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Updated: Aug 24, 2026

Simultaneous Assessment of Kinship, Division Number, and Phenotype via Flow Cytometry for Hematopoietic Stem and Progenitor Cells
Published on: March 24, 2023
Bifurcations in a white-blood-cell production model
Samuel Bernard1, Jacques Bélair, Michael C Mackey
1Département de mathématiques et de statistique & Centre de recherches mathématiques, université de Montréal, Montréal, Québec H3C 3J7, Canada. bernard@dms.umontreal.ca
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.
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