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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]