Existence and uniqueness results for a neutral erythropoiesis model with iterative production and harvesting terms

The main objective of this work is to study the existence, uniqueness and stability of positive periodic solutions for a first-order neutral differential equation with iterative terms which models the regulation of red blood cell production under a harvesting strategy. Benefiting from the Krasnoselskii's fixed point theorem as well as some properties of an obtained Green's function, we establish the existence of the solutions and taking advantage of the Banach fixed point theorem, we prove that the proposed equation has exactly one solution that depends continuously on parameters. Finally, two examples are exhibited to show the efficiency and application of our findings which are completely new and enrich the existing literature.