Oscillations in a white blood cell production model with multiple differentiation stages

J Math Biol. 2020 Feb;80(3):575-600. doi: 10.1007/s00285-019-01432-6. Epub 2019 Sep 26.


In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analytical expression for the bifurcation point depending on model parameters. The Hopf bifurcation is a unique feature of the multi-compartment structure as it does not exist in the corresponding two-compartment model. It appears for a parameter set different from the parameters identified for healthy hematopoiesis and requires changes in at least two cell properties. Model analysis allows identifying a range of biologically plausible parameter sets that can explain persistent oscillations of white blood cell counts observed in some hematopoietic diseases. Relating the identified parameter sets to recent experimental and clinical findings provides insights into the pathological mechanisms leading to oscillating blood cell counts.

Keywords: Hematopoiesis; Hopf bifurcation; Mathematical model; Oscillating blood cell counts; Stem cells.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Computer Simulation*
  • Hematopoiesis*
  • Humans
  • Leukocyte Count
  • Leukocytes / cytology*
  • Leukocytes / pathology*
  • Models, Biological*
  • Neutropenia / pathology*
  • Periodicity

Supplementary concepts

  • Cyclic neutropenia