Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model

In this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form βS(t)∫0hf(τ)G(I(t−τ))dτ. Applying Lyapunov functional techniques in the recent paper [Y. Nakata, Y. Enatsu, Y. Muroya, On the global stability of an SIRS epidemic model with distributed delays, Discrete Contin. Dyn. Syst. Supplement (2011) 1119–1128], we establish sufficient conditions of the rate of immunity loss for the global asymptotic stability of an endemic equilibrium for the model. In particular, we offer a unified construction of Lyapunov functionals for both cases of R0≤1R0≤1 and R0>1R0>1, where R0R0 is the basic reproduction number.