Research Article

Optimal Control of a Cancer Cell Model with Delay

C. Collins^a1, K.R. Fister^a2 c1 and M. Williams^a3

^a1 Department of Mathematics, University of Tennessee, Knoxville, TN 37996 USA

^a2 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 USA

^a3 Department of Mathematics, University of Nebraska, Lincoln, NE 68588 USA

Abstract

In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence of an optimal control has also been proven. Optimality conditions and characterization of the control are discussed.

(Online publication April 28 2010)

Key Words:

• cancer dynamics;
• optimal control

Mathematics Subject Classification:

• 34A12;
• 34H05

Correspondence:

^c1 Corresponding author. E-mail: renee.fister@murraystate.edu