Modelos matemáticos del decrecimiento poblacional por migración: Uso de funciones lineales y exponenciales decrecientes

This study stems from the growing relevance of migration as a demographic, economic, and social phenomenon that directly impacts the population structure of communities. This led to the design of linear models, useful in stable scenarios, and exponential models, suitable for migration crisis contexts characterized by abrupt reductions. The results show that the linear model reflects a constant and predictable decline, while the exponential model captures the accelerated dynamics of migration, with a sharp initial drop followed by stabilization. The combination of both approaches, along with the inclusion of mixed models and additional variables (public policies, employment, international agreements), allows for a more analytical representation of migration dynamics. The use of computer simulations with software such as R and Python is also highlighted, as they facilitate scenario projection and parameter validation. The findings reveal the academic and practical value of the research, guiding urban planning, the formulation of inclusive policies, and the management of demographic crises. This underscores the urgent need to adopt interdisciplinary approaches that integrate mathematics, sociology, and economics to understand the complexity of migration and its socioeconomic repercussions