The effect of interurban movements on the spatial distribution of population

Abstract

Understanding how interurban movements can modify the spatial distribution of the population is important for transport planning but is also a fundamental ingredient for epidemic modeling. We illustrate this on vacation trips for all transportation modes in China during the Lunar New Year and compare the results for 2019 with the ones for 2020 where travel bans were applied for mitigating the spread of a novel coronavirus (COVID-19). We first show that inter-urban travel flows are broadly distributed and display both large temporal and spatial fluctuations, making their modeling very difficult. When flows are larger, they appear to be more dispersed over a larger number of origins and destinations, creating de facto hubs that can spread an epidemic at a large scale. These movements quickly induce (in about a week for this case) a very strong population concentration in a small set of cities. We characterize quantitatively the return to the initial distribution by defining a pendular ratio which allows us to show that this dynamics is in general very slow and even stopped for the 2020 Lunar New Year due to travel restrictions. Travel restrictions obviously limit the spread of the diseases between different cities, but have thus the counter-effect of keeping high concentration in a small set of cities, a priori favoring intra-city spread, unless individual contacts are strongly limited. These results shed some light on the statistics of interurban movements and how they modify the national distribution of populations, a crucial ingredient for devising effective control strategies at a national level.