Electron. J. Diff. Equ.,
Vol. 2016 (2016), No. 140, pp. 1-20.
Age-structured model of hematopoiesis dynamics with growth
factor-dependent coefficients
Mostafa Adimy, Youssef Bourfia, My Lhassan Hbid, Catherine Marquet
Abstract:
We propose and analyze an age-structured partial differential model for
hematopoietic stem cell dynamics, in which proliferation, differentiation
and apoptosis are regulated by growth factor concentrations.
By integrating the age-structured system over the age and
using the characteristics method, we reduce it to a delay differential system.
We investigate the existence and stability of the steady states of the reduced
delay differential system. By constructing a Lyapunov function, the trivial
steady state, describing cell's dying out, is proven to be globally
asymptotically stable when it is the only equilibrium of the system.
The asymptotic stability of the positive steady state, the most
biologically meaningful one, is analyzed using the characteristic equation.
This study may be helpful in understanding the uncontrolled proliferation
of blood cells in some hematological disorders.
Submitted February 9, 2016. Published June 10, 2016.
Math Subject Classifications: 34D20, 34D23, 34K06, 92C37.
Key Words: Age-structured partial differential equation;
delay differential system; Lyapunov function;
characteristic equation; cell dynamic.
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Mostafa Adimy
INRIA, Université Lyon
Université Lyon 1, Institut Camille Jordan
43 Bd. du 11 novembre 1918
F-69200 Villeurbanne Cedex, France
email: mostafa.adimy@inria.fr
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Youssef Bourfia
Université Cadi Ayyad
Faculté des Sciences Semlalia
Département de Mathématiques
UMMISCO-Marrakech (IRD-UPMC), BP. 2390, Marrakesh, Morocco.
email: bourfiayoussef@gmail.com
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My Lhassan Hbid
Université Cadi Ayyad
Faculté des Sciences Semlalia
Département de Mathématiques
UMMISCO-Marrakech (IRD-UPMC), BP. 2390, Marrakesh, Morocco
email: hbid@uca.ma
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Catherine Marquet
Université de Pau
Laboratoire de Mathématiques Appliquées
CNRS UMR 5142, Avenue de l'université
64000 Pau, France
email: catherine.marquet@univ-pau.fr
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