Caputo Fractional Modeling of Brain Drain Dynamics With Job Creation Effects: Applications to Nigeria, Pakistan, and Iran

Brain drain poses a critical threat to sustainable development in many developing nations. This study develops a Caputo-fractional-order compartmental model of emigration applied to Nigeria, Pakistan, and Iran. The model distinguishes aspirational and desperation-driven migrants, as well as successful and unsuccessful outcomes, and incorporates a logistic job-creation function to link employment opportunities with migration pressures. Analytical results establish the existence, uniqueness, and local stability of solutions, while the basic reproduction number R0 defines the threshold for sustained emigration. Using particle swarm optimization and migration data, parameter estimation and sensitivity analysis identify recruitment, emigration rates, and job creation capacity as key drivers. Simulations highlight country-specific trends: in Nigeria, limited job creation accelerates outflows; in Iran, structural sociopolitical factors prevail; and in Pakistan, persistent losses reflect poor opportunities. The fractional-order approach was employed to capture memory effects more effectively than the classical differential approach, offering a robust tool for mathematical model design.