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  4. Global dynamics of a diffusive SARS-CoV-2 model with antiviral treatment and fractional Laplacian operator

Global dynamics of a diffusive SARS-CoV-2 model with antiviral treatment and fractional Laplacian operator

MMC.
2024;
Volume 11, Number 1
: pp. 319–332
https://doi.org/10.23939/mmc2024.01.319
Received: June 28, 2023
Revised: March 08, 2024
Accepted: March 10, 2024

El Hassani A., Bettioui B., Hattaf K., Achtaich N.  Global dynamics of a diffusive SARS-CoV-2 model with antiviral treatment and fractional Laplacian operator.  Mathematical Modeling and Computing. Vol. 11, No. 1, pp. 319–332 (2024)

Authors:
  1. A. El Hassani
  2. B. Bettioui
  3. K. Hattaf
  4. N. Achtaich
1
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca
2
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca; Centre Régional des Métiers de l'Education et de la Formation (CRMEF)
3
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca; Centre Régional des Métiers de l'Education et de la Formation (CRMEF)
4
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca

In this paper, we propose and investigate the global dynamics of a SARS-CoV-2 infection model with diffusion and antiviral treatment.  The proposed model takes into account the two modes of transmission (virus-to-cell and cell-to-cell), the lytic and nonlytic immune responses.  The diffusion into the model is formulated by the regional fractional Laplacian operator.  Furthermore, the global asymptotic stability of equilibria is rigorously established by means of a new proposed method constructing Lyapunov functions for a class of partial differential equations (PDEs) with regional fractional Laplacian operator.  The proposed method is applied to the classical reaction-diffusion equations with normal diffusion.

SARS-CoV-2; COVID-19; regional fractional Laplacian operator; diffusion; Lyapunov functions; global stability
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