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An age-structured SVIR epidemic model with vaccination. (Chinese. English summary) Zbl 1324.92056

Summary: The dynamical behavior of an age-structured SVIR epidemic model with vaccination is mathematically analyzed. An explicit formula is obtained for the basic reproductive number \(R(\psi)\) with respect to the vaccination policy \(\psi\) and age \(a\), and it is proved that the disease-free steady state is globally asymptotically stable if \(R(0, a)\) is less than one; and is unstable if \(R(\psi,a)\) is large than one. Moreover, it is showed that the age-structured model has at least an endemic steady state for \(R(\psi, a)>1\).

MSC:

92D30 Epidemiology
92C60 Medical epidemiology
34D23 Global stability of solutions to ordinary differential equations
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