A Numerical Method for Analyzing the Effects of Migration on Regional Population Change

Migration is a crucial determinant in regional population dynamics, influencing demographic equilibrium, labor market structure, and socio-economic development. This paper presents a numerical methodology to quantify and analyze the effects of migration on regional population change using a mathematically formalized model integrating partial differential equations (PDE), numerical interpolation, and validated datasets from international population databases. The methodological framework is structured upon the spatial-temporal population balance equation, discretized via finite difference methods (FDM). An empirical application based on Eurostat’s migration and population dataset (2000–2020) evaluates the model’s effectiveness across selected European regions. The model reveals that net migration, even when marginal, exhibits nonlinear amplification effects on population projections over time due to feedback mechanisms in birth-death dynamics. The numerical simulations validate the sensitivity of regional populations to migratory trends, offering a precise computational lens for demographers and policymakers alike.This work is motivated by the work of [33-53]).