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Abstract
In this article, we developed a fractional-order mathematical model to study the dynamics of farmers transitioning to other professions, incorporating memory effects through Caputo-type fractional derivatives. We ensured the model's biological viability by proving non-negativity and boundedness of solutions, and demonstrated existence and uniqueness using fixed-point theory. The model has non-negative equilibrium points, with local and global stability conditions analyzed. The basic reproduction number R0 was determined, showing that when R0<1, the equilibrium point E1 is locally asymptotically stable. The stability of the endemic equilibrium E* was assessed using the Routh-Hurwitz criterion. The global stability of the equilibrium points is also analyzed using the Lyapunov function. Sensitivity analysis identified optimal intervention strategies, and numerical simulations confirmed the theoretical findings.
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