STABILITY ANALYSIS OF AN SEIR MODEL WITH VACCINATION

In this paper an SEIR epidemic model with vaccination is investigated. It is assumed that the incidence is a general nonlinear function. Lyapunov's method, Hurwitz's criterion and Li's geometrical approach are used to study the dynamic behavior of the possible equilibria: the disease-free equilibrium and the endemic equilibrium. The e ect of vaccination rate can be easily seen on the reproduction number R0 and consequently on the existence of the endemic equilibrium. Further, the reproduction number plays a big role on the stability analysis: if R0 1, the disease-free equilibrium is proven to be globally asymptotically stable and the disease dies out, while if R0 > 1, the endemic equilibrium is shown to be globally asymptotically stable in the interior of the feasible region.