On the stability of a maturity structured model of cellular proliferation

TL;DR

This paper investigates the stability of a complex mathematical model describing blood cell production, revealing how immature cell populations influence overall system stability and providing conditions for stability and instability.

Contribution

It introduces a detailed stability analysis of a nonlinear maturity-structured PDE model with delays, highlighting the role of immature cells in system dynamics.

Findings

Conditions for global stability of the trivial solution

Criteria for instability based on immature cell behavior

Dependence of system stability on maturation delay and population dynamics

Abstract

We analyse the asymptotic behaviour of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial differential equations, with a retardation of the maturation variable and a time delay depending on this maturity. We show that the stability of this system depends strongly on the behaviour of the immature cells population. We obtain conditions for the global stability and the instability of the trivial solution.