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Mathematical Modeling of Cholera Dynamics and Analysis Using Caputo fractional Operator with Optimal Control |
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PP: 87-117 |
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doi:10.18576/pfda/110107
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Author(s) |
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Tulu Leta Tirfe,
Legesse Lemecha Obsu,
Eshetu Dadi Gurmu,
Mohamed Hafez,
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Abstract |
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| In this study, we developed a cholera model using the Caputo fractional operator with optimal control strategies to address the dynamic nature of cholera transmission, employing bifurcation analysis. Initially, by applying fixed point theory, we analyzed the existence and uniqueness of the solutions of fractional order derivatives. Furthermore, utilizing the next-generation matrix, we computed the basic reproduction number, crucial for assessing disease dynamics. If this number falls below unity, the equilibrium point remains disease-free, both locally and globally stable, as verified through the Jacobian matrix, Metzler matrix, and Lyapunov function. Otherwise, cholera persistence equilibrium occurs. In addition, we extended the model to include optimal control by integrating three controls: a prevention effort to protect susceptible individuals from contracting the disease and Vibrio cholera, a treatment for those infected with cholera through quarantine, and water sanitation strategies to reduce infectious transmission. These controls were determined using the Pontryagin minimum principle. The model validation was done using numerical experiments. Based on the numerical simulation of fractional order, we observed that the order of derivatives has an impact on controlling disease transmission. The study of this work underscores the benefit of integrating fractional order derivatives with optimal control strategies to mitigate cholera outbreaks effectively. The proposed optimal control framework provides a systematic approach to evaluate the impact of various interventions and inform public health policies. Future research directions include model extensions to incorporate spatial heterogeneity and real-world data integration to further enhance the applicability and robustness of the control strategies.
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