A model of an optimal control for a discrete-time of brain drain

Abstract

In this paper, we focus on the study of a mathematical model of the phenomenon of professional skills emigration in a region, by proposing a dynamic system model of non-linear differential equations in discrete time, considering four types of variables named: Permanents, Candidates, Emigrants, and Returnees. Our relevant objective is to find an optimal strategy to minimize the number of qualified individuals leaving their territory as well as candidates considering leaving their territory. The characterization of the optimal control analysis is based on Pontryagin’s maximum principle, aimed at characterizing an optimal control that minimizes the number of Emigrants and potential Candidates for emigration, in order to maximize the number of Returnees and Permanents. Numerical simulation was performed using MATLAB. Consequently, numerical illustrations of the obtained results are presented, confirming the effectiveness of the optimization strategy followed.