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Abstract
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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 (Br) and the reproductive number for humoral immune response (RH) as a natural
reaction of antibodies. We support the analytical results through numerical simulations.
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