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

On the stability of a nonlinear maturity structured model of cellular proliferation? Mostafa Adimy‡, Fabien Crauste‡ and Laurent Pujo-Menjouet† Year 2004 ‡ Laboratoire de Mathematiques Appliquees, FRE 2570, Universite de Pau et des Pays de l'Adour, Avenue de l'universite, 64000 Pau, France. E-mail: , E-mail: † Department of Physiology, McGill University, McIntyre Medical Sciences Building, 3655 Promenade Sir William Osler, Montreal, QC, Canada H3G 1Y6. E-mail: Abstract We analyse the asymptotic behaviour 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 behaviour of the immature cells 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. 1 Introduction and motivation This paper is devoted to the analysis of a maturity structured model which involves descriptions of process of blood production in the bone marrow (hematopoiesis).

• univ-pau


• population depends


• cellular proliferation


• mature cells


• side also accounts


• universite de pau et des pays de l'adour


• pujo-menjouet stability


• results