Analysis of a SEIV epidemic model with a nonlinear incidence rate

In this paper, a SEIV epidemic model with a nonlinear incidence rate is investigated. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. It is shown that if the basic reproduction number _R0<1${\mathfrak{R}}_0<1$, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist. Moreover, we show that if the basic reproduction number _R0>1${\mathfrak{R}}_0>1$, the disease is uniformly persistent and the unique endemic equilibrium of the system with saturation incidence is globally asymptotically stable under certain conditions.