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On the stability of hematopoietic model with feedback control

Mostafa Adimy 1, 2 Catherine Marquet 3 
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]
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
Abstract : We propose and analyze a mathematical model of the production and regulation of blood cell population in the bone marrow (hematopoiesis). This model includes the primitive hematopoietic stem cells (PHSC), the three lineages of their progenitors and the corresponding mature blood cells (red blood cells, white cells and platelets). The resulting mathematical model is a nonlinear system of differential equations with several delays corresponding to the cell cycle durations for each type of cells. We investigate the local asymptotic stability of the trivial steady state by analyzing the roots of the characteristic equation. We also prove by a Lyapunov function the global asymptotic stability of this steady state. This situation illustrates the extinction of the cell population in some pathological cases.
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Submitted on : Monday, December 10, 2012 - 11:26:33 AM
Last modification on : Monday, November 7, 2022 - 5:24:33 PM



Mostafa Adimy, Catherine Marquet. On the stability of hematopoietic model with feedback control. Comptes Rendus. Mathématique, 2012, 350 (3-4), pp.173-176. ⟨10.1016/j.crma.2012.01.014⟩. ⟨hal-00763154⟩



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