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Analysis of Cholera Model Transmission Dynamics Via Classical and ABC Fractional Derivatives |
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PP: 135-154 |
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doi:10.18576/pfda/120109
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Author(s) |
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Tulu Leta Tirfe,
Legesse Lemecha Obsu,
Eshetu Dadi Gurmu,
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Abstract |
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| This study develops a mathematical model for cholera transmission dynamics using the Susceptible -Asymptomatic -Infected- Quarantined- Recovered- Bacterium formulation,incorporating both classical and Atangana-Baleanu fractional-order derivatives. The model is expressed as a system of fractional differential equations (FDEs) to characterize the non-local memory effects inherent in cholera transmission. The well-posedness of the model is established by proving the existence, uniqueness, and positivity of solutions using fixed-point theory. The basic reproduction number is derived via the next-generation matrix method, serving as a threshold parameter to determine disease persistence or eradication. Local and global stability analyses of equilibrium states are performed using the Jacobian matrix,Metzler matrix theory, and Lyapunov function techniques. Numerical simulations employing the Adams-Moulton scheme illustrate the influence of memory-dependent dynamics,revealing that lower fractional orders slow the spread of infection by regulating bacterial growth and host-pathogen interactions. These results underscore the utility of fractional-order modeling in epidemiology, suggesting that incorporating memory effects enhances the predictive capability of disease models. Future research should focus on integrating optimal control strategies to mitigate cholera outbreaks effectively.
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