Research and Reports on Mathematics.

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Global Stability Analysis of an SEIR Epidemic Model with Relapse and General Incidence Rates

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. Also some numerical simulations are given to illustrate numerically our theoretical results.

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