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2014 The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation
Jinqing Zhao, Maoxing Liu, Wanwan Wang, Panzu Yang
Abstr. Appl. Anal. 2014(SI01): 1-14 (2014). DOI: 10.1155/2014/610959

Abstract

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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Jinqing Zhao. Maoxing Liu. Wanwan Wang. Panzu Yang. "The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation." Abstr. Appl. Anal. 2014 (SI01) 1 - 14, 2014. https://doi.org/10.1155/2014/610959

Information

Published: 2014
First available in Project Euclid: 6 October 2014

MathSciNet: MR3182294
Digital Object Identifier: 10.1155/2014/610959

Rights: Copyright © 2014 Hindawi

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Vol.2014 • No. SI01 • 2014
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