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Minimax Theory and its Applications 06 (2021), No. 2, 281--294
Copyright Heldermann Verlag 2021

A System-Optimization Model for Multiclass Human Migration with Migration Costs and Regulations Inspired by the Covid-19 Pandemic

Giorgia Cappello
Department of Mathematics and Computer Science, University of Catania, Italy

Patrizia Daniele
Department of Mathematics and Computer Science, University of Catania, Italy

Anna Nagurney
Department of Operations and Information Management, Isenberg School of Management, University of Massachusetts, Amherst, U.S.A.

In the last several decades, the main causes of human migration have included: poverty, war and political strife, climate change, tsunamis, earthquakes, as well as economic and educational possibilities. In this paper, we present a system-optimized network model for multiple migration classes with migration costs and regulations inspired by the Covid-19 pandemic. We derive the variational inequality formulation associated with the system-optimization problem which consists of maximizing the total societal welfare. Lagrange analysis is also performed in order to obtain a precise evaluation of the multiclass human migration phenomenon. This work adds to the literature on system-optimization of human migration in the presence of regulations and with the explicit inclusion of migration costs.

Keywords: Human migration, regulations, Covid-19 pandemic, nonlinear optimization, variational inequalities, Lagrange theory.

MSC: 46N10, 90C26, 90C33.

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