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Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling

Mostafa Adimy 1, * Fabien Crauste 1, 2, * 
* Corresponding author
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]
Abstract : We illustrate the appearance of oscillating solutions in delay differential equations modeling hematopoietic stem cell dynamics. We focus on autonomous oscillations, arising as consequences of a destabilization of the system, for instance through a Hopf bifurcation. Models of hematopoietic stem cell dynamics are considered for their abilities to describe periodic hematological diseases, such as chronic myelogenous leukemia and cyclical neutropenia. After a review of delay models exhibiting oscillations, we focus on three examples, describing different delays: a discrete delay, a continuous distributed delay, and a state-dependent delay. In each case, we show how the system can have oscillating solutions, and we characterize these solutions in terms of periods and amplitudes.
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Submitted on : Tuesday, December 18, 2012 - 10:44:08 AM
Last modification on : Monday, May 16, 2022 - 3:12:01 PM

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Mostafa Adimy, Fabien Crauste. Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2012, 7 (6), pp.1-22. ⟨10.1051/mmnp/20127601⟩. ⟨hal-00766339⟩

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