Controlling a model for bone marrow dynamics in cancer chemotherapy | Zendy

Urszula Ledzewicz | Zendy; Heinz Schättler | Zendy

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Controlling a model for bone marrow dynamics in cancer chemotherapy

Author(s) -

Urszula Ledzewicz,

Heinz Schättler

Publication year - 2004

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2004.1.95

Subject(s) - optimal control , singular control , transversality , mathematics , control theory (sociology) , cancer chemotherapy , mathematical optimization , control (management) , chemotherapy , computer science , mathematical analysis , medicine , surgery , artificial intelligence

This paper analyzes a mathematical model for the growth of bone marrow cells under cell-cycle-specific 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 effect ) 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 verifiable 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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