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Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model

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  • El Attouga, Sanae
  • Bouggar, Driss
  • El Fatini, Mohamed
  • Hilbert, Astrid
  • Pettersson, Roger

Abstract

A stochastic SIRS epidemic model with generalized nonlinear incidence and Lévy noise is investigated. First, we show the existence and uniqueness of a global positive solution. Then, we establish sufficient conditions for the extinction and persistence of the disease. The main results are proved under weak assumptions regarding the incidence function, the obtained results are proved under a Lévy-type perturbation without requiring the finiteness of its activity. Finally, numerical simulations are realized to illustrate the main results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:618:y:2023:i:c:s037843712300256x
    DOI: 10.1016/j.physa.2023.128701
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    References listed on IDEAS

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