Biomathematical Models with State-Dependent Delays for Granulocytopoiesis

Hofer, Eberhard P.; Tibken, Bernd; Lehn, Frank

doi:10.1007/978-3-662-04331-8_23

Online Optimization of Large Scale Systems 2001

DOI: 10.1007/978-3-662-04331-8_23

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Biomathematical Models with State-Dependent Delays for Granulocytopoiesis

Eberhard P. Hofer

Bernd Tibken

Frank Lehn

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2010

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“…Numerical methods for solving state-dependent delay differential equations have been investigated by Hofer, Tibken, and Lehn [35], Shampine [56], and the references therein. Despite the difficulty related to the analysis of state-dependent delay differential equations, they have been used in some applied works-in cell biology, for instance, by Bélair [13], Bélair, Mackey, and Mahaffy [14], Hbid, Sanchez, and Bravo de la Parra [34], Hofer, Tibken, and Lehn [36], and Mahaffy, Bélair, and Mackey [49], but also in automatic [61].…”

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confidence: 99%

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

Adimy¹,

Crauste²,

Hbid³

et al. 2010

SIAM J. Appl. Math.

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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.

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confidence: 99%

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

Adimy¹,

Crauste²,

Hbid³

et al. 2010

SIAM J. Appl. Math.

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Biomathematical Models with State-Dependent Delays for Granulocytopoiesis

Cited by 1 publication

References 8 publications

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

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

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