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. Copyright © 2015 John Wiley & Sons, Ltd.