# On the Dynamics of an Impulsive Model of Hematopoiesis

Mathematical Modelling of Natural Phenomena (2009)

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

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topKou, 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 - Adimy, M.

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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