Abstract and Applied Analysis

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

Jinqing Zhao, Maoxing Liu, Wanwan Wang, and Panzu Yang

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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 R 0 1 . Furthermore, we derive that the disease will be persistent when R 0 > 1 . Finally, a series of numerical simulations are presented to illustrate our mathematical findings. A new result is given such that, when R 0 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.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 610959, 14 pages.

First available in Project Euclid: 6 October 2014

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Zhao, Jinqing; Liu, Maoxing; Wang, Wanwan; Yang, Panzu. The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 610959, 14 pages. doi:10.1155/2014/610959. https://projecteuclid.org/euclid.aaa/1412607553

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