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On the stability of a nonlinear maturity structured model of cellular proliferation
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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.Citation: -
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