A necessary and sufficient condition for the existence of positive periodic solutions of a model of hematopoiesis

In this paper, we derive a sufficient condition as well as a necessary condition for existence of positive periodic solutions of the hematopoiesis model with periodic coefficients x′(t)=−δ(t)x(t)+p(t)⋅x(t−τ(t))1+[x(t−τ(t))]n,t≥0, where δ,p∈C(R+,(0,∞)) and τ∈C(R+,R+) are TT-periodic functions. When p(t)=γδ(t)p(t)=γδ(t) with γ>0γ>0, a sufficient and necessary condition for the existence of a positive TT-periodic solution is established.