Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets
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Date
2022-06
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Abstract
Fractional order and fractal order are mathematical tools that can be used to model realworld
problems. In order to demonstrate the usefulness of these operators, we develop
a new fractal-fractional model for the propagation of the Zika virus. This model includes
insecticide-treated nets and the generalized fractal-fractional Mittag-Leffler kernel. The
existence, uniqueness, and Ulam–Hyres stability conditions for the given system are
determined. Using the Newton polynomial, the numerical scheme is described. From
the numerical simulations, we notice that a change in the fractal-fractional order directly
affects the dynamics of the Zika virus. We also notice that the use of fractal order only
converges to faster than the use of fractional order only. Testing the inherent potency of
insecticide-treated nets when the fractal-fractional order is 0.99 indicates that increased
use of insecticide-treated nets increases the number of healthy humans. The fractalfractional
analysis captures the geometric pattern of the Zika virus that is repeated at
every scale, which cannot be captured by classical geometry. This backs up the idea that
the best way to control the disease is to know enough about how it spread in the past.
Description
This article is published by Elsevier 2022 and is also available at https://doi.org/10.1016/j.physa.2022.127809
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Physica A 603 (2022) 127809