In this paper we propose the global dynamics of an SIRI epidemic model with latency and a general nonlinear incidence function. The model is based on the susceptible-infective-recovered (SIR) compartmental structure with relapse (SIRI). Sufficient conditions for the global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Lyapunov-LaSalle theorem. Also some numerical simulations are given to illustrate this result.

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In this paper, we propose the global dynamics of an SIR epidemic model with distributed latent period, immunity, relapse, homestead-isolation of the susceptible and infectious individuals and general incidence rate. The resulting model has a disease-free equilibrium and if [Formula: see text] then the SIR epidemic model admits a unique endemic equilibrium. By using suitable Lyapunov functionals and LaSalle’s invariance principle, the global stability of the disease-free equilibrium and the endemic equilibrium is established, under suitable monotonicity conditions on the incidence function.

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