Browsing by Author "Wireko, Fredrick Asenso"

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    A fractal–fractional order model for exploring the dynamics of Monkeypox disease
    (Elsevier, 2023-08) Wireko, Fredrick Asenso; Adu, Isaac Kwasi; Sebil, Charles; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246X
    This study explores the biological behaviour of the Monkeypox disease using a fractal–fractional operator. We discuss the existence and uniqueness of the solution of the model using the fixed-point concept. We further show that the Monkeypox fractal–fractional model is stable through the Hyers–Ulam and Hyers–Ulam Rassias stability criteria. The epidemiological threshold of the model is obtained. The numerical simulation for the proposed model is obtained using the Newton polynomial. For instance, the disease dies out at lower fractional values. We investigated the effects of some key parameters on the dynamics of the disease. The variation of the parameters shows that quarantine and isolation are effective approaches to managing, controlling, or eradicating the Monkeypox disease.
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    Modelling the dynamics of Ebola disease transmission with optimal control analysis
    (Springer, 2024-04) Adu, Isaac Kwasi; Wireko, Fredrick Asenso; Nana‑Kyere, Sacrifice; Appiagyei, Ebenezer; ‑Nor Osman, Mojeeb A. L.‑Rahman E. L.; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246X
    Ebola disease is a highly infectious and often deadly disease caused by the Ebola virus. Ebola can spread among humans through direct contact with the blood, secretions, organs, or other bodily fluids of infected people, as well as surfaces and materials contaminated with fluids of infected people. This article examines a non-linear mathematical model of Ebola, considering environmental contamination and safe burier. The boundedness, non-negativity, and well-posedness of the proposed model are obtained. The Ebola-free equilibrium, Ebola-present equilibrium and Ebola reproduction number ( R0 ) are determined. A sensitivity analysis is conducted on the Ebola reproduction number to identify the factors that affect the output of R0 . Furthermore, we found that the proposed Ebola model displays forward bifurcation, which means that Ebola spread can be suppressed by bringing the Ebola reproduction number down to unity. The numerical simulation of the proposed model without optimal control demonstrated that Ebola can be controlled by lowering the frequency of interaction with infectious people and contaminated environments, educating the public about Ebola reinfection, vaccinating recovered Ebola patients, and stepping up educational campaigns against funeral customs like bathing corpses. Based on these, we formulated an optimal control and a cost-effectiveness analysis was conducted on the model to establish the strategy or strategies that can be best used to control Ebola spread with a minimal cost. The study revealed that the most economical method involves personal protection, vaccination, and ensuring a secure burial.
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    Non-optimal and optimal fractional control analysis of measles using real data
    (Elsevier, 2024-07) Wireko, Fredrick Asenso; Asamoah, Joshua Kiddy K.; Adu, Isaac Kwasi; Ndogum, Sebastian; 0000-0002-7066-246X
    This study employs fractional, non-optimal, and optimal control techniques to analyze measles transmission dynamics using real-world data. Thus, we develop a fractional-order compartmental model capturing measles transmission dynamics. We then formulate an optimal control problem to minimize the disease burden while considering constraints such as vaccination resources and intervention costs. The proposed model’s positivity, boundedness, measles reproduction number, and stability are obtained. The sensitivity analysis using the partial rank correlation coefficient is shown for the fractional orders of 0.99 and 0.90. It is noticed that the rate of recruitment into the susceptible population (𝜋), the rate at which individuals in the latent class become asymptomatic (𝛼1), and the transmission rate (𝛽) contribute positively to the spread of the disease, while the rate at which individuals in the asymptomatic class become symptomatic (𝛼2), the vaccination rate for the first measles dose (𝛾1), and the rate at which individuals in the latent class recover from measles (𝛿1) contribute significantly to the reduction of measles in the community. Utilizing numerical simulations and sensitivity analyses, we identify optimal control strategies that balance the trade-offs between intervention efficacy, resource allocation, and societal costs. Our findings provide insights into the effectiveness of fractional optimal control strategies in mitigating measles outbreaks and contribute to developing more robust and adaptive disease control policies in real-world scenarios.