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Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals

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  • Driss Kiouach
  • Yassine Sabbar

Abstract

The aim of this paper is to generalize the nonlinear incidence rate of a stochastic SIRS (susceptible-infected-recovered-susceptible) epidemic model. Our basic model was enriched with the hypotheses of vertical transmission and transfer from infected to susceptible individuals, to approach the reality. Our analysis showed that the model is well-posed. Under some conditions imposed on the intensity of the white noise perturbation, the global stability of the system is proven. Furthermore, the threshold of our model which determines the extinction and persistence of the disease is established. Numerical examples are realized to prove the rigor of our theoretical results.

Suggested Citation

  • Driss Kiouach & Yassine Sabbar, 2018. "Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-13, May.
    • Handle: RePEc:hin:jnddns:7570296
    DOI: 10.1155/2018/7570296
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    Cited by:

    1. Yassine Sabbar & Asad Khan & Anwarud Din, 2022. "Probabilistic Analysis of a Marine Ecological System with Intense Variability," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    2. Sabbar, Yassine & Kiouach, Driss & Rajasekar, S.P. & El-idrissi, Salim El Azami, 2022. "The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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