---
abstract: 'In this paper, we investigate a nonlinear partial differential equation, arising from a model of cellular proliferation. This model describes the production of blood cells in the bone marrow. It is represented by a partial differential equation with a retardation of the maturation variable and a distributed temporal delay. Our aim is to prove that the behaviour of primitive cells influences the global behaviour of the population.'
author:
- 'Mostafa Adimy[^1] and Fabien Crauste[^2]'
date: Year 2002
title: '[**Global Stability of a Partial Differential Equation with Distributed Delay due to Cellular Replication[^3]**]{}'
---

[*Laboratoire de Mathématiques Appliquées\
Université de Pau et des Pays de l’Adour\
Avenue de l’université, 64000 Pau, France*]{}

Introduction and motivation {#introduction}
===========================

This paper analyses a general model of the blood production system based on a model proposed by Mackey and Rey in 1993 [@mackey1993]. The initial form of this model is a time-age-maturity structured system and it describes the dynamics of proliferative stem cells and precursors in the bone marrow. It consists in a population of cells which are capable of both proliferation and maturation.

In this model, the period of life of each cell is divided into a resting phase and a 