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We study a class of SIRS epidemic dynamical models with a general non-linearincidence rate and transfer from infectious to susceptible. The incidence rateincludes a wide range of monotonic, con- cave incidence rates and somenon-monotonic or concave cases. We apply LaSalle's invariance principle andLyapunov's direct method to prove that the disease-free equilibrium is globallyasymptotically stable if the basic reproduction number R0 lesser or equal to 1,and the endemic equilibrium is globally asymptotically stable if R0 > 1, undersome conditions imposed on the incidence function f(S; I).

GLOBAL stability for SIRS epidemic models with general incidence rate and tranfer from infectious to susceptible