On the Dynamics of an Impulsive Model of Hematopoiesis

¹ Department of Applied Mathematics, Donghua University, Shanghai 201620, P. R. China
² Laboratoire de Mathématiques Appliquées, UMR CNRS 5142 & INRIA, ANUBIS, Université de Pau, 64000 Pau, France
³ Institut Mathématiques de Bordeaux, UMR CNRS 5251 & INRIA, ANUBIS Université Victor Segalen Bordeaux 2, 33076 Bordeaux, France

Corresponding author: kouchunhai@dhu.edu.cn

Abstract

We propose and analyze a nonlinear mathematical model of hematopoiesis, describing the dynamics of stem cell population subject to impulsive perturbations. This is a system of two age-structured partial differential equations with impulses. By integrating these equations over the age, we obtain a system of two nonlinear impulsive differential equations with several discrete delays. This system describes the evolution of the total hematopoietic stem cell populations with impulses. We first examine the asymptotic behavior of the model in the absence of impulsions. Secondly, we add the impulsive perturbations and we investigate the qualitative behavior of the model including the global asymptotic stability of the trivial solution and the existence of periodic solution in the case of periodic impulsive perturbations. Finally, numerical simulations are carried out to illustrate the behavior of the model. This study maybe helpful to understand the reactions observed in the hematopoietic system after different forms of stress as direct destruction by some drugs or irradiation.