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Global attractivity of the model for the survival of red blood cells with several delays. (English) Zbl 0958.92010
Summary: We consider a model for the survival of red blood cells with several delays $dN(t)/dt= -\mu N(t)+ \sum^m_{i=1} P_ie^{-r_iN (t-\tau_i)},\;t\geq 0, \tag{*}$ and establish a sufficient condition under which the positive equilibrium $$N^*$$ of (*) is a global attractor. Our criteria generalize and improve corresponding results obtained by M. Wazewska-Czyzewska and A. Lasota [Ann. Pol. Math. Soc., Appl. Math. 6, 23-40 (1976)], I. Györi and G. Ladas [Oscillation theory of delay differential equations: with applications. (1991; Zbl 0780.34048)], and by J. Li [J. Biomath. 9, No. 1, 91-95 (1994; Zbl 0817.34046)].

##### MSC:
 92C30 Physiology (general) 37N25 Dynamical systems in biology 34K20 Stability theory of functional-differential equations
##### Keywords:
global attractivity; survival of red blood cells; delays