Controlling a model for bone marrow dynamics in cancer chemotherapy

Urszula Ledzewicz, Heinz Schättler
<span title="">2004</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="" style="color: black;">Mathematical Biosciences and Engineering</a> </i> &nbsp;
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 1objective. We apply the Maximum Principle, followed by high-order necessary conditions for optimality of singular arcs and give
more &raquo; ... ufficient 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. 2000 Mathematics Subject Classification. 49J15,92C50.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.3934/mbe.2004.1.95</a> <a target="_blank" rel="external noopener" href="">pmid:20369962</a> <a target="_blank" rel="external noopener" href="">fatcat:jbepsca43bfnno4nlhifiduzla</a> </span>
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