Fractional-order model of the post-disaster period: study on the earthquakes in Türkiye

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.