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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 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.

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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:610959
    DOI: 10.1155/2014/610959
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    References listed on IDEAS

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    1. Witbooi, Peter J., 2013. "Stability of an SEIR epidemic model with independent stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4928-4936.
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    5. Zhao, Yanan & Jiang, Daqing & O’Regan, Donal, 2013. "The extinction and persistence of the stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4916-4927.
    6. Stephen Eubank & Hasan Guclu & V. S. Anil Kumar & Madhav V. Marathe & Aravind Srinivasan & Zoltán Toroczkai & Nan Wang, 2004. "Modelling disease outbreaks in realistic urban social networks," Nature, Nature, vol. 429(6988), pages 180-184, May.
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    Cited by:

    1. Willie Kouam & Yezekael Hayel & Gabriel Deugoue & Charles Kamhoua, 2025. "Exploring Centrality Dynamics for Epidemic Control in Complex Networks: An Asymmetrical Centralities Game Approach," Dynamic Games and Applications, Springer, vol. 15(3), pages 947-979, July.

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