On the stability of a nonlinear maturity structured model of cellular proliferation

Mostafa Adimy; Fabien Crauste; Laurent Pujo-Menjouet

doi:10.3934/dcds.2005.12.501

Article Contents

2005, Volume 12, Issue 3: 501-522. Doi: 10.3934/dcds.2005.12.501

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On the stability of a nonlinear maturity structured model of cellular proliferation

1.
Laboratoire de Mathématiques Appliquées, FRE 2570, Université de Pau et des Pays de l'Adour, Avenue de l'université, 64000 Pau
2.
Department of Physiology, McGill University, McIntyre Medical Sciences Building, 3655 Promenade Sir William Osler, Montreal, QC, Canada H3G 1Y6

Received: September 30, 2003

Revised: August 31, 2004

Published: March 2005

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Abstract

We analyze the asymptotic behavior of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial differential equations, with a retardation of the maturation variable and a time delay depending on this maturity. We show that the stability of this system depends strongly on the behavior of the immature cell population. We obtain conditions for the global stability and the instability of the trivial solution.

Keywords:

Nonlinear partial differential equation,
maturity structured model,
blood production system,
delay depending on the maturity,
global stability,
instability.

Mathematics Subject Classification: 35B40, 92C37, 92D25.

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