On the stability of a maturity structured model of cellular proliferation

Mostafa Adimy (1) , Fabien Crauste (1) , Laurent Pujo-Menjouet (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Department of Physiology [Montréal]

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.

Mots clés: nonlinear partial differential equation; maturity structured model; blood production system; delay depending on the maturity; global stability; instability

Domaines: Equations aux dérivées partielles [math.AP]

Mostafa Adimy, Fabien Crauste, Laurent Pujo-Menjouet. On the stability of a maturity structured model of cellular proliferation. Discrete and Continuous Dynamical Systems - Series A, 2005, 12 (3), pp.501-522. ⟨10.3934/dcds.2005.12.501⟩. ⟨hal-00375940⟩