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Dynamics of an imprecise SIRS model with Lévy jumps

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Listed:
  • Bao, Kangbo
  • Zhang, Qimin
  • Rong, Libin
  • Li, Xining

Abstract

Sudden environmental perturbations may affect population dynamics. Parameters of mathematical models can also be imprecise due to uncertainties and unknown data. How sudden environmental noise and parameter imprecision influence the dynamics of epidemic systems remains unclear. This paper studies a stochastic Susceptible–Infected–Recovered–Susceptible (SIRS) model that includes Lévy jumps and interval parameters. We prove that the model has a unique global positive solution. Sufficient conditions for persistence and extinction of the disease are obtained. Large noise intensity is able to suppress the emergence of disease outbreaks. Numerical simulations are carried out to show the influence of stochastic noise on disease dynamics. These results suggest that Lévy jumps and imprecise parameters can greatly affect the long-term behavior of the epidemic system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:520:y:2019:i:c:p:489-506
    DOI: 10.1016/j.physa.2019.01.027
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    References listed on IDEAS

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    1. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
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    Cited by:

    1. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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