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Threshold behavior of a stochastic SIS model with Le´vy jumps

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  • Zhou, Yanli
  • Yuan, Sanling
  • Zhao, Dianli

Abstract

In this paper, the dynamics of a stochastic SIS model with Lévy jumps are investigated. We first prove that this model has a unique global positive solution starting from the positive initial value. Then, taking the accumulated jump size into account, we find a threshold of the model, denoted by R˜0, which completely determines the extinction and prevalence of the disease: if R˜0<1, the disease dies out exponentially with probability one; if R˜0>1, the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease. From the view of epidemiology, the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics. Moreover, we find that Lévy noise can suppress disease outbreak. Finally, we introduce some numerical simulations to support the main results obtained.

Suggested Citation

  • Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:255-267
    DOI: 10.1016/j.amc.2015.11.077
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    Cited by:

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    9. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    10. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.
    11. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    12. 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).
    13. 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.
    14. Liu, Chao & Wang, Luping & Zhang, Qingling & Li, Yuanke, 2018. "Modeling and dynamical analysis of a triple delayed prey–predator–scavenger system with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1216-1239.
    15. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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