long-term management of the disease, i.e., when the complete eradication of the tumor is not achievable. In particular, we focus on moving beyond the classical clinical approach of giving the patient the maximal tolerated drug dose (MTD), which does not properly exploit the fight among sensitive and resistant cells for the available resources. Here, we employ a Lotka-Volterra model to describe the competing subpopulations, and we enclose this system within the ensemble control framework. In the first part, we establish general results suitable for application to various cancers. Then, we carry out numerical simulations in the setting of prostate cancer treated with androgen deprivation therapy, yielding a computed policy that is reminiscent of the medical 'active surveillance' paradigm. Finally, inspired by the numerical evidence, we propose a variant of the celebrated adaptive therapy (AT), which we call 'Off-On' AT.