The behavior of an SVIR epidemic model with stochastic perturbation. (English) Zbl 1406.92644

Summary: We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number \(R_0\). We deduce the globally asymptotic stability of the disease-free equilibrium when \(R_0 \leq 1\) and the perturbation is small, which means that the disease will die out. When \(R_0 > 1\), we derive that the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. The key to our analysis is choosing appropriate Lyapunov functions.


92D30 Epidemiology
92C60 Medical epidemiology
34D23 Global stability of solutions to ordinary differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
Full Text: DOI


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