Spatiotemporal Spread of Infectious Diseases and Intra- or Intertransmission: A Gravity Model Approach

We use the gravity model to explain the spatiotemporal patterns of the spread of three infectious diseases: SARS-CoV, influenza A (H1N1), and SARS-CoV-2 (also known as COVID-19). We log-linearise the gravity model to run a negative binomial regression analysis that describes the relationship between the cumulative number of confirmed cases within a 10-day window and socioeconomic variables such as population size, gross domestic product per capita, and distance between capital cities and the city where the first confirmed case was reported (i.e., Hong Kong, Mexico City, and Wuhan). We also introduce two additional variables, the number of confirmed cases with a 1- day lag and a restriction dummy variable which is coded as 1 after a government introduces a policy to restrict the entry of foreign nationals and otherwise 0, to control for internal transmission and the emergence of multiple sources of transmission. For all three infectious diseases, population and economic variables are positively related to the cumulative number of confirmed cases within a 10-day window. The values for these variables are also statistically significant at any conventional significance level throughout the transmission period. However, the significance of geographical distance varies. In the early stage when there is a single geographical source of transmission, the further the distance from the origin, the lower the cumulative number of confirmed cases. In the intermediate stage where transmission of the disease is explosive, there are multiple geographical sources and the distance variable loses its explanatory power. In the containment stage where the spread of disease is more likely to occur within a country, not between countries, geographical distance becomes statistically significant again and is positively associated with the cumulative number of confirmed cases. The gravity model can be effectively used to explain the spatiotemporal dynamics of infectious disease transmission.