# American Institute of Mathematical Sciences

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2004, 1(1): 95-110. doi: 10.3934/mbe.2004.1.95

## Controlling a model for bone marrow dynamics in cancer chemotherapy

 1 Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1653, United States 2 Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899, United States

Received  February 2004 Revised  March 2004 Published  March 2004

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. Mathematical Biosciences & Engineering, 2004, 1 (1) : 95-110. doi: 10.3934/mbe.2004.1.95
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