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The Threshold of a Stochastic SIQR Epidemic Model with Lévy Jumps

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Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics

Abstract

The government policy has always attached importance to the control of the infectious diseases in the population. The analysis of a stochastic SIQR epidemic model provides us a useful tool for controlling many diseases. Unfortunately, the previous model cannot be applied to massive diseases, such as avian influenza. Therefore, we need to improve it. In this paper, we take the lead in using the stochastic differential equation with Lévy jumps to study the asymptotic behavior of the stochastic SIQR model. Taking the accumulated jump size into account, the threshold of our epidemic model is investigated. Then, we establish sufficient conditions for persistence in mean and extinction of the disease. Numerical examples are realized to confirm the theoretical results.

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Authors and Affiliations

  1. MSTI Team, High School of Technology, Ibn Zohr University, Agadir, Morocco

    Driss Kiouach & Yassine Sabbar

Authors
  1. Driss Kiouach
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  2. Yassine Sabbar
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Corresponding author

Correspondence to Yassine Sabbar .

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Editors and Affiliations

  1. Federal University of Rio de Janeiro, President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Rio de Janeiro, Brazil

    Rubem P. Mondaini

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Kiouach, D., Sabbar, Y. (2019). The Threshold of a Stochastic SIQR Epidemic Model with Lévy Jumps. In: Mondaini, R. (eds) Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-23433-1_7

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