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

Fabien Crauste (1)

1 ICJ - Institut Camille Jordan

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.

Mots clés: hematopoietic stem cell dynamics; stability switch; second degree exponential polynomial; Lyapunov function; nonlinear delay differential system

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Biologie cellulaire

Fabien Crauste. Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch. Mathematical Modelling of Natural Phenomena, 2009, 4 (2), pp.28-47. ⟨10.1051/mmnp/20094202⟩. ⟨hal-00542663⟩