American Institute of Mathematical Sciences

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January  2006, 6(1): 129-150. doi: 10.3934/dcdsb.2006.6.129

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  November 2004 Revised  August 2005 Published  October 2005

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.
Keywords: cancer chemotherapy models, drug resistance., Optimal control theory.
Mathematics Subject Classification: Primary: 49J15; Secondary: 93C5.
Citation: Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129
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