dePillis2007 - Chemotherapy for tumors An analysis of the dynamics and a study of quadratic and linear optimal controls

Abstract
We investigate a mathematical model of tumor–immune interactions with chemotherapy, and strategies
for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the
optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form
of the model allows us to test and compare various optimal control strategies, including a quadratic control,
a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for
the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out
the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation
of regions on which the singular control is optimal.
2006 Elsevier Inc. All rights reserved.