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Issue Math. Model. Nat. Phenom.
Volume 4, Number 2, 2009
Delay equations in biology
Page(s) 119 - 139
DOI 10.1051/mmnp/20094206
Published online 26 March 2009

Math. Model. Nat. Phenom. Vol. 4, No. 2, 2009, pp. 119-139
DOI: 10.1051/mmnp/20094206

New Computational Tools for Modeling Chronic Myelogenous Leukemia

M. M. Peet1, P. S. Kim2, S.-I. Niculescu3 and D. Levy4

1  Illinois Institute of Technology, Chicago, USA
2  Department of Mathematics, University of Utah, Salt Lake City 84102, USA
3  Laboratoire des Signaux et Systèmes, CNRS-Supélec, 91192 Gif-sur-Yvette, France
4  Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park 20742, USA

mpeet@iit.edu

Published online: 26 March 2009

Abstract
In this paper, we consider a system of nonlinear delay-differential equations (DDEs) which models the dynamics of the interaction between chronic myelogenous leukemia (CML), imatinib, and the anti-leukemia immune response. Because of the chaotic nature of the dynamics and the sparse nature of experimental data, we look for ways to use computation to analyze the model without employing direct numerical simulation. In particular, we develop several tools using Lyapunov-Krasovskii analysis that allow us to test the robustness of the model with respect to uncertainty in patient parameters. The methods developed in this paper are applied to understanding which model parameters primarily affect the dynamics of the anti-leukemia immune response during imatinib treatment. The goal of this research is to aid the development of more efficient modeling approaches and more effective treatment strategies in cancer therapy.


Mathematics Subject Classification. 34D10, 34K60, 92-08, 92C50

Key words: delay-differential equations -- model verification -- optimization -- polynomials -- sum-ofsquares -- stability -- Lyapunov-Krasovskii -- chronic myelogenous leukemia -- imatinib


© EDP Sciences 2009


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