Geodesic
Spatiotemporal dynamics of a fractional model for hepatitis B virus infection with cellular immunity
Moussa Bachraoui1 ; Mohamed Ait Ichou2 ; Khalid Hattaf1, 3 ; Noura Yousfi1
1 Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco.
2 Laboratory of Mathematics and Applications (LMA), École Normale Supérieure, Hassan II University of Casablanca, Casablanca, Morocco.
3 Centre Régional des Métiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco.
Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 5.

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In this paper, we propose and investigate a fractional diffusive model for hepatitis B virus (HBV) infection with capsids and immune response presented by cytotoxic T lymphocyte (CTL) cells. We derive the conditions for global asymptotic stability of the steady states of the model in terms of the basic reproduction number R0 and the immune response reproduction number R1. By constructing appropriate Lyapunov functionals, it is shown that the infection-free equilibrium is globally asymptotically stable when R0 ≤ 1, the immune-free infection equilibrium is globally asymptotically stable when R1 ≤ 1 R0 and the infection equilibrium with CTL immune response is globally asymptotically stable when R1 > 1. Numerical simulations are performed to illustrate the analytical results.
DOI : 10.1051/mmnp/2020058

Moussa Bachraoui 1 ; Mohamed Ait Ichou 2 ; Khalid Hattaf 1, 3 ; Noura Yousfi 1

1 Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco.
2 Laboratory of Mathematics and Applications (LMA), École Normale Supérieure, Hassan II University of Casablanca, Casablanca, Morocco.
3 Centre Régional des Métiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco. 
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Moussa Bachraoui; Mohamed Ait Ichou; Khalid Hattaf; Noura Yousfi. Spatiotemporal dynamics of a fractional model for hepatitis B virus infection with cellular immunity. Mathematical modelling of natural phenomena, Tome 16 (2021), article  no. 5. doi : 10.1051/mmnp/2020058. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2020058/

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