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

## TL;DR

This paper demonstrates the occurrence of a super-critical Hopf bifurcation in a multi-stage white blood cell production model, explaining persistent oscillations observed in certain hematopoietic diseases.

## Contribution

It provides an explicit analytical expression for the bifurcation point and highlights the unique oscillatory behavior arising from the multi-compartment structure.

## Key findings

- Identifies parameter ranges leading to oscillations
- Connects model results with clinical observations
- Shows oscillations are absent in simpler models

## Abstract

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.