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cancer dynamics

Mathematical Modelling of Natural Phenomena (1)

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Optimal Control of a Cancer Cell Model withDelay
C. Collins, K.R. Fister, M. Williams
Journal:

Mathematical Modelling of Natural Phenomena / Volume 5 / Issue 3 / 2010

Published online by Cambridge University Press:

28 April 2010, pp. 63-75

Print publication:

2010
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In this paper, we look at a model depicting the relationship of cancer cells in differentdevelopment stages with immune cells and a cell cycle specific chemotherapy drug. Themodel 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 thenumber of tumor cells. Global existence of a solution has been shown for this model andexistence of an optimal control has also been proven. Optimality conditions andcharacterization of the control are discussed.