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<p>The dynamics of a SIS epidemic model with vaccination and a saturated incidence rate in specific stochastic environments are examined with vaccination and a saturated incidence rate in specific stochastic environments. The study focuses on the system’s long-term behavior and aims to establish sufficient conditions for disease extinction and persistence. In cases where persistence occurs, a stationary distribution is investigated. Additionally, it is proven that the density functions converge in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1338_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> to an invariant density under certain conditions. These results enhance understanding of the SIS epidemic model with vaccination, building upon and extending previous research in this field.</p>

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Disease Dynamics of a Probabilistic Model with Vaccination Under Regime Switching

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • T. Caraballo,
  • A. Nait Brahim,
  • A. Settati,
  • A. Lahrouz,
  • T. Amtout

摘要

The dynamics of a SIS epidemic model with vaccination and a saturated incidence rate in specific stochastic environments are examined with vaccination and a saturated incidence rate in specific stochastic environments. The study focuses on the system’s long-term behavior and aims to establish sufficient conditions for disease extinction and persistence. In cases where persistence occurs, a stationary distribution is investigated. Additionally, it is proven that the density functions converge in \(L^1\) L 1 to an invariant density under certain conditions. These results enhance understanding of the SIS epidemic model with vaccination, building upon and extending previous research in this field.