Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch

F. Crauste

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 2, page 28-47
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Crauste, F.. "Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch." Mathematical Modelling of Natural Phenomena 4.2 (2009): 28-47. <http://eudml.org/doc/222258>.

@article{Crauste2009,
abstract = { 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. },
author = {Crauste, F.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {nonlinear delay differential system; second degree exponential polynomial; Lyapunov function; stability switch; hematopoietic stem cell dynamics; nonlinear delay differential systems; second degree exponential polynomial; Lyapunov functional; hematopoietic stem cell dynamics},
language = {eng},
month = {3},
number = {2},
pages = {28-47},
publisher = {EDP Sciences},
title = {Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch},
url = {http://eudml.org/doc/222258},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Crauste, F.
TI - Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/3//
PB - EDP Sciences
VL - 4
IS - 2
SP - 28
EP - 47
AB - 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.
LA - eng
KW - nonlinear delay differential system; second degree exponential polynomial; Lyapunov function; stability switch; hematopoietic stem cell dynamics; nonlinear delay differential systems; second degree exponential polynomial; Lyapunov functional; hematopoietic stem cell dynamics
UR - http://eudml.org/doc/222258
ER -

References

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