Abstract: An SIRS epidemic model with an age-dependent vaccination is considered.By using the theory of differential or integral equation,an explicit formula for the vaccine-dependent reproductive number R(ψ) is first obtained.Next,it is showed that the disease-free steady state is locally asymptotically stable if R(ψ) is less than one and unstable if R(ψ) is larger than one.If R(0)1,then the disease-free equilibrium is global attractor.Moreover,there exists an endemic steady state in this model which is unstable un...