title: Bifurcations in a white-blood-cell production model.
abstract: 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.
authors.affiliation: Département de mathématiques et de statistique & Centre de recherches mathématiques, université de Montréal, Montréal, Québec H3C 3J7, Canada. bernard@dms.umontreal.ca
authors.forename: Samuel
authors.initials: S
authors.lastname: Bernard
authors.forename: Jacques
authors.initials: J
authors.lastname: Bélair
authors.forename: Michael C
authors.initials: MC
authors.lastname: Mackey
mesh_terms: D000818:Animals; D017209:Apoptosis; D004285:Dogs; D006402:Hematologic Diseases; D006410:Hematopoiesis; D006412:Hematopoietic Stem Cells / Q000166:cytology; D007958:Leukocyte Count; D007962:Leukocytes / Q000166:cytology*; D008433:Mathematics; D008954:Models, Biological; D010507:Periodicity