Large time behavior of nonautonomous differential systems modeling antibiotic‐resistant bacteria in rivers.

In this paper, we study a general nonautonomous model for bacterial dynamics in rivers. The mathematical model is represented by a nonautonomous system of nonlinear ordinary differential equations. We show the existence of a bounded positive invariant and attracting set. By using the Lyapunov function method, we establish global stability of steady‐state solutions of the associated autonomous system. Second, the existence of positive periodic solutions of the nonautonomous system is proven using a continuation theorem based on coincidence degree theory. [ABSTRACT FROM AUTHOR]