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Analysis of a Stochastic SIR Model with Vaccination and Nonlinear Incidence Rate

Author

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  • Amine El Koufi
  • Jihad Adnani
  • Abdelkrim Bennar
  • Noura Yousfi

Abstract

We expand an SIR epidemic model with vertical and nonlinear incidence rates from a deterministic frame to a stochastic one. The existence of a positive global analytical solution of the proposed stochastic model is shown, and conditions for the extinction and persistence of the disease are established. The presented results are demonstrated by numerical simulations.

Suggested Citation

  • Amine El Koufi & Jihad Adnani & Abdelkrim Bennar & Noura Yousfi, 2019. "Analysis of a Stochastic SIR Model with Vaccination and Nonlinear Incidence Rate," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-9, August.
    • Handle: RePEc:hin:jnijde:9275051
    DOI: 10.1155/2019/9275051
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    Cited by:

    1. Caroline Hillairet & Olivier Lopez, 2021. "Propagation of cyber incidents in an insurance portfolio: counting processes combined with compartmental epidemiological models," Post-Print hal-02564462, HAL.
    2. Caroline Hillairet & Olivier Lopez, 2020. "Propagation of cyber incidents in an insurance portfolio: counting processes combined with compartmental epidemiological models," Working Papers hal-02564462, HAL.

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