Math. Model. Nat. Phenom.
Volume 5, Number 3, 2010Mathematical modeling in the medical sciences
|Page(s)||63 - 75|
|Published online||28 April 2010|
Optimal Control of a Cancer Cell Model with Delay
Department of Mathematics, University of Tennessee,
2 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 USA
3 Department of Mathematics, University of Nebraska, Lincoln, NE 68588 USA
* Corresponding author. E-mail:
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.
Mathematics Subject Classification: 34A12 / 34H05
Key words: cancer dynamics / optimal control
© EDP Sciences, 2010
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