# Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays

M. Adimy; F. Crauste; A. El Abdllaoui

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 1, Issue: 2, page 1-22
- ISSN: 0973-5348

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topAdimy, M., Crauste, F., and El Abdllaoui, A.. "Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays." Mathematical Modelling of Natural Phenomena 1.2 (2010): 1-22. <http://eudml.org/doc/222380>.

@article{Adimy2010,

abstract = {
We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takes
into account a finite number of stages in blood production, characterized by cell maturity levels,
which enhance the difference, in the hematopoiesis process, between dividing cells that
differentiate (by going to the next stage) and dividing cells that keep the same maturity level (by
staying in the same stage). It is described by a system of n nonlinear differential equations
with n delays. We study some fundamental properties of the solutions, such as boundedness and
positivity, and we investigate the existence of steady states. We determine some conditions for the
local asymptotic stability of the trivial steady state, and obtain a sufficient condition for its
global asymptotic stability by using a Lyapunov functional. Then we prove the instability of axial
steady states. We study the asymptotic behavior of the unique positive steady state and obtain the
existence of a stability area depending on all the time delays. We give a numerical illustration of
this result for a system of four equations.
},

author = {Adimy, M., Crauste, F., El Abdllaoui, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {Hematopoiesis modelling; system of delay equations; global and local asymptotic stability;
Lyapunov functional; hematopoiesis modelling; Lyapunov functional},

language = {eng},

month = {3},

number = {2},

pages = {1-22},

publisher = {EDP Sciences},

title = {Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays},

url = {http://eudml.org/doc/222380},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Adimy, M.

AU - Crauste, F.

AU - El Abdllaoui, A.

TI - Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/3//

PB - EDP Sciences

VL - 1

IS - 2

SP - 1

EP - 22

AB -
We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takes
into account a finite number of stages in blood production, characterized by cell maturity levels,
which enhance the difference, in the hematopoiesis process, between dividing cells that
differentiate (by going to the next stage) and dividing cells that keep the same maturity level (by
staying in the same stage). It is described by a system of n nonlinear differential equations
with n delays. We study some fundamental properties of the solutions, such as boundedness and
positivity, and we investigate the existence of steady states. We determine some conditions for the
local asymptotic stability of the trivial steady state, and obtain a sufficient condition for its
global asymptotic stability by using a Lyapunov functional. Then we prove the instability of axial
steady states. We study the asymptotic behavior of the unique positive steady state and obtain the
existence of a stability area depending on all the time delays. We give a numerical illustration of
this result for a system of four equations.

LA - eng

KW - Hematopoiesis modelling; system of delay equations; global and local asymptotic stability;
Lyapunov functional; hematopoiesis modelling; Lyapunov functional

UR - http://eudml.org/doc/222380

ER -

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