Optimal control for a class of compartmental models in cancer chemotherapy

• Autorzy: Andrzej Świerniak , Urszula Ledzewicz , Heinz Schättler
• Języki publikacji: EN

Abstrakty

EN

We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples.

Słowa kluczowe

EN

necessary and sufficient conditions for optimality; cancer chemotherapy; optimal control; compartmental models

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: 13
• Numer: 3
• Strony: 357-368

Daty

wydano

2003

otrzymano

2003-03-01

poprawiono

2003-06-01

Twórcy

autor

Andrzej Świerniak

• Institute of Automatic Control, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland

autor

Urszula Ledzewicz

• Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, Il, 62026-1653, USA

autor

Heinz Schättler

• Department of Systems Science and Mathematics, Washington University, St. Louis, Mo, 63130-4899, USA

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