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On the Dynamics of an Impulsive Model of Hematopoiesis

Published online by Cambridge University Press:  26 March 2009

C. Kou ,
M. Adimy  and
A. Ducrot
C. Kou*
Affiliation:
Department of Applied Mathematics, Donghua University, Shanghai 201620, P. R. China
M. Adimy
Affiliation:
Laboratoire de Mathématiques Appliquées, UMR CNRS 5142 & INRIA, ANUBIS, Université de Pau, 64000 Pau, France
A. Ducrot
Affiliation:
Institut Mathématiques de Bordeaux, UMR CNRS 5251 & INRIA, ANUBIS Université Victor Segalen Bordeaux 2, 33076 Bordeaux, France
*
[email protected]
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Abstract

We propose and analyze a nonlinear mathematical model of hematopoiesis,describing the dynamics of stem cell population subject to impulsiveperturbations. This is a system of two age-structured partial differentialequations with impulses. By integrating these equations over theage, we obtain a system of two nonlinear impulsive differential equations withseveral discrete delays. This system describes the evolution of the totalhematopoietic stem cell populations with impulses. We first examine theasymptotic behavior of the model in the absence of impulsions.Secondly, we add the impulsive perturbations and we investigate the qualitativebehavior of the model including the global asymptotic stability of the trivialsolution and the existence of periodic solution in the case of periodicimpulsive perturbations. Finally, numerical simulations are carriedout to illustrate the behavior of the model. This study maybe helpful tounderstand the reactions observed in the hematopoietic system after differentforms of stress as direct destruction by some drugs or irradiation.

Keywords

model of hematopoiesis; impulsion; delay; asymptotic stability;Lyapunov functional; periodic solution
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 2: Delay equations in biology , 2009 , pp. 68 - 91
Copyright
© EDP Sciences, 2009

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