On periodic solutions of a recruitment model with iterative terms and a nonlinear harvesting

We consider a first-order delay differential equation involving iterative terms. We prove the existence of positive periodic and bounded solutions by utilizing the Schauder's fixed point theorem combined with the Green's functions method. Furthermore, by virtue of the Banach contraction principle, the uniqueness and stability of the solution are also analyzed. Our new results are illustrated with two examples that show the feasibility of our main findings.