American Institute of Mathematical Sciences

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2005, 2(3): 657-670. doi: 10.3934/mbe.2005.2.657

Analysis and Optimization of Drug Resistant an Phase-Specific Cancer

Andrzej Swierniak 1, and  Jaroslaw Smieja 1,

1. 

Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice, Poland

Received  January 2005 Revised  August 2005 Published  August 2005

This paper presents analysis and biomedical implications of a certain class of bilinear systems that can be applied in modeling of cancer chemotherapy. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy in their different aspects. The methodology of analysis of such models, based on system decomposition, is discussed. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the second one is infinite-dimensional and tridiagonal. Then the optimal control problem is defined in $l^1$ space. To derive necessary conditions for optimal control, the model description is transformed into an integrodifferential one.
Keywords: infinite dimensional systems, biomedical modeling, multivariable control..
Mathematics Subject Classification: 92D25, 93C23, 92C5.
Citation: Andrzej Swierniak, Jaroslaw Smieja. Analysis and Optimization of Drug Resistant an Phase-Specific Cancer. Mathematical Biosciences & Engineering, 2005, 2 (3) : 657-670. doi: 10.3934/mbe.2005.2.657
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