GLOBAL stability for SIRS epidemic models with general incidence rate and tranfer from infectious to susceptible (1707.06601v1)

Abstract: 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).