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Bifurcations in a white-blood-cell production model

Authors :
Samuel Bernard
Jacques Bélair
Michael C. Mackey
Bernard, Samuel
Institut Camille Jordan [Villeurbanne] (ICJ)
École Centrale de Lyon (ECL)
Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL)
Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon)
Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)
Département de Mathématiques et de Statistiques [UdeM- Montréal]
Université de Montréal (UdeM)
Centre for Nonlinear Dynamics (CND)
McGill University = Université McGill [Montréal, Canada]
Source :
Comptes Rendus Biologies, Comptes Rendus Biologies, Elsevier, 2004, 327 (3), pp.201-10
Publication Year :
2004
Publisher :
Elsevier BV, 2004.

Abstract

International audience; We study the dynamics of a model of white-blood-cell (WBC) production. The model consists of two compartmental differential equations with two discrete delays. We show that from normal to pathological parameter values, the system undergoes supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles. We characterize the steady states of the system and perform a bifurcation analysis. Our results indicate that an increase in apoptosis rate of either hematopoietic stem cells or WBC precursors induces a Hopf bifurcation and an oscillatory regime takes place. These oscillations are seen in some hematological diseases.

Details

ISSN :
16310691
Volume :
327
Database :
OpenAIRE
Journal :
Comptes Rendus Biologies
Accession number :
edsair.doi.dedup.....36ebbe05a0a8d4b289fc7932e305f2e4
Full Text :
https://doi.org/10.1016/j.crvi.2003.05.005