SIRS epidemic models with latent periods and specific non-monotone incidence rates are investigated. By applying monotone iterative techniques, the authors establish sufficient conditions for the global asymptotic stability of the endemic equilibrium of the system which gives a partial answer to an open problem of H.-F. Huo
and Z.-P. Ma
[Dynamics of a delayed epidemic model with non-monotonic incidence rate. Commun. Nonlinear Sci. Numer. Simul. 15, No. 2, 459–468 (2010; Zbl 1221.34197
)]. Moreover, combining both monotone iterative techniques and Lyapunov functional techniques for the SIRS model by perturbations, they derive another type of sufficient conditions for the global asymptotic stability of the endemic equilibrium.