Chemotherapy and Immunotherapy for Tumors: A Study of Quadratic Optimal Control

In this work, we start by Kuznetsov’s model which describes the interaction between two cell populations: tumor cells and effector cells. We insert in this model controls corresponding to two types of treatment: chemotherapy and immunotherapy, which leads to a controlled dynamic system. The goal of this paper is to minimize the density of tumor cells as well as the dose of treatment. We seek for an optimal treatment which will be characterized by using Pontryagin’s Maximum Principle.