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Abstract
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The prime objective of the current study is to propose a novel mathematical framework
under the fractional-order derivative, which describes the complex within-host behavior of SARS-CoV-
2 by taking into account the effects of memory and carrier. To do this, we formulate a mathematical
model of SARS-CoV-2 under the Caputo fractional-order derivative. We derived the conditions for
the existence of equilibria of the model and computed the basic reproduction number R0. We used
mathematical analysis to establish the proposed model’s local and global stability results. Some
numerical resolutions of our theoretical results are presented. The main result of this study is that
as the fractional derivative order increases, the approach of the solution to the equilibrium points
becomes faster. It is also observed that the value of R0 increases as the value of b and pv increases.
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