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

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  • Jinqing Zhao
  • Maoxing Liu
  • Wanwan Wang
  • Panzu Yang

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 . 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.

Suggested Citation

  • Jinqing Zhao & Maoxing Liu & Wanwan Wang & Panzu Yang, 2014. "The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, March.
    • Handle: RePEc:hin:jnlaaa:610959
    DOI: 10.1155/2014/610959
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    Cited by:

    1. Wang, Ze & Gao, Xiangyun & Tang, Renwu & Liu, Xueyong & Sun, Qingru & Chen, Zhihua, 2019. "Identifying influential nodes based on fluctuation conduction network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 355-369.
    2. Yang, Qiwen & Zhu, Xuzhen & Tian, Yang & Wang, Guanglu & Zhang, Yuexia & Chen, Lei, 2021. "The influence of heterogeneity of adoption thresholds on limited information spreading," Applied Mathematics and Computation, Elsevier, vol. 411(C).

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