The Behavior of an SVIR Epidemic Model with Stochastic Perturbation
Keyword(s):
We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction numberR0. We deduce the globally asymptotic stability of the disease-free equilibrium whenR0≤ 1and the perturbation is small, which means that the disease will die out. WhenR0>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.
2016 ◽
Vol 09
(03)
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pp. 1650042
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2019 ◽
Vol 8
(2)
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pp. 32
2016 ◽
Vol 96
(11)
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pp. 1935-1960
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Keyword(s):
2015 ◽
Vol 2015
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pp. 1-10
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2012 ◽
Vol 28
(12)
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pp. 2545-2560
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2009 ◽
Vol 2009
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pp. 1-17
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