Analysis of a Nonlinear Delay Differential-Difference Biological Model*

Recently, a new model describing the cell dynamics in hematopoiesis was proposed. It can be described as a delay differential-difference model. Under some conditions on the biological parameters, it admits two equilibrium points. The first one is the O-equilibrium and the second one, which does not always exist, is a strictly positive point. We propose a Lyapunov functional construction in order to investigate the stability properties of both equilibria. For the 0 equilibrium, we establish the global exponential stability when the positive equilibrium does not exist. For the positive equilibrium, we establish its local exponential stability, estimate the decay rate of solutions and provide a subset of its basin of attraction.