Existence regions of positive periodic solutions for a discrete hematopoiesis model with unimodal production functions

A discrete model describing the increase and decrease of blood cells is considered in this
paper. This hematopoiesis model is a discretization of a delay differential equation with
unimodal production function whose coefficients and delay are periodic discrete functions
with ω-period. This paper is concerned with the existence of positive ω-periodic solutions.
Our results are proved by using the well-known continuation theorem of coincidence degree
theory. The existence range of the positive ω-periodic solutions is also clarified. A
concrete example and its simulation are also given to illustrate our result. Finally, we
examine how positive numbers and coefficients making up our model influence the upper
and lower limits of blood cell counts.