A Variational Formulation for a Human Migration Problem

Many social and economical factors affect the dynamics of human populations, such as poverty, violence, war, dictatorships, persecutions, tsunamis, floods, earthquakes, family reunification as well as economic and educational possibilities or a job. In this paper, we consider a network based model where the aim of each migration class is to maximize the attractivenss of the origin country and we prove that the optimization model can be formulated in terms of a Nash equilibrium problem and a variational inequality. Finally, some numerical results applied to the human migration from Africa to Europe are presented and analyzed.