Time evolution and convergence of simple migration models

Abstract

In this project, we consider two of the most fundamental mobility models, Gravity and Radiation model, and investigate their long-term trends. The analysis consists of determining the model's steady states and investigating their temporal dynamics for different applications and scenarios. We find that a simple Gravity model results in two different long-term solutions, depending on its parametrization, which are independent of spatial population divisions and initial population distributions. The Radiation model on the other hand shows a strong dependency on spatial properties, due to its usage of intervening opportunities. We find that the dynamics differ significantly when it is applied to gridded population division or on population distribution divided into heterogeneous administrative units, like national counties or municipalities.