Annals of Mathematical Sciences and Applications

In this paper, we give a brief survey of Lyapunov functionals for compartmental epidemic models with distributed time delays based on the SIR model proposed by Beretta and Takeuchi (J. Math. Biol., 1995). We then consider various models with an exposed compartment such as SEIR, SEIQR, SEIAR, and SEIS models. Based on the suitable construction of Lyapunov functionals, we establish the global stability of the disease free equilibrium and endemic equilibrium (if it exists) for these models.