Global stability of a fractional virus infection model in the presence of humoral immunity and two classes of infected cell

Global stability of a fractional virus infection model

Résumé

‎It is well known that the benefit of fractional differentiation‎ ‎makes strong utility to model natural realities with vast range‎

‎memory‎, ‎hereditary properties‎, ‎and viral infections such as SARS‎, ‎COVID‎, ‎HIV‎, ‎and Dengue fever‎. ‎According to biological evidence‎,

‎complicated systems are more inclined to stability in comparison‎ ‎to simple systems‎, ‎so in this article‎, ‎we focused on a fractional‎ ‎derivative order system‎. ‎Adequate qualifications for the global‎ ‎steady state of stationary‎ ‎points of a Caputo fractional derivative order system with Beddington-DeAngelis functional response will be obtained by using Lyapunov's‎ ‎method and LaSalle's invariance principle‎. ‎We prove the global stability of the equilibria of the system by the values of the primary reproductive number $({B_r})$‎ ‎and the reproductive number for humoral immune response $(R_{H})$ as a natural reaction of antibodies‎. ‎We support the analytical results through numerical simulations‎.