Oscillation and global attractivity in hematopoiesis model with delay time

摘要

In this paper we shall consider the nonlinear delay differential equations with delay time (∗) p′(t)=(βpm(t−τ))/(1+pn(t−τ))−γp(t) that is proposed as a model of hematopoiesis (blood cell production), where p(t) denotes the density of mature cells in blood circulation and the time delay τ is the time between the production of immature cells in the bone marrow and their maturation for release in the circulating bloodstreams. Our aim is to give sufficient condition for oscillation of all positive solutions of (∗) about the positive steady state and obtain some sufficient conditions for the global attractivity. Our results extend and improve the well-known oscillation results of (∗) when m=0.