Analysis of a fractional-order mathematical model for occupational transition from farming to other sectors

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.