An intentional random mathematical model for immigration: A case study of Spain

This paper presents a random discrete mathematical population model for immigration. This model incorporates not only rational factors, such as the economic gradient between destination and origin countries, geographical factors, and regulatory laws but also hidden intentional factors, such as the political interests of governments and the involvement of migrant smuggling by criminal organizations, which exploit immigration as a strategic tool. These non-rational factors are modeled as sudden, random arrival flow waves, represented by a Poisson distribution. The study’s time frame is short to ensure the reliability of economic forecasts for the coming years. Although the study focuses on Spain, the proposed approach is applicable to other geographic areas with appropriate data. The results obtained from this model can be applied to predict the national budget necessary for host countries to address this complex social phenomenon.