The Threshold of a Stochastic SIQR Epidemic Model with Lévy Jumps

Driss Kiouach () and Yassine Sabbar ()
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Driss Kiouach: Ibn Zohr University, MSTI Team, High School of Technology
Yassine Sabbar: Ibn Zohr University, MSTI Team, High School of Technology

A chapter in Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics, 2019, pp 87-105 from Springer

Abstract: 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.

Keywords: Epidemic model; Lévy jumps; Threshold; Persistence in mean; Extinction (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-23433-1_7

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DOI: 10.1007/978-3-030-23433-1_7

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