Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics

TL;DR

This paper analyzes a delay differential equation model of pluripotent stem cell dynamics, establishing stability conditions and demonstrating how distributed delays can induce Hopf bifurcations, leading to oscillatory behavior.

Contribution

It provides delay-independent stability criteria and reveals how distributed delays can destabilize the system, causing Hopf bifurcations in stem cell population models.

Findings

Stability conditions are independent of delay.

Distributed delay can destabilize the system.

Hopf bifurcations can occur due to delay effects.

Abstract

We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell cycle duration and is uniformly distributed on an interval. We obtain stability conditions independent of the delay. We also show that the distributed delay can destabilize the entire system. In particularly, it is shown that Hopf bifurcations can occur.