Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays

Abstract

In this paper, for SIRS epidemic models with a class of nonlinear incidence rates and distributed delays of the forms β S ( t ) ∫ 0 h k ( τ ) G ( I ( t − τ ) ) d τ , we establish the global asymptotic stability of the disease-free equilibrium E 0 for R 0 < 1 , and applying new monotone techniques, we obtain sufficient conditions which ensure the global asymptotic stability of the endemic equilibrium of the system. The obtained results improve those in Xu and Ma (2009) [Stability of a delayed SIRS epidemic model with a nonlinear incidence rate, Chaos Solitons Fractals 41 (2009) 2319–2325], and are very useful for a large class of SIRS models.