Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets. (English) Zbl 1528.92031

Addai, Emmanuel; Zhang, Lingling; Ackora-Prah, Joseph; Gordon, Joseph Frank; Asamoah, Joshua Kiddy K.; Essel, John Fiifi

Physica A 603, Article ID 127809, 31 p. (2022).

Summary: Fractional order and fractal order are mathematical tools that can be used to model real-world 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 fractal-fractional 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.

MSC:

92D30

Epidemiology

Keywords:

Zika virus; Atangana-Baleanu; Mittag-Leffler kernel; fractal-fractional derivatives; Newton polynomial; Hyers-Ulam stability

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