A generalized viral immunological model in presence of adaptive immunity with lytic and non-lytic effects

Volume 34, Issue 1, pp 11--26 https://dx.doi.org/10.22436/jmcs.034.01.02

Publication Date: February 12, 2024 Submission Date: September 28, 2023 Revision Date: November 23, 2023 Accteptance Date: January 03, 2024

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Authors

M. I. El Karimi - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P.O. Box 7955 Sidi Othman, Casablanca, Morocco. K. Hattaf - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P. O. Box 7955, Sidi Othman, Casablanca, Morocco. - Equipe de Recherche en Modelisation et Enseignement des Mathematiques (ERMEM), Centre Regional des Metiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco. N. Yousfi - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P. O. Box 7955, Sidi Othman, Casablanca, Morocco.

Abstract

This article develops a new mathematical model that describes the dynamics of viral infections in presence of adaptive immunity. The developed model accounts for the presence of a non-cytolytic cure and considers both cell-to-cell and virus-to-cell transmission modes, along with the lytic and non-lytic effects of both cellular and humoral immune responses. Moreover, the well-posedness of the model is demonstrated through the non-negativity and boundedness of its solutions. Also, five equilibriums are established and five threshold parameters are derived to ensure the global stability of these equilibria. Finally, the dynamics of the model have been shown through numerical illustrations using specific parameters related to human immunodeficiency virus (HIV) infection.

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Keywords

• Immunology
• viral infection
• mode of transmission
• mathematical modeling
• global stability

MSC

•  34A12
•  34D05
•  34D23
•  92B05

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