  We establish and prove a fixed point theorem from which some sufficient
conditions on the existence of positive almost periodic solutions for a model
of hematopoiesis with oscillatory circulation loss rate are deduced. Some
particular assumption under the nonlinearity of the equation has been
previously considered by authors as fundamental for the study of almost
periodic solutions of the model. The aim of this paper is to establish results
without such assumption. Some examples are given to illustrate our results.
