| Issue |
Math. Model. Nat. Phenom.
Volume 4, Number 2, 2009
Delay equations in biology
|
|
|---|---|---|
| Page(s) | 28 - 47 | |
| DOI | https://doi.org/10.1051/mmnp/20094202 | |
| Published online | 26 March 2009 | |
Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch
Université de Lyon, Université Lyon1, CNRS UMR 5208 Institut
Camille Jordan - F - 69200 Villeurbanne Cedex, France
Corresponding author: crauste@math.univ-lyon1.fr
A nonlinear system of two delay differential equations is proposed to model hematopoietic stem cell dynamics. Each equation describes the evolution of a sub-population, either proliferating or nonproliferating. The nonlinearity accounting for introduction of nonproliferating cells in the proliferating phase is assumed to depend upon the total number of cells. Existence and stability of steady states are investigated. A Lyapunov functional is built to obtain the global asymptotic stability of the trivial steady state. The study of eigenvalues of a second degree exponential polynomial characteristic equation allows to conclude to the existence of stability switches for the unique positive steady state. A numerical analysis of the role of each parameter on the appearance of stability switches completes this analysis.
Mathematics Subject Classification: 34K99 / 34K60 / 34D20 / 11D61 / 92C37
Key words: nonlinear delay differential system / second degree exponential polynomial / Lyapunov function / stability switch / hematopoietic stem cell dynamics
© EDP Sciences, 2009
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