  We study a class of SIRS epidemic dynamical models with a general non-linear
incidence rate and transfer from infectious to susceptible. The incidence rate
includes a wide range of monotonic, con- cave 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 R0 lesser or equal to 1,
and the endemic equilibrium is globally asymptotically stable if R0 > 1, under
some conditions imposed on the incidence function f(S; I).
