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Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps

Author

Listed:
  • Ge, Qing
  • Ji, Guilin
  • Xu, Jiabo
  • Fan, Xiaolin

Abstract

In this paper, Brownian motion and Lévy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0,R̄0 are showed. We find that if R˜0<1, the disease may die out, and when R̄0>1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.

Suggested Citation

  • Ge, Qing & Ji, Guilin & Xu, Jiabo & Fan, Xiaolin, 2016. "Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1120-1127.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:1120-1127
    DOI: 10.1016/j.physa.2016.06.116
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    References listed on IDEAS

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    1. Zhou, Yanli & Zhang, Weiguo, 2016. "Threshold of a stochastic SIR epidemic model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 204-216.
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    5. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
    6. Zhao, Dianli & Zhang, Tiansi & Yuan, Sanling, 2016. "The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 372-379.
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    Cited by:

    1. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Liu, Liya & Hu, Jingwei, 2020. "Analysis of a hybrid switching SVIR epidemic model with vaccination and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Zeng, Ting & Teng, Zhidong & Li, Zhiming & Hu, Junna, 2018. "Stability in the mean of a stochastic three species food chain model with general Le´vy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 258-265.

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