An Inversion of the Constitution of the Baidu Migration Scale Index

Abstract

Baidu migration scale index represents the human migration scale of a specific area in China, and it has been used widely in geo-economics, demography, and epidemiology. Nowadays, Baidu migration index is adopted as a key data source for studying epidemic models of COVID-19. But the index is just a dimensionless number, its constitution method is still ambiguous. In this paper, the index is assumed as an elementary function mapping result of the real human migrate populations. According to a hidden equation existing in the data set, the mapping function is deduced to be a linear function y=kx. Another key phenomenon in the data set is the minimum interval of the migration index. All the migration index values and their differentials are exactly divisible by this interval. Through Fermat-Euler Theorem, we prove the coprimeness of the human migrate populations, and then the relationship between the minimum interval and minimum counting unit of the migrate populations is built, which means k=3.24×10−5. In the experiments, the migration records between 01/01/2020−04/30/2020 are examined to verify the correctness of the hidden equation: while the rounding error is considered, there about 93.81% of the city-to-city migration records, 82.65% city-to-province migration records and 84.87% province-to-province migration records can support the equation exactly;the maximum absolute error of the violation records is 357 peoples, which corresponds to about 0.5% relative error. The verifications support the self-consistency of the proposed linear mapping function. Copyright ©2020 Journal of University of Electronic Science and Technology of China. All rights reserved.