Controlling a model for bone marrow dynamics in cancer chemotherapy
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Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1653
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Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899
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Received:
01 February 2004
Accepted:
29 June 2018
Published:
01 March 2004
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MSC :
49J15, 92C50.
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This paper analyzes a mathematical model for the growth of bone
marrow cells under cell-cycle-speci c cancer chemotherapy originally proposed
by Fister and Panetta [8]. The model is formulated as an optimal control
problem with control representing the drug dosage (respectively its eff ect)
and objective of Bolza type depending on the control linearly, a so-called $L^1$-objective. We apply the Maximum Principle, followed by high-order necessary
conditions for optimality of singular arcs and give sufficient conditions for optimality based on the method of characteristics. Singular controls are eliminated
as candidates for optimality, and easily veri able conditions for strong local
optimality of bang-bang controls are formulated in the form of transversality
conditions at switching surfaces. Numerical simulations are given.
Citation: Urszula Ledzewicz, Heinz Schättler. Controlling a model for bone marrow dynamics in cancer chemotherapy[J]. Mathematical Biosciences and Engineering, 2004, 1(1): 95-110. doi: 10.3934/mbe.2004.1.95
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Abstract
This paper analyzes a mathematical model for the growth of bone
marrow cells under cell-cycle-speci c cancer chemotherapy originally proposed
by Fister and Panetta [8]. The model is formulated as an optimal control
problem with control representing the drug dosage (respectively its eff ect)
and objective of Bolza type depending on the control linearly, a so-called $L^1$-objective. We apply the Maximum Principle, followed by high-order necessary
conditions for optimality of singular arcs and give sufficient conditions for optimality based on the method of characteristics. Singular controls are eliminated
as candidates for optimality, and easily veri able conditions for strong local
optimality of bang-bang controls are formulated in the form of transversality
conditions at switching surfaces. Numerical simulations are given.
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