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

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.

💡 Research Summary

The paper presents a rigorous mathematical investigation of a delayed differential equation model that describes the population dynamics of pluripotent hematopoietic stem cells (HSCs) responsible for blood production in the bone marrow. Unlike many earlier models that assume a fixed, discrete cell‑cycle time, the authors incorporate a uniformly distributed delay over an interval (