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New Computational Tools for ModelingChronic Myelogenous Leukemia

Published online by Cambridge University Press:  26 March 2009

M. M. Peet ,
P. S. Kim ,
S.-I. Niculescu  and
D. Levy
M. M. Peet*
Affiliation:
Illinois Institute of Technology, Chicago, USA
P. S. Kim
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City 84102, USA
S.-I. Niculescu
Affiliation:
Laboratoire des Signaux et Systèmes, CNRS-Supélec, 91192 Gif-sur-Yvette, France
D. Levy
Affiliation:
Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park 20742, USA
*
mpeet@iit.edu
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Abstract

In this paper, we consider a system of nonlinear delay-differential equations(DDEs) which models the dynamics of the interaction between chronic myelogenousleukemia (CML), imatinib, and the anti-leukemia immune response. Because of thechaotic nature of the dynamics and the sparse nature of experimental data, welook for ways to use computation to analyze the model without employing directnumerical simulation. In particular, we develop several tools usingLyapunov-Krasovskii analysis that allow us to test the robustness of the modelwith respect to uncertainty in patient parameters. The methods developed in thispaper are applied to understanding which model parameters primarily affect thedynamics of the anti-leukemia immune response during imatinib treatment. Thegoal of this research is to aid the development of more efficient modelingapproaches and more effective treatment strategies in cancer therapy.

Keywords

delay-differential equationsmodel verificationoptimizationpolynomialssum-ofsquaresstabilityLyapunov-Krasovskiichronic myelogenous leukemiaimatinib
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 2: Delay equations in biology , 2009 , pp. 119 - 139
Copyright
© EDP Sciences, 2009

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