Existence of positive almost-periodic solutions for a Nicholson's blowflies model

This article concerns the existence of solutions to a first-order differential equation with time-varying delay, which is known as a Nicholson's blowflies model. By using fixed a point theorem and the Lyapunov functional method, we establish the existence and locally exponential stability of almost periodic solutions for the model. Also, we apply our results to two examples, for which some earlier results can not be applied.