This article is cited in 10 scientific papers (total in 10 papers)
Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a heterogeneous tumor
A. V. Antipov, A. S. Bratus'
Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
A mathematical model of tumor cell population dynamics is considered. The tumor is assumed to consist of cells of two types: amenable and resistant to chemotherapeutic treatment. It is assumed that the growth of the cell populations of both types is governed by logistic equations. The effect of a chemotherapeutic drug on the tumor is specified by a therapy function. Two types of therapy functions are considered: a monotonically increasing function and a nonmonotone one with a threshold. In the former case, the effect of a drug on the tumor is stronger at a higher drug concentration. In the latter case, a threshold drug concentration exists above which the effect of the therapy reduces. The case when the total drug amount is subject to an integral constraint is also studied. A similar problem was previously studied in the case of a linear therapy function with no constraint imposed on the drug amount. By applying the Pontryagin maximum principle, necessary optimality conditions are found, which are used to draw important conclusions about the character of the optimal therapy strategy. The optimal control problem of minimizing the total number of tumor cells is solved numerically in the case of a monotone or threshold therapy function with allowance for the integral constraint on the drug amount.
mathematical model of optimal chemotherapy, optimal control problem, numerical methods.
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Computational Mathematics and Mathematical Physics, 2009, 49:11, 1825–1836
A. V. Antipov, A. S. Bratus', “Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a heterogeneous tumor”, Zh. Vychisl. Mat. Mat. Fiz., 49:11 (2009), 1907–1919; Comput. Math. Math. Phys., 49:11 (2009), 1825–1836
Citation in format AMSBIB
\by A.~V.~Antipov, A.~S.~Bratus'
\paper Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a~heterogeneous tumor
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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Bratus A.S., Kovalenko S.Yu., Fimmel E., “On Viable Therapy Strategy For a Mathematical Spatial Cancer Model Describing the Dynamics of Malignant and Healthy Cells”, Math. Biosci. Eng., 12:1 (2015), 163–183
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