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

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

Physica A: Statistical Mechanics and its Applications, 2023, vol. 618, issue C

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.

Keywords: Stochastic SIRS epidemic model; Lévy noise; General nonlinear incidence; Extinction; Persistence (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:618:y:2023:i:c:s037843712300256x

DOI: 10.1016/j.physa.2023.128701

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