Bifurcations in a white-blood-cell production model
| Autor: | Samuel Bernard, Jacques Bélair, Michael C. Mackey |
|---|---|
| Přispěvatelé: | 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] |
| Rok vydání: | 2004 |
| Předmět: |
Periodicity
MESH: Periodicity Differential equation Quantitative Biology::Tissues and Organs [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] MESH: Hematopoiesis [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS] Apoptosis Models Biological General Biochemistry Genetics and Molecular Biology MESH: Hematopoietic Stem Cells Quantitative Biology::Cell Behavior MESH: Dogs MESH: Leukocytes Leukocyte Count symbols.namesake Dogs White blood cell Leukocytes medicine Animals MESH: Animals Bifurcation [INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM] Hopf bifurcation [SDV.BIBS] Life Sciences [q-bio]/Quantitative Methods [q-bio.QM] General Immunology and Microbiology MESH: Apoptosis Dynamics (mechanics) Mathematical analysis MESH: Mathematics MESH: Models Biological General Medicine Delay differential equation Hematopoietic Stem Cells MESH: Hematologic Diseases Hematologic Diseases [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM] Hematopoiesis medicine.anatomical_structure Bifurcation analysis MESH: Leukocyte Count Production model symbols [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM] General Agricultural and Biological Sciences Mathematics |
| Zdroj: | Comptes Rendus Biologies Comptes Rendus Biologies, Elsevier, 2004, 327 (3), pp.201-10 |
| ISSN: | 1631-0691 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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