Positive periodic solutions for systems of impulsive delay differential equations

A class of periodic differential $n$-dimensional systems with patch structure with (possibly infinite) delay and nonlinear impulses is considered. These systems incorporate very general nonlinearities and impulses whose signs may vary. Criteria for the existence of at least one positive periodic solution are presented, extending and improving previous ones established for the scalar case. Applications to systems inspired in mathematical biology models, such as impulsive hematopoiesis and Nicholson-type systems, are also included.