Global stability of an SEIR epidemic model with age-dependent latency and relapse

In this paper, an SEIR epidemic model for a disease with age-dependent latency and relapse is proposed. Such a model is very appropriate for tuberculosis and herpes. The basic reproduction number ℜ0ℜ0 is defined and proved as a classic threshold parameter. Asymptotic smoothness of solutions and uniform persistence of the system are shown via reformulating the system as a system of Volterra integral equations. The local stability and global stability of equilibria are obtained by analyzing the corresponding characteristic equations and constructing the proper Volterra-type Lyapunov functionals, respectively. Finally, some special cases of the model as key functions reducing to constant are discussed in the last section.