Global stability of an SVIR model with age of vaccination

Vaccination is important for the elimination of infectious diseases. In this paper, a basic SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible again when vaccine loses its protective properties with time. The vaccination classes satisfy partial differential equations for the vaccination age. By means of LaSalle’s invariance principle and constructing suitable Lyapunov function(al)s, the dynamical property of the model is established. It is shown that the global stability results of the infection-free equilibrium and the endemic equilibrium depend only on the basic reproductive number R0(ψ)R0(ψ). Finally, some numerical simulations are carried out to illustrate the main results. The combined effects of the vaccination rate and the age factor on the dynamics of the disease are displayed.