Analysis for an age-structured SVIR epidemic model with vaccination

In this paper, an age-structured SVIR epidemic model with vaccination is established and analyzed. By using the theory and methods of epidemic dynamics, and the stability theory and methods in differential and integral equations, an explicit formula for the basic reproductive number R(ψ) with respect to the vaccination policy ψ and age a is obtained, and it is proved that the disease-free steady state is globally asymptotically stable for R₀ is less than one; and is unstable for R₀ is large than one. Moreover, it is proved that there exists at least an endemic steady state for R(ψ, a) >; 1.