Spatiotemporal dynamics of a fractional model for hepatitis B virus infection with cellular immunity

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.

^* Corresponding author: k.hattaf@yahoo.fr

Received: 25 May 2020
Accepted: 19 December 2020

Abstract

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.