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Oscillation and global attractivity in hematopoiesis model with delay time. (English) Zbl 1026.34082

Summary: Here, we consider the nonlinear delay differential equations with delay time

p ' (t)=β p m (t-τ)/1 + p n (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 a sufficient condition for the oscillation of all positive solutions to (*) about the positive steady state and to obtain some sufficient conditions for the global attractivity. Our results extend and improve the well-known oscillation results to (*) when m=0.


MSC:
34K11Oscillation theory of functional-differential equations
92C30Physiology (general)
34K60Qualitative investigation and simulation of models