Box model for channels of human migration

TL;DR

This paper presents a mathematical model of human migration channels using the truncated Waring distribution, showing how migrant distribution depends on entry points and destination popularity.

Contribution

It introduces a novel application of the truncated Waring distribution to model migration flows through finite channels of countries or cities.

Findings

Migration concentration increases in popular destination countries.

The number of migrants in the channel depends on entry rates.

Large destinations attract a significant proportion of migrants.

Abstract

We discuss a mathematical model of migration channel based on the truncated Waring distribution. The truncated Waring distribution is obtained for a more general model of motion of substance through a channel containing finite number of boxes. The model is applied then for case of migrants moving through a channel consisting of finite number of countries or cities. The number of migrants in the channel strongly depends on the number of migrants that enter the channel through the country of entrance. It is shown that if the final destination country is very popular then large percentage of migrants may concentrate there.