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Analysis of a hybrid switching SVIR epidemic model with vaccination and Lévy noise

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  • Cao, Zhongwei
  • Shi, Yuee
  • Wen, Xiangdan
  • Liu, Liya
  • Hu, Jingwei

Abstract

This paper is concerned with the dynamical behavior of a hybrid switching SVIR epidemic model with vaccination and Lévy noise. Besides a standard geometric Brownian motion, another two driving processes are considered: a stationary Poisson point process and a continuous time finite-state Markov chain. To begin with, we obtain sufficient conditions for persistence in the mean of the disease. Then we establish sufficient conditions for extinction of the disease. Furthermore, in the case of persistence, we also obtain sufficient conditions for the existence of positive recurrence of the solutions by constructing a suitable stochastic Lyapunov function with regime switching.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315626
    DOI: 10.1016/j.physa.2019.122749
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
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    8. Liu, Qun & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 140-147.
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    Cited by:

    1. El Attouga, Sanae & Bouggar, Driss & El Fatini, Mohamed & Hilbert, Astrid & Pettersson, Roger, 2023. "Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).

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