Open Access
2014 The Behavior of an SVIR Epidemic Model with Stochastic Perturbation
Yanan Zhao, Daqing Jiang
Abstr. Appl. Anal. 2014: 1-7 (2014). DOI: 10.1155/2014/742730


We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number R0. We deduce the globally asymptotic stability of the disease-free equilibrium when R0 1 and the perturbation is small, which means that the disease will die out. When R0>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.


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Yanan Zhao. Daqing Jiang. "The Behavior of an SVIR Epidemic Model with Stochastic Perturbation." Abstr. Appl. Anal. 2014 1 - 7, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022996
MathSciNet: MR3228087
Digital Object Identifier: 10.1155/2014/742730

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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