TRANSMISSION DYNAMICS OF CHOLERA DISEASE USING FRACTIONAL--ORDER MODEL
Keywords:
Cholera, fractional order derivatives, simulations, convergence, reproduction numberAbstract
Traditional epidemic models usually use integer-order derivatives, which often fail to capture inherent memory and hereditary effects involved in the transmission of diseases. This work presents a cholera model of fractional order that is formulated within the Atangana–Baleanu fractional derivative, which possesses a non-local and nonsingular kernel. The existence and uniqueness of the proposed model were analyzed uti lizing Banach’s and Krasnoselskii’s fixed point theorems, while the stability analysis results indicated that the disease-free equilibrium of the model is locally asymptotically stable if the basic reproduction number is less than unity. Numerical simulations are presented using the predictor–corrector scheme in the Atan gana–Baleanu framework, showing the significant impact of the fractional order on the system dynamics. Our results suggest that the memory-dependent transmission patterns exhibited by cholera are captured more exactly by the fractional-order formulation than its classical integer-order counterpart. Overall, this paper confirms the mathematical flexibility and improved realism of the Atangana–Baleanu fractional oper ator within the context of modeling cholera dynamics and further advances the theoretical developments underlying fractional epidemic modeling.
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