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Dynamic Analysis of SLIR Model Describing the Effectiveness of Quarantine Against the Spread of COVID-19

In: Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells

Author

Listed:
  • Omar Khyar

    (Mohammedia University Hassan II-Casablanca, Department of Mathematics, Faculty of Sciences and Technology)

  • Karam Allali

    (Mohammedia University Hassan II-Casablanca, Department of Mathematics, Faculty of Sciences and Technology)

Abstract

The disease caused by COVID-19 was declared a pandemic by the World Health Organization on March 11, 2020. Identified for the first time in the city of Wuhan, the Chinese authorities have mandated a quarantine strategy in the city of Wuhan in order to limit the spread of COVID-19 in a wider spectrum. Inspired by this prevention protocol against this new virus, the majority of the countries in the world have also adopted strict quarantine measures to fight against this new coronavirus pneumonia. In this article, we will establish a six-compartment SLIR model taking into account quarantine strategy, in which the dynamics of the COVID-19 epidemic is modeled by a system of six nonlinear differential equations, describing the interactions between susceptible, exposed, infected, and recovered. The basic reproduction number R 0 depending on the quarantine strategy efficacy is calculated. We give the equilibrium points of the system, then we discuss, according to the value of R 0, the global stability of the equilibrium solutions. Numerical simulations are presented in order to validate our theoretical results and we discuss the effectiveness of quarantine measures in the fight against the spread of the pandemic caused by COVID-19.

Suggested Citation

  • Omar Khyar & Karam Allali, 2021. "Dynamic Analysis of SLIR Model Describing the Effectiveness of Quarantine Against the Spread of COVID-19," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, pages 243-259, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-73241-7_15
    DOI: 10.1007/978-3-030-73241-7_15
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