Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases

TL;DR

This paper presents a mathematical model of hematopoiesis using delay differential equations to explain periodic blood diseases, highlighting how feedback loop destabilization causes oscillations in blood cell levels.

Contribution

It introduces a novel delay differential equation model for hematopoiesis that explains periodic blood diseases through bifurcation analysis.

Findings

Existence of Hopf bifurcation in the model.

Long period oscillations can be simulated.

Feedback loop destabilization causes oscillations.

Abstract

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to carry out explanation on some blood diseases, characterized by oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is analyzed. The existence of a Hopf bifurcation for a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors. This stresses the localization of periodic hematological diseases in the feedback loop.