The first case of COVID-19 that was confirmed in Wuhan, Hubei Province China on December 31, 2019, rapidly spread worldwide. Understanding the factors that affect the time it takes for the first COVID-19 infection to be observed will help countries consider the courses of action that they should take in the early stages of the next pandemic. Vigdorovits (2020) considered a gravity model that expressed time to first case as a function of multiple socio-economic factors. Assuming that objective variables follow a Gompertz distribution, he estimated the parameters of the gravity model using accelerated failure time (AFT) survival analysis. However, the distribution of the time to the first case is a bimodal distribution. Therefore, in this study, we estimated the parameters using a bimodal regression model. Our analysis shows that in the early stage of the outbreak, the infection spread to Asian countries that are close to China and to developed countries in Europe and the United States due to the movement of people by airplane. This finding is different from those of previous studies. We have also found that after the middle period of infection, cases spread to countries with large populations in Africa and South America.

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  In this paper, we define some indicators to evaluate and compare spatial data structures. Echelon dendrogram generated by Echelon analysis is used for visualization of the spatial data structure. First, we focus on the shape of the Echelon dendrogram and create a “pattern”. The “pattern” can quantitatively evaluate the spatial data structure using six indicators. In addition