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: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/610959 |
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| _version_ | 1849472145768316928 |
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| author | Jinqing Zhao Maoxing Liu Wanwan Wang Panzu Yang |
| author_facet | Jinqing Zhao Maoxing Liu Wanwan Wang Panzu Yang |
| author_sort | Jinqing Zhao |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-e0028ea6734f477b9ead4bdcf66dd981 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e0028ea6734f477b9ead4bdcf66dd9812025-08-20T03:24:36ZengWileyAbstract 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2014/610959 |
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