Un mod\`ele non-lin\'eaire de prolif\'eration cellulaire : extinction des cellules et invariance

TL;DR

This paper investigates a nonlinear PDE model of blood cell production, demonstrating solution uniqueness depends on small stem cells and establishing invariance properties in the system.

Contribution

It introduces a nonlinear age-maturity structured model with distributed delay and proves solution uniqueness based on stem cell populations and invariance.

Findings

Solution uniqueness depends on small maturity cells

Invariance properties are established for the model

The model captures key features of blood cellular production

Abstract

This paper analyses a nonlinear age-maturity structured system which arises as a model of the blood cellular production in the bone marrow. The resulting model is a nonlinear first-order partial differential equation in which there is a distributed temporal delay and a retardation in the maturation variable. We prove that uniqueness of solutions depends only on small maturity cells (stem cells) and we give a result of invariance.