A note on global stability of an SEI epidemic model with acute and chronic stages

In this paper, we have investigated the dynamic behavior of an SEI model with acute and chronic stages. Firstly by using Theorem 4.1 of Busenberg and van den Driessche [S. Busenberg, P. van den Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol., 28 (1990), 257-270], we have shown that if the basic reproduction number R0 > 1, the unique endemic equilibrium is global asymptotically stable. The results obtained here improved the main results of Yuan and Yang [J. Yuan, Z. Yang, Global dynamics of an SEI model with acute and chronic stages, J. Comput. Appl. Math. (2007), doi: 10.1016/j.cam.2007.01.042]. Then the criterion for robustness of the system is established under stochastic perturbations. Finally, numerical simulations are performed to illustrate the analytical results.