The behavior of an SVIR epidemic model with stochastic perturbation
type: Item
instance of: scholarly article
title: The behavior of an SVIR epidemic model with stochastic perturbation
zbMATH Open document ID: 1406.92644
DOI: 10.1155/2014/742730
author: Yanan Zhao
author: Daqing Jiang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 7022996
zbMATH Keywords: SVIR epidemic model
zbMATH Keywords: stochastic perturbation
zbMATH Keywords: vaccination
zbMATH Keywords: global asymptotic stability
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/742730
OpenAlex ID: W2013014867
Wikidata QID: Q59041133
cites work: Contributions to the mathematical theory of epidemics. II. —The problem of endemicity
cites work: Qualitative analyses of SIS epidemic model with vaccination and varying total population size
cites work: Global Results for an Epidemic Model with Vaccination that Exhibits Backward Bifurcation
cites work: Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times.
cites work: Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination
cites work: Complexity of an SIR epidemic dynamics model with impulsive vaccination control
cites work: Exclusion and persistence in deterministic and stochastic chemostat models
cites work: A note on nonautonomous logistic equation with random perturbation
cites work: Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation
cites work: Global stability of two-group SIR model with random perturbation
cites work: The extinction and persistence of the stochastic SIS epidemic model with vaccination
cites work: Dynamics of stochastically perturbed SIS epidemic model with vaccination
cites work: The threshold of a stochastic SIRS epidemic model with saturated incidence
cites work: Environmental Brownian noise suppresses explosions in population dynamics.
cites work: Q4338975
description: scientific article; zbMATH DE number 7022996