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) ∫h 0 f (τ )G(I(t τ ))dτ . Applying Lyapunov functional techniques in the recent paper (Y. Nakata, Y. Enatsu and Y. Muroya, On the global stability of an SIRS epidemic model with distributed delays, accepted), 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 1 and R0 > 1, where R0 is the basic reproduction number.

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