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.
Beyer, R.M., Schewe, J., & Lotze-Campen, H. (2022). Gravity models do not explain, and cannot predict, international migration dynamics. Humanities and Social Sciences Communications, 9(1):56. https://doi.org/10.1057/s41599-022-01067-x
Clark, G.L., & Ballard, K.P. (1980). Modeling out-migration from depressed regions: The significance of origin and destination characteristics. Environment and Planning A, 12(7):799-812. https://doi.org/10.1068/a120799
Cymbranowicz, K. (2018). “Fortress Europe” or “Open Door Policy”-attempts to solve the refugee and migration crisis in the European union in 2011-2017. International Business and Global Economy, 37(1):53-70. https://doi.org/10.4467/23539496IB.18.004.9377
David, F.N., & Johnson, N.L. (1952). The truncated poisson. Biometrics, 8(4):275-285. https://doi.org/10.2307/3001863
Faus, J., & Landauro, I. (2021). Spain Vows to Restore Order After Thousands Swim into Ceuta from Morocco. Reuters. Available from: https://www.reuters.com/world/europe/ spain-deploys-army-ceuta-patrol-border-with-morocco-after-migrants-break-2021-05-18 [Last accessed on 2023 Mar 03].
Greenhill, K.M. (2010). Weapons of Mass Migration: Forced Displacement, Coercion, and Foreign Policy. New York: Cornell University Press.
Greenhill, K.M. (2016). Migration as a weapon in theory and in practice. Military Review, 96(6):23-36.
Greenhill, K.M. (2021). Morocco “Weaponized” Migration to Punish Spain. That’s More Common than you Think. The Washington Post. Available from: https://www. washingtonpost.com/politics/2021/06/01/morocco-weaponized-migration-punish-spain-thats-more-common-than-you-think [Last accessed on 2023 Mar 02].
Greenwood, M.J. (1985). Human migration: Theory, models, and empirical studies. Journal of Regional Science, 25(4):521-544. https://doi.org/10.1111/j.1467-9787.1985.tb00321.x
Ho, M.S.D., & Wijnkoop, M. (2022). The Instrumentalization of Migration. A Geopolitical Perspective and Toolbox. Clingendael. Netherlands Institute of International Relations. Available from: https://www.clingendael.org/ sites/default/files/2022-12/report_the_instrumentalization_ of_migration.pdf [Last accessed on 2023 Oct 25].
INE. (2023). Foreign Migrations. National Results. Available from: https://www.ine.es/jaxit3/tabla.htm?t=24306&l=1 [Last accessed on 2023 Mar 13].
Koca, B.T. (2015). Deconstructing Turkey’s “open door” policy towards refugees from Syria. Migration Letters, 12(3):209-225. https://doi.org/10.33182/ml.v12i3.275
La Información. (2020). Noviembre Marca Récord de Llegadas de Migrantes a Canarias en un mes: 8.157. [November Marks a Record for Migrant Arrivals to the Canary Islands in One Month: 8,157]. Available from: https://www.lainformacion. com/asuntos-sociales/noviembre-marca-record-llegadas-inmigrantes-canarias/2822712 [Last accessed on 2023 Oct 25] [Article in Spanish].
Lee, E.S. (1966). A theory of migration. Demography, 3(1):47-57. https://doi.org/10.2307/2060063
Letouzé E, Purser M, Rodríguez F, et al., 2009, Revisiting the Migration-Development Nexus: A Gravity Model Approach. United Nations Development Programme. Human Development Research Paper (HDRP) Series, Vol. 44. p1–42. Available from: https://hdr.undp.org/system/ files/documents/hdrp200944pdf.pdf [Last accessed on 2023 Oct 25].
Masucci, A.P., Serras, J., Johansson, A., & Batty, M. (2013). Gravity versus radiation models: On the importance of scale and heterogeneity in commuting flows. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 88(2):022812. https://doi.org/10.1103/physreve.88.022812
Ministerio del Interior (España). (2023). Number of Foreigners Entering Spanish Territory by Sea without Authorization Between 1999 and 2022 [Graph]. Statista. Available from: https://www.statista.com/statistics/1187510/irregular-immigrants-arriving-in-spain-by-sea [Last accessed on 2023 Mar 03].
