Stability of immature cell dynamics in healthy and unhealthy hematopoiesis

摘要

A nonlinear system with distributed delays is studied. The model takes into account the fast self-renewal dynamics observed in Acute Myeloid Leukemia (AML). Stability and instability conditions are derived for the zero equilibrium of the AML model. Notice that, biologically, the zero equilibrium means the eradication of all malignant cells, which is the aim of the anti-AML therapy. The novelty of this work is that we consider time-varying biological parameters reflecting the fact that the differentiating and self-renewing parameters become time-variant both under the effect of the disease and the drugs. A simpler case of the studied model is well suited to describe the healthy hematopoiesis. In this case, we focus on the stability of the positive steady state since it reflects the surviving of all healthy blood cells. Via a construction of a novel Lyapunov functional, we derive sufficient conditions for the local exponential stability of the favourable equilibrium and we propose an estimate of its basin of attraction.