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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 610959, 14 pages
Research Article

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

Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

Received 29 November 2013; Accepted 12 January 2014; Published 13 March 2014

Academic Editor: Kaifa Wang

Copyright © 2014 Jinqing Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 . Furthermore, we derive that the disease will be persistent when . Finally, a series of numerical simulations are presented to illustrate our mathematical findings. A new result is given such that, when , 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.