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Numerical Investigation of Fractional Order Buruli Ulcer Model |
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PP: 17-35 |
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doi:10.18576/pfda/120102
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Author(s) |
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Mohamed A. Hafez,
Mohamed Qasymeh,
Ali Akgu ̈l,
Zafar Iqbal,
Nauman Ahmed,
Umaima Akhtar,
Betty Wan Voon,
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Abstract |
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| In this study, the transmission of buruli ulcer disease was examined. For this purpose, a classical Buruli ulcer model is converted into a fractional-order epidemic model by introducing the Caputo fractional differential operator. It was found that the system has two equilibrium points: disease-free and endemic equilibrium. Furthermore, the stability of the model is observed using a Jacobian matrix. Subsequently, the Grunwald Letnikov approximation is hybridized with a non-standard finite difference design to solve the problem. Because the state variables describe the number of individuals, they cannot be negative. The main properties of the numerical design, that is, the positivity, boundedness, and convergence towards the true equilibrium points, were investigated via simulations. Numerical graphs reflect the reliability and efficacy of the proposed numerical template. |
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