Global stability properties of age-dependent epidemic models with varying rates of recurrence

The purpose of this paper is to study the global stability properties of equilibria for age-dependent epidemiological models in presence of recurrence phenomenon. In these systems, the recurrence rate depends on asymptomatic-infection-age. The models are appropriate for human herpes virus (HSV-1 and HSV-2) and varicella-zoster virus. We derived explicit formulas for the basic reproductive number, which completely characterizes the global behaviour of solutions to the models: if the basic reproductive number is less than or equal to unity, the disease will die out; if the basic reproductive number is greater than unity, the disease will be persistent. Volterra-type Lyapunov functions are constructed to establish the global asymptotic stability of the infection-free and endemic steady states.