Mathematical and sociological investigation of two-region migration model in bigeometric calculus

The two-region migration model is an important tool for analyzing population movements and evaluating their economic, social, and environmental impacts. This model mathematically examines the reasons and consequences of individuals that migrate from one region to another, thereby shedding light on issues such as labor force distribution, income differences, urbanization dynamics, and regional development. This migration model, which has a significant impact on classical analyses, is defined in bigeometric calculus, and solved by the bigeometric Laplace transform. In addition, the numerical patterns and curves presented by mathematical modeling in these two migration analyses are interpreted within the framework of sociological theories, thus demonstrating that the phenomenon of migration is not only quantitative but is also too complex to be limited to socially constructed numerical data and is closely linked to the historical process.