On the modeling of migration phenomena on small networks

Abstract

This paper deals with the modeling of migration phenomena in a small network of nations, with the aim of investigating the influence that the wealth and the welfare policies have on this phenomena. The modeling approach is based on the kinetic theory of active particles, while individuals over the network are distinguished by a scalar variable (the activity) which expresses their social state. The dynamics is induced both by the communication of individuals over the network and by the welfare policy within each nation, which is expressed in terms of competitive and altruistic interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The existence and uniqueness of the solution is discussed and some specific case-studies are proposed in order to carry out simulations and to investigate the emerging behaviors.