The dynamics of an SVIR epidemiological model with infection age

In this paper, we study the global dynamics of an susceptible, vaccinated, infectious and recovered epidemiological model with infection-age structure. Biologically, we assume that effective contacts between vaccinated individuals and infectious individuals are less than that between susceptible individuals and infectious individuals. Using Lyapunov functions, we show that the global stability of each equilibrium is completely determined by the basic reproduction number R-0: if R-0 <= 1, then the diseasefree equilibrium is globally asymptotically stable; while if R-0 > 1, then there exists a unique endemic equilibrium which is globally asymptotically stable.