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stability switch

Mathematical Modelling of Natural Phenomena (1)

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Delay Model of Hematopoietic Stem Cell Dynamics:Asymptotic Stability and Stability Switch
F. Crauste
Journal:

Mathematical Modelling of Natural Phenomena / Volume 4 / Issue 2 / 2009

Published online by Cambridge University Press:

26 March 2009, pp. 28-47

Print publication:

2009
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A nonlinear system of two delay differential equations is proposed to modelhematopoietic stem cell dynamics. Each equation describes the evolution of asub-population, either proliferating or nonproliferating. The nonlinearityaccounting for introduction of nonproliferating cells in the proliferating phaseis assumed to depend upon the total number of cells. Existence and stabilityof steady states are investigated. A Lyapunov functional is built to obtain theglobal asymptotic stability of the trivial steady state. The study ofeigenvalues of a second degree exponential polynomial characteristic equationallows to conclude to the existence of stability switches for the uniquepositive steady state. A numerical analysis of the role of each parameter on theappearance of stability switches completes this analysis.