Dynamics of a generalized age-structured model for HBV infection with capsids in presence of two treatments

Volume 34, Issue 3, pp 243--256 https://dx.doi.org/10.22436/jmcs.034.03.04

Publication Date: March 18, 2024 Submission Date: December 07, 2023 Revision Date: January 15, 2024 Accteptance Date: February 09, 2024

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Authors

E. M. Warrak - 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

The main aim of this paper is to propose and analyze the dynamics of a generalized age-structured model for hepatitis B virus (HBV) infection with HBV DNA-containing capsids and two treatments. Such treatments are pegylated interferon and lamivudine drugs which are used to block new infections of liver cells and stop viral infection. We first investigate the existence and uniqueness of solutions to the proposed model, as well as the existence of equilibria. Furthermore, the uniform persistence and the stability analysis are rigorously established by means of characteristic equations and Lyapunov functionals.

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Keywords

• HBV infection
• age-structure
• general incidence rate
• uniform persistence
• stability analysis

MSC

•  35B35
•  37C75
•  92D25

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