Global stability of an SEIR model with infectious force in latent and infected

Abstract

This paper considers an SEIR model with infectious force in latent and infected. By means of Lyapunov function and LaSalles invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the sufficient conditions for the global stability of the unique endemic equilibrium by the compound matrix theory. In addition, it is verified that there is phenomena of limit cycle according to simulations.