First-order periodic coupled systems with orderless lower and upper solutions

We present some existence and localization results for periodic solutions of first-order coupled nonlinear systems of two equations, without requiring periodicity for the nonlinearities. The arguments are based on Schauder's fixed point theorem together with not necessarily well -ordered upper and lower solutions. A real-case scenario shows the applicability of our results to some population dynamics models, describing the interaction between a criminal and a non-criminal population with a law enforcement component.