Existence, positivity and stability for a nonlinear model of cellular proliferation

TL;DR

This paper analyzes a nonlinear PDE model of blood cell production, establishing existence, positivity, and stability of solutions, with implications for understanding cellular proliferation dynamics.

Contribution

It introduces a novel nonlinear PDE model with delay effects for cellular proliferation and proves its well-posedness and stability properties.

Findings

Unique global solution exists under Lipschitz condition

Solutions remain positive over time

Trivial equilibrium is locally and globally stable

Abstract

In this paper, we investigate a system of two nonlinear partial differential equations, arising from a model of cellular proliferation which describes the production of blood cells in the bone marrow. Due to cellular replication, the two partial differential equations exhibit a retardation of the maturation variable and a temporal delay depending on this maturity. We show that this model has a unique solution which is global under a classical Lipschitz condition. We also obtain the positivity of the solutions and the local and global stability of the trivial equilibrium.