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

Abstract

• Hematopoiesis model with multiple unimodal production functions is proposed to elucidate the dynamics of blood cells. • Periodic behavior of the density of mature blood cells is investigated. • It is easy to check whether the obtained condition is satisfied or not. • Existence region of positive periodic solutions is clarified by using the continuation theorem of coincidence degree theory. • Positive parameters and variable coefficients of our model can be estimated from clinical data on health and blood disease. 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 delays 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.