Human migration networks and policy interventions: bringing population distributions in line with system optimization

In this paper, we demonstrate that, through policy interventions, in the form of subsidies, a system-optimum for a multiclass human migration network can be achieved, despite the migrants, who can be refugees, behaving in a user-optimized manner. The formulation and analysis are conducted using variational inequality theory. The policy intervention allows governmental decision-makers to moderate the flow of migrants while enhancing societal welfare. An algorithm is proposed and applied to compute the solutions to a series of numerical examples, with changes in initial populations and utility functions, inspired by a pandemic, followed by a natural disaster.