Spatiotemporal dynamics of RNA viruses in the presence of immunity and treatment: case of SARS-CoV-2

2024;
: pp. 518–527

Revised: May 21, 2024
Accepted: May 28, 2024

El Karimi M. I., Hattaf K., Yousfi N. Spatiotemporal dynamics of RNA viruses in the presence of immunity and treatment: case of SARS-CoV-2.  Mathematical Modeling and Computing. Vol. 11, No. 2, pp. 518–527 (2024)

Authors:
1
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)
2
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca; Equipe de Recherche en Modélisation et Enseignement des Mathématiques (ERMEM), 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

In this paper, we develop a mathematical model using partial differential equations to investigate the behavior of RNA viruses in the presence of antiviral treatment.  The developed model includes both cell-to-cell and virus-to-cell modes of transmission.  Initially, we establish the well-posedness of the model by demonstrating the existence and uniqueness of solutions, as well as their positivity and boundedness.  Additionally, we identify and analyze the stable equilibrium states, their global stability depending on specific threshold parameters, using Lyapunov functions.  To corroborate our theoretical findings, we provide illustrations through numerical simulations.

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