Risk Index of Regional Infection Expansion of COVID-19: Moving Direction Entropy Study Using Mobility Data and Its Application to Tokyo
Authors: Ohsawa Yukio , Sun Yi , Sekiguchi Kaira , Kondo Sae , Maekawa Tomohide , Takita Morihito , Tanimoto Tetsuya , Kami Masahiro 
Published: July 2024

Background
Policies, such as stay home, bubbling, and stay with your community, recommending that individuals reduce contact with diverse communities, including families and schools, have been introduced to mitigate the spread of the COVID-19 pandemic. However, these policies are violated if individuals from various communities gather, which is a latent risk in a real society where people move among various unreported communities.

Objective
We aimed to create a physical index to assess the possibility of contact between individuals from diverse communities, which serves as an indicator of the potential risk of SARS-CoV-2 spread when considered and combined with existing indices.

Methods
Moving direction entropy (MDE), which quantifies the diversity of moving directions of individuals in each local region, is proposed as an index to evaluate a region’s risk of contact of individuals from diverse communities. MDE was computed for each inland municipality in Tokyo using mobility data collected from smartphones before and during the COVID-19 pandemic. To validate the hypothesis that the impact of intercommunity contact on infection expansion becomes larger for a virus with larger infectivity, we compared the correlations of the expansion of infectious diseases with indices, including MDE and the densities of supermarkets, restaurants, etc. In addition, we analyzed the temporal changes in MDE in municipalities.

Results
This study had 4 important findings. First, the MDE values for local regions showed significant invariance between different periods according to the Spearman rank correlation coefficient (>0.9). Second, MDE was found to correlate with the rate of infection cases of COVID-19 among local populations in 53 inland regions (average of 0.76 during the period of expansion). The density of restaurants had a similar correlation with COVID-19. The correlation between MDE and the rate of infection was smaller for influenza than for COVID-19, and tended to be even smaller for sexually transmitted diseases (order of infectivity). These findings support the hypothesis. Third, the spread of COVID-19 was accelerated in regions with high-rank MDE values compared to those with high-rank restaurant densities during and after the period of the governmental declaration of emergency (P<.001). Fourth, the MDE values tended to be high and increased during the pandemic period in regions where influx or daytime movement was present. A possible explanation for the third and fourth findings is that policymakers and living people have been overlooking MDE.

Conclusions
We recommend monitoring the regional values of MDE to reduce the risk of infection spread. To aid in this monitoring, we present a method to create a heatmap of MDE values, thereby drawing public attention to behaviors that facilitate contact between communities during a highly infectious disease pandemic.