IJAM, Volume 28, No. 2 (2015)

Abstract. In this paper, an SEIR epidemic model with waning preventive vaccine is investigated. The results of our mathematical analysis indicate that the dynamics of the system is almost determined by the basic reproduction number. If the basic reproduction number is less than unity, it is proven that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, there exists a unique endemic equilibrium and sufficient conditions are obtained for the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are carried out to illustrate the main results.