Title: Qualitative analysis of a fractional model for HBV infection with capsids and adaptive immunity

Authors: Moussa Bachraoui; Khalid Hattaf; Noura Yousfi

Addresses: Faculty of Sciences Ben M'sik, Laboratory of Analysis, Modeling and Simulation (LAMS), Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca, Morocco ' Centre Régional des Métiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco ' Faculty of Sciences Ben M'sik, Laboratory of Analysis, Modeling and Simulation (LAMS), Hassan II University of Casablanca, P.O. Box 7955 Sidi Othman, Casablanca, Morocco

Abstract: This paper presents a mathematical model governed by fractional differential equations (FDEs) that describes the dynamics of hepatitis B virus (HBV) infection in within human body. The FDE model takes into account the HBV DNA-containing capsids, and the adaptive immunity mediated by cytotoxic T lymphocytes (CTL) cells and antibodies. Also, the incidence of infection is presented by Hattaf-Yousfi functional response that includes various forms existing in the literature. Moreover, the qualitative properties of the FDE model is rigorously established. Finally, numerical simulations are presented to support the theoretical results.

Keywords: HBV infection; adaptive immunity; fractional differential equations; Caputo fractional derivative; Hattaf-Yousfi functional response; global dynamics.

DOI: 10.1504/IJDSDE.2022.123410

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.2, pp.146 - 162

Received: 05 Jun 2019
Accepted: 23 Jun 2020
Published online: 20 Jun 2022 *

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