Global stability for SIRS epidemic models with general incidence rate and transfer from infectious to susceptible

We study a class of SIRS epidemic dynamical models with a general nonlinear incidence rate and transfer from infectious to susceptible. The incidence rate includes a wide range of monotonic, concave incidence rates and some non-monotonic or concave cases. We apply LaSalle's invariance principle and Lyapunov's direct method to prove that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number R-0 <= 1, and the endemic equilibrium is globally asymptotically stable if R-0 > 1, under some conditions imposed on the incidence function f(S, I).