# On the Dynamics of an Impulsive Model of Hematopoiesis

• Volume: 4, Issue: 2, page 68-91
• ISSN: 0973-5348

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## Abstract

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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.

## How to cite

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Kou, C., Adimy, M., and Ducrot, A.. "On the Dynamics of an Impulsive Model of Hematopoiesis." Mathematical Modelling of Natural Phenomena 4.2 (2009): 68-91. <http://eudml.org/doc/222403>.

@article{Kou2009,
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. },
author = {Kou, C., Adimy, M., Ducrot, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {model of hematopoiesis; impulsion; delay; asymptotic stability; Lyapunov functional; periodic solution; model of hematopoiesis; impulses; delay; asymptotic stability; periodic solution},
language = {eng},
month = {3},
number = {2},
pages = {68-91},
publisher = {EDP Sciences},
title = {On the Dynamics of an Impulsive Model of Hematopoiesis},
url = {http://eudml.org/doc/222403},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Kou, C.
AU - Ducrot, A.
TI - On the Dynamics of an Impulsive Model of Hematopoiesis
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/3//
PB - EDP Sciences
VL - 4
IS - 2
SP - 68
EP - 91
AB - 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.
LA - eng
KW - model of hematopoiesis; impulsion; delay; asymptotic stability; Lyapunov functional; periodic solution; model of hematopoiesis; impulses; delay; asymptotic stability; periodic solution
UR - http://eudml.org/doc/222403
ER -

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