Chemotherapy for Tumors: a Study of Linear Optimal Control

This work is based on the Kuznetsov model which is composed of two ordinary differential equations describing the dynamics of tumor and effector cells as well as their interaction. We introduce in this model a control variable which describes a chemotherapy treatment. The goal is to characterize a minimum dose that minimizes the density of tumor cells to reduce the impact of treatment side effects on the patient's health. The necessary optimality conditions are provided. Since the control variable appears linearly in the assiciated problem, optimal controls are concatenations of bang-bang and singular arcs.