Global Stability of an SIS Epidemic Model with Age of Vaccination

In this paper, an SIS epidemic model with age of vaccination is investigated. Asymptotic smoothness of the semi-flow is proved. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state is discussed. It is shown that if the basic reproduction number is greater than unity, the system is permanent. By constructing two Lyapunov functionals, it is proved that the endemic steady state is globally asymptotically stable if the basic reproduction number is greater than unity, and sufficient conditions are derived for the global asymptotic stability of the disease-free steady state. Numerical simulations are given to illustrate the asymptotic stabilities of the disease-free steady state and endemic state.

Automated summary

This paper investigates an SIS epidemic model with age of vaccination. It proves the asymptotic smoothness of the semi-flow and discusses the local stability of a disease-free steady state and an endemic steady state by analyzing the corresponding characteristic equations. It shows that the system is permanent if the basic reproduction number is greater than unity. By constructing two Lyapunov functionals, it proves that the endemic steady state is globally asymptotically stable when the basic reproduction number is greater than unity, and derives sufficient conditions for the global asymptotic stability of the disease-free steady state. Numerical simulations are provided to illustrate the asymptotic stabilities of the disease-free steady state and endemic state.