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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 R 0 > 1 , 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. [ABSTRACT FROM AUTHOR]

In this paper we study the global dynamics of an SIRSI epidemic model with a distributed latent period and a general non-linear incidence function. By using suitable Lyapunov functionals and LaSalle's invariance principle, the global stability of a disease-free equilibrium and an endemic equilibrium is established for the SIRSI epidemic model with a distributed latent period. [ABSTRACT FROM AUTHOR]

In this paper we propose the global dynamics of an SEIRI epidemic model with a general nonlinear incidence function. The model is based on the susceptible-exposed-infective-recovered (SEIR) compartmental structure with relapse (SEIRI). Sufficient conditions for the local and global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Routh-Hurwitz criterion and Lyapunov-LaSalle theorem. [ABSTRACT FROM AUTHOR]