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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)+ i=1 m b i (t) 1+x n (t-τ i (t))·

By using a fixed point theorem, some criteria are established for the existence of the unique positive ω-periodic solution of the above model. They show that this periodic solution is a global attractor of all other positive solutions.

MSC:
34K60Qualitative investigation and simulation of models
34K13Periodic solutions of functional differential equations
92C50Medical applications of mathematical biology
34K25Asymptotic theory of functional-differential equations