Noulas, A., Scellato, S., Lambiotte, R., Pontil, M., & Mascolo, C. (2012). A tale of many cities: Universal patterns in human urban mobility. PLoS One, 7(9):e37027. https://doi.org/10.1371/journal.pone.0037027
Real Decreto 629/2022 de 26 de Julio, por el que se modifica el Reglamento de la Ley Orgánica 4/2000, sobre derechos y libertades de los extranjeros en España y su integración social, tras su reforma por Ley Orgánica 2/2009, aprobado por el Real Decreto 557/2011, de 20 de Abril. [Royal Decree 629/2022 of July 26, which modifies the Regulation of Organic Law 4/2000, on the rights and freedoms of foreigners in Spain and their social integration, after its reform by Organic Law 2/2009, approved by Royal Decree 557/2011, of April 20]. Boletín Oficial del Estado, 27 de julio de 2022, num. 179:107697-107715. Available from: https:// www.boe.es/eli/es/rd/2022/07/26/629 [Last accessed on 2023 Mar 05]. [Article in Spanish].
Real Decreto 903/2021 de 19 de Octubre, por el que se modifica el Reglamento de la Ley Orgánica 4/2000, sobre derechos y libertades de los extranjeros en España y su integración social, tras su reforma por Ley Orgánica 2/2009, aprobado por el Real Decreto 557/2011, de 20 de abril. [Royal Decree 903/2021 of October 19, which modifies the Regulation of Organic Law 4/2000, on the rights and freedoms of foreigners in Spain and their social integration, after its reform by Organic Law 2/2009, approved by Royal Decree 557/2011, of April 20]. Boletín Oficial del Estado, 19 de Diciembre de 2021, núm. 303 (2015), 119702-119716. Available from: https://www.boe.es/eli/es/rd/2021/10/19/903 [Last accessed on 2023 Mar 04] [Article in Spanish].
Robinson, C., & Dilkina, B. (2018). A Machine Learning Approach to Modeling Human Migration. In: Proceedings of the 1st ACM SIGCAS Conference on Computing and Sustainable Societies. COMPASS ’18. Association for Computing Machinery, Menlo Park and San Jose, USA, pp.1-8. https://doi.org/10.1145/3209811.3209868
Schneider, M. (1959). Gravity models and trip distribution theory. Papers in Regional Science, 5(1):51-56. https://doi.org/10.1111/j.1435-5597.1959.tb01665.x
Steger, N.D. (2017). The Weaponization of Migration: Examining Migration as a 21st Century Tool of Political Warfare [Master’s Thesis, Naval Postgraduate School, Monterey, California]. Available from: https://apps.dtic.mil/dtic/tr/ fulltext/u2/1053475.pdf [Last accessed on 2023 Oct 25].
Stouffer, S.A. (1940). Intervening opportunities: A theory relating mobility and distance. American Sociological Review, 5(6):845-867. https://doi.org/10.2307/2084520
Torres, R., & Fernández, M.J. (2021). La economía Española en recuperación: Oportunidades y desafíos [The Spanish economy in recovery: Opportunities and challenges]. Cuadernos de Información Económica, 283:1-10. Available from: https://www.funcas.es/articulos/la-economia-espanola-en-recuperacion-oportunidades-y-desafios [Last accessed on 2023 Mar 13] [Article in Spanish].
Torres, S., Company, R., & Jódar, L. (2022). Modeling immigration in Spain: Causes, size and consequences. Mathematics, 10(9):1371. https://doi.org/10.3390/math10091371
United Nations Office on Drugs and Crime. (2017). The Concept of “Financial or Other Material Benefit” in the Smuggling of Migrants Protocol. Available from: https://www.unodc. org/documents/human-trafficking/migrant-smuggling/ issue-papers/unodc_issue_paper_the_profit_element_in_ the_smuggling_of_migrants_protocol.pdf [Last accessed on 2023 Mar 01].
Yang, Y., Herrera, C., Eagle, N., & González, M.C. (2014). Limits of predictability in commuting flows in the absence of data for calibration. Scientific Reports, 4(1):5662. https://doi.org/10.1038/srep05662
Yiğiter, A., & İnal, C. (2006). Right truncated homogeneous poisson process. Pakistan Journal of Statistics, 22(1):69-78.
Zipf, G.K. (1946). The P1 P2/D hypothesis: On the intercity movement of persons. American Sociological Review, 11(6):677-686. https://doi.org/10.2307/2087063