A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia

TL;DR

This paper develops and analyzes a mathematical model of blood cell production, revealing conditions for stability and oscillations, which could help understand periodic blood diseases.

Contribution

It introduces a novel age-structured PDE model for hematopoiesis with delay effects and analyzes stability and bifurcations.

Findings

Trivial equilibrium is globally stable when unique.

Nontrivial equilibrium can become unstable via Hopf bifurcation.

Numerical simulations support analytical stability and oscillation results.

Abstract

This paper is devoted to the analysis of a mathematical model of blood cells production in the bone marrow (hematopoiesis). The model is a system of two age-structured partial differential equations. Integrating these equations over the age, we obtain a system of two nonlinear differential equations with distributed time delay corresponding to the cell cycle duration. This system describes the evolution of the total cell populations. By constructing a Lyapunov functional, it is shown that the trivial equilibrium is globally asymptotically stable if it is the only equilibrium. It is also shown that the nontrivial equilibrium, the most biologically meaningful one, can become unstable via a Hopf bifurcation. Numerical simulations are carried out to illustrate the analytical results. The study maybe helpful in understanding the connection between the relatively short cell cycle durations and the relatively long periods of peripheral cell oscillations in some periodic hematological diseases.