The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation

The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation

We investigate a stochastic SI epidemic model in the complex networks. We show that this model has a unique global positive solution. Then we consider the asymptotic behavior of the model around the disease-free equilibrium and show that the solution will oscillate around the disease-free equilibriu...

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Main Authors: Jinqing Zhao, Maoxing Liu, Wanwan Wang, Panzu Yang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/610959
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spelling doaj-e0028ea6734f477b9ead4bdcf66dd9812020-11-24T22:51:31ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/610959610959The Stability of SI Epidemic Model in Complex Networks with Stochastic PerturbationJinqing Zhao0Maoxing Liu1Wanwan Wang2Panzu Yang3Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaWe investigate a stochastic SI epidemic model in the complex networks. We show that this model has a unique global positive solution. Then we consider the asymptotic behavior of the model around the disease-free equilibrium and show that the solution will oscillate around the disease-free equilibrium of deterministic system when R0≤1. Furthermore, we derive that the disease will be persistent when R0>1. Finally, a series of numerical simulations are presented to illustrate our mathematical findings. A new result is given such that, when R0≤1, with the increase of noise intensity the solution of stochastic system converging to the disease-free equilibrium is faster than that of the deterministic system.http://dx.doi.org/10.1155/2014/610959
collection DOAJ
language English
format Article
sources DOAJ
author Jinqing Zhao
Maoxing Liu
Wanwan Wang
Panzu Yang
spellingShingle Jinqing Zhao
Maoxing Liu
Wanwan Wang
Panzu Yang
The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation
Abstract and Applied Analysis
author_facet Jinqing Zhao
Maoxing Liu
Wanwan Wang
Panzu Yang
author_sort Jinqing Zhao
title The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation
title_short The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation
title_full The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation
title_fullStr The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation
title_full_unstemmed The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation
title_sort stability of si epidemic model in complex networks with stochastic perturbation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We investigate a stochastic SI epidemic model in the complex networks. We show that this model has a unique global positive solution. Then we consider the asymptotic behavior of the model around the disease-free equilibrium and show that the solution will oscillate around the disease-free equilibrium of deterministic system when R0≤1. Furthermore, we derive that the disease will be persistent when R0>1. Finally, a series of numerical simulations are presented to illustrate our mathematical findings. A new result is given such that, when R0≤1, with the increase of noise intensity the solution of stochastic system converging to the disease-free equilibrium is faster than that of the deterministic system.
url http://dx.doi.org/10.1155/2014/610959
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AT maoxingliu thestabilityofsiepidemicmodelincomplexnetworkswithstochasticperturbation
AT wanwanwang thestabilityofsiepidemicmodelincomplexnetworkswithstochasticperturbation
AT panzuyang thestabilityofsiepidemicmodelincomplexnetworkswithstochasticperturbation
AT jinqingzhao stabilityofsiepidemicmodelincomplexnetworkswithstochasticperturbation
AT maoxingliu stabilityofsiepidemicmodelincomplexnetworkswithstochasticperturbation
AT wanwanwang stabilityofsiepidemicmodelincomplexnetworkswithstochasticperturbation
AT panzuyang stabilityofsiepidemicmodelincomplexnetworkswithstochasticperturbation
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