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Atangana Baleanu Caputo Fractional Order Modeling and Analysis for the Transmission of Coffee Berry Disease |
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PP: 229-243 |
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doi:10.18576/pfda/110202
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Author(s) |
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Abayneh Kebede Fantaye,
Kokobe Teferedegn Ergete,
Faisal Alshowaikh,
Mohamed Hafez,
Betty Wan Niu Voon,
Shawkat Alkhazaleh,
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Abstract |
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| Coffee Berry Diseases (CBD) pose significant threats to coffee production worldwide, affecting the livelihoods of millions of farmers and the global coffee market. Fractional calculus provides a powerful framework for describing non-local and memory- dependent phenomena, making it suitable for modeling the long-range interactions inherent in CBD spread. This study aims to formulate and analyze fractional order model for CBD transmission dynamics in the sense of Atangana Baleanu Caputo (ABC). Fixed point theorems were utilized to test the existence and uniqueness of the model’s solutions using the Caputo operator. The basic reproduction number was calculated utilizing the next-generation matrix. The model has locally asymptotically stable equilibrium positions (disease- free and endemic). Furthermore, the Lyapunov function was used to conduct a global stability analysis of the equilibrium locations. A numerical simulation of the CBD model was created using the fractional Adam-Bashforth-Moulton approach to validate the analytical findings. Our findings contribute to the development of more accurate predictive models and inform the design of targeted interventions to mitigate the impact of CBD on coffee production systems.
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