Browsing by Author "Essel, John Fiifi"

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    A fractional order age-specific smoke epidemic model
    (Elsevier, 2023) Addai, Emmanuel; Asamoah, Joshua Kiddy K.; Zhang, Lingling; Essel, John Fiifi; 0000-0002-7066-246X
    This paper presents a nonlinear fractional mathematical model for the smoke epidemic that includes two age groups. To solve the smoke epidemic, the Atangana-Baleanu-Caputo fractional derivative is used. The Banach and Krasnoselskii type fixed point theorem is used to determine existence and uniqueness. We explored model stability using the Hyers-Ulam form of stability. Using Lagrange interpolation, the behaviour of the smoke epidemic of the 2-age group model is generated. The numerical simulation shows that the model has po- tential for both groups, and that age-specific interventions can be used to reduce smoking rates in the general population.
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    Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets
    (2022-06) Addai, Emmanuel; Zhang, Lingling; Ackora-Prah, Joseph; Gordon, Joseph Frank; Asamoah, Joshua Kiddy K.; Essel, John Fiifi; 0000-0002-7066-246X
    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.