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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 $$p'(t)=\bigl( \beta p^m(t-\tau) \bigr)/ \bigl(1+p^n (t-\tau) \bigr)- \gamma p(t),\tag*$$ 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 $\tau$ 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:
 34K11 Oscillation theory of functional-differential equations 92C30 Physiology (general) 34K60 Qualitative investigation and simulation of models
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##### References:
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