On the stability of a maturity structured model of cellular proliferation

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

2009-04-16

arxiv.org/abs/0904.2492v1

Discrete and Continuous Dynamical Systems: Series A 12, 3 (2005) 501-522

Mathematics

Analysis of PDEs

Scientific paper

10.3934/dcds.2005.12.501

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.

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