Global stability of a partial differential equation with distributed delay due to cellular replication

TL;DR

This paper analyzes a nonlinear PDE model of blood cell production with distributed delay, demonstrating how primitive cell behavior impacts overall population stability.

Contribution

It introduces a PDE model with distributed delay for cellular proliferation and proves the influence of primitive cells on global population stability.

Findings

Primitive cell behavior affects population stability

Established conditions for global stability of the model

Extended understanding of delay effects in cellular proliferation

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.