Stability and Hopf Bifurcation for a Cell Population Model with State-Dependent Delay

We propose a mathematical model describing the dynamics of a hematopoietic stem cell population. The method of characteristics reduces the age-structured model to a system of differential equations with a state-dependent delay. A detailed stability analysis is performed. A sufficient condition for t...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 70; no. 5; pp. 1611 - 1633
Main Authors Adimy, Mostafa, Crauste, Fabien, Hbid, My Lhassan, Qesmi, Redouane
Format Journal Article
LanguageEnglish
Published Society for Industrial and Applied Mathematics 01.01.2010
Subjects
Analysis of PDEs
Cellular Biology
Life Sciences
Mathematics
Quantitative Methods
functional differential equation
hematopoietic stem cells
Lyapunov-Razumikhin function
Hopf bifurcation
state-dependent delay
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Summary:We propose a mathematical model describing the dynamics of a hematopoietic stem cell population. The method of characteristics reduces the age-structured model to a system of differential equations with a state-dependent delay. A detailed stability analysis is performed. A sufficient condition for the global asymptotic stability of the trivial steady state is obtained using a Lyapunov-Razumikhin function. A unique positive steady state is shown to appear through a transcritical bifurcation of the trivial steady state. The analysis of the positive steady state behavior, through the study of a first order exponential polynomial characteristic equation, concludes the existence of a Hopf bifurcation and gives criteria for stability switches. A numerical analysis confirms the results and stresses the role of each parameter involved in the system on the stability of the positive steady state.
ISSN:0036-1399
1095-712X
DOI:10.1137/080742713