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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
2. Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899

## Abstract    Related pages

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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Citation: Urszula Ledzewicz, Heinz Schättler. Controlling a model for bone marrow dynamics in cancer chemotherapy. Mathematical Biosciences and Engineering, 2004, 1(1): 95-110. doi: 10.3934/mbe.2004.1.95

• 1. E Rainarli, K E Dewi, The Analysis of Fixed Final State Optimal Control in Bilinear System Applied to Bone Marrow by Cell-Cycle Specific (CCS) Chemotherapy, Journal of Physics: Conference Series, 2017, 824, 012029, 10.1088/1742-6596/824/1/012029
• 2. Urszula Ledzewicz, Heinz Schättler, Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy, Mathematical Biosciences, 2007, 206, 2, 320, 10.1016/j.mbs.2005.03.013
• 3. H. Schättler, Local Fields of Extremals for Optimal Control Problems with State Constraints of Relative Degree 1, Journal of Dynamical and Control Systems, 2006, 12, 4, 563, 10.1007/s10883-006-0005-y
• 4. Jessica J. Cunningham, Joel S. Brown, Robert A. Gatenby, Kateřina Staňková, Optimal Control to Develop Therapeutic Strategies for Metastatic Castrate Resistant Prostate Cancer, Journal of Theoretical Biology, 2018, 10.1016/j.jtbi.2018.09.022