Global Stability Analysis of Strictly Positive Steady State for a Surviving Hematopoietic Stem Cells Models

Most of recent mathematical models that describe hematopoietic stem cells (HSCs) are nonlinear with distributed delays. One difficult issue about these models is the analysis of the global asymptotic stability of positive steady states. In this paper we address the problem of global stability of positive steady states of HSCs. A positive equilibrium characterizes the system in normal situation (i.e. hematopoietic stem cells survive) and hence, it is very important for practical considerations. We start the study using a model that does not include fast self-renewal, then we elaborate the stability conditions for the model with fast self-renewal. To this end, we first use a nonlinear transformation to obtain a delay-free model which is equivalent to the original time-delayed one in terms of system-average. Then, we analyze the stability properties of the positive equilibrium points by constructing particular Lyapunov functions. The results are illustrated with numerical simulations of different cases.