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Stability Analysis of Cell Dynamics in Leukemia

Published online by Cambridge University Press:  25 January 2012

H. Özbay ,
C. Bonnet ,
H. Benjelloun  and
J. Clairambault
H. Özbay*
Affiliation:
Dept. of Electrical and Electronics Eng., Bilkent University, Ankara, 06800, Turkey
C. Bonnet
Affiliation:
INRIA Saclay - Île-de-France, Equipe DISCO, LSS - SUPELEC 3 rue Joliot Curie, 91192 Gif-sur-Yvette, France
H. Benjelloun
Affiliation:
Ecole Centrale Paris, Grande Voie des Vignes, Châtenay-Malabry, France
J. Clairambault
Affiliation:
INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesney INSERM team U 776 “Biological Rhythms and Cancers”, Hôpital Paul-Brousse 14 Av. Paul-Vaillant-Couturier, 94807 Villejuif, France
*
⋆ Corresponding author. E-mail: hitay@bilkent.edu.tr
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Abstract

In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics.

The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.

Keywords

acute leukemiadistributed delaysglobal stabilityabsolute stability
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 1: Cancer modeling , 2012 , pp. 203 - 234
Copyright
© EDP Sciences, 2012

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