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Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics

Mostafa Adimy 1, 2, 3 Abdennasser Chekroun 1, 3, 4 Tarik-Mohamed Touaoula 4
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
3 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We investigate a system of two nonlinear age-structured partial differential equations describing the dynamics of proliferating and quiescent hematopoietic stem cell populations. The method of characteristics reduces the age-structured model to a system of coupled delay differential and renewal difference equations with continuous time and distributed delay. By constructing a Lyapunov-Krasovskii functional, we give a necessary and sufficient condition for the global asymptotic stability of the trivial steady state, which describes the population dying out. We also give sufficient conditions for the existence of unbounded solutions, which describes the uncontrolled proliferation of hematopoietic stem cell population. This study may be helpful in understanding the behavior of hematopoietic cells in some hematological disorders.
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Mostafa Adimy, Abdennasser Chekroun, Tarik-Mohamed Touaoula. Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics. Applicable Analysis, Taylor & Francis, 2016, pp.1 - 12. ⟨10.1080/00036811.2016.1139698⟩. ⟨hal-01396691⟩

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