A note on global attractivity in models of hematopoiesis

Abstract

We consider the delay differential equations $P'(t) = \frac{{\beta _0 \theta ^n [P(t - \tau )]^j }}{{\theta ^n + [P(t - \tau )]^n }} - \delta P(t),{\rm{ }}j = 0,1,$ which were proposed by Mackey and Glass as a model of blood cell production. We suggest new conditions sufficient for the positive equilibrium of the equation considered to be a global attractor. In contrast to the Lasota-Wazewska model, we establish the existence of the number δ_j = δ_j(n, τ) > 0 such that the equilibrium of the equation under consideration is a global attractor for all δ ε (0, δ_j] independently of β₀ and θ.