Drug resistance in cancer chemotherapy as an optimal control problem

Urszula Ledzewicz; Heinz Schättler

doi:10.3934/dcdsb.2006.6.129

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2006, Volume 6, Issue 1: 129-150. Doi: 10.3934/dcdsb.2006.6.129

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Drug resistance in cancer chemotherapy as an optimal control problem

Urszula Ledzewicz^1, and
Heinz Schättler^2,

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

Received: October 31, 2004

Revised: July 31, 2005

Published: December 2005

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Abstract

We analyze non cell-cycle specific mathematical models for drug resistance in cancer chemotherapy. In each model developing drug resistance is inevitable and the issue is how to prolong its onset. Distinguishing between sensitive and resistant cells we consider a model which includes interactions of two killing agents which generate separate resistant populations. We formulate an associated optimal control problem for chemotherapy and analyze the qualitative structure of corresponding optimal controls.

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Mathematics Subject Classification: Primary: 49J15; Secondary: 93C50.

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