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Threshold of a stochastic SIR epidemic model with Lévy jumps

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  • Zhou, Yanli
  • Zhang, Weiguo

Abstract

This paper mainly investigates the effect of the Lévy jumps on the dynamics of a stochastic SIR epidemic model. Taking the accumulated jump size into account, a threshold of the considered model has been found out, denoted by R˜0, which can determine the extinction and persistence in mean of the epidemic. More specifically, if R˜0<1, the disease ultimately vanishes from the population; whereas if R˜0>1, the disease persists in the population. Numerical simulations have been carried out to illustrate the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:446:y:2016:i:c:p:204-216
    DOI: 10.1016/j.physa.2015.11.023
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    1. 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.
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    Cited by:

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    3. Cheng, Yan & Li, Mingtao & Zhang, Fumin, 2019. "A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 62-70.
    4. Bao, Kangbo & Zhang, Qimin & Rong, Libin & Li, Xining, 2019. "Dynamics of an imprecise SIRS model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 489-506.
    5. Chen, Xingzhi & Xu, Xin & Tian, Baodan & Li, Dong & Yang, Dan, 2022. "Dynamics of a stochastic delayed chemostat model with nutrient storage and Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    6. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.
    7. Li, Xiaoyang & Huang, Guohe & Wang, Shuguang & Zhang, Xiaoyue & Luo, Bin, 2025. "Synergistic Management of Water, energy, and carbon: A case Study from Shandong Province, China," Applied Energy, Elsevier, vol. 381(C).
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    9. Marina Bershadsky & Leonid Shaikhet, 2025. "Stability Analysis of a Mathematical Model for Infection Diseases with Stochastic Perturbations," Mathematics, MDPI, vol. 13(14), pages 1-14, July.
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    11. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2024. "A novel SIRS epidemic model for two diseases incorporating treatment functions, media coverage, and three types of noise," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    12. 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.
    13. 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.
    14. Sabbar, Yassine & Kiouach, Driss & Rajasekar, S.P. & El-idrissi, Salim El Azami, 2022. "The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    15. Liu, Chao & Tian, Yilin & Chen, Peng & Cheung, Lora, 2024. "Stochastic dynamic effects of media coverage and incubation on a distributed delayed epidemic system with Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    16. Zhao, Zhuoying & Zhang, Xinhong, 2025. "Unraveling the transmission mechanism of animal disease: Insight from a stochastic eco-epidemiological model driven by Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    17. Mario Lefebvre, 2024. "Modeling and Optimal Control of Infectious Diseases," Mathematics, MDPI, vol. 12(13), pages 1-12, July.

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