Fractional-order model of the post-disaster period: study on the earthquakes in Türkiye
Abstract
In this study, the mathematical model that examined the relationships between the variables of the population that continued to live in the disaster area, the population that migrated to another region, the number of newly built independent sections in the disaster area the post-disaster, and the socio-economic development index (SEDI) of the disaster area is expressed through fractional-order differential equations (FODEs) and qualitative analysis of the model is carried out. Furthermore, the relationship between migrated and non-migrated populations is presented in the model with four different functional responses. In real-world applications of the model, some earthquakes in Türkiye, which are similar to each other in many ways, are taken into account. Therefore, data after the Gölcük earthquake in 1999 are used, and parameters, derivative order, and functional response are determined by considering the minimum root mean squared error (RMSE). Then, the performance of the proposed model with these values is shown in the Elbistan earthquake in 2023. Finally, the 5-year and 10-year estimates of the non-migratory population, the migrated population, the number of newly built independent sections, and the SEDI index values are presented for Elbistan.
Keywords
Fractional-order differential equation, functional response, earthquakes; socio-economic development index, root mean squared error
Project Number
TUBITAK 123F220
Thanks
This study was supported by the Scientific and Technological Research Council of Türkiye (TUBITAK) under the Grant Number 123F220. The authors thank to TUBITAK for their support.
References
- [1] Chaudhary, M.T. and Piracha, A. Natural disasters-origins, impacts, management. Encyclopedia, 1(4), 1101-1131, (2021).
- [2] Asian Disaster Reduction Center. Natural disaster data book 2022 (an analytical overview). (2022). https://www.adrc.asia/publications/databook/ORG/databook_2022/ pdf/DataBook2022.pdf
- [3] AFAD, Afet Türleri, (2023). https://www.afad.gov.tr/afet-turleri
- [4] Verdière, N., Lanza, V., Charrier, R., Provitolo, D., Dubos-Paillard, E., Bertelle, C. and Alaoui, A. Mathematical modeling of human behaviors during catastrophic events. In Proceedings, 4th International Conference on Complex Systems and Applications (ICCSA), pp. 67-74, Le Havre, France, (2014, June).
- [5] Paul, B.K. Evidence against disaster-induced migration: the 2004 tornado in north-central Bangladesh. Disasters, 29(4), 370-385, (2005).
- [6] Tuncer, G. Türkiye’de sosyo-ekonomik gelişmişliğin mekânsal eşitsizliği. Journal of Economics Public Finance Business, 2(2), 69-80, (2019).
- [7] Boğaziçi University, Kandilli Observatory and Earthquake Research Institute, Regional Earthquake-Tsunami Monitoring and Evaluation Center, (2024). http://udim.koeri.boun. edu.tr/zeqmap/hgmmap.asp
- [8] Ozaslan, M., Dincer, B. and Ozgur, H. Regional disparities and territorial indicators in Turkey: Socio-economic development index (SEDI). In Proceedings, 46th Congress of the European Regional Science Association: "Enlargement, Southern Europe and the Mediterranean" (ERSA), pp. 1-34, Volos, Greece, (2006, August).
- [9] Du, M., Wang, Z. and Hu, H. Measuring memory with the order of fractional derivative. Scientific Report, 3, 3431, (2013).
- [10] Avci, D., Ozdemir, N. and Yavuz, M. Fractional optimal control of diffusive transport acting on a spherical region. In Methods of Mathematical Modelling (pp. 63-82). Boca Raton, USA: CRC Press, (2019).