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Existence and global attractivity of unique positive periodic solution for a model of hematopoiesis. (English) Zbl 1155.34041
The authors consider the generalized model of hematopoiesis $$x'(t)=-a(t)x(t)+\sum_{i=1}^m\frac{b_i(t)}{1+x^n(t-\tau_i(t))}.$$ By using a fixed point theorem, some criteria are established for the existence of the unique positive $\omega$-periodic solution of the above model. They show that this periodic solution is a global attractor of all other positive solutions.

##### MSC:
 34K60 Qualitative investigation and simulation of models 34K13 Periodic solutions of functional differential equations 92C50 Medical applications of mathematical biology 34K25 Asymptotic theory of functional-differential equations
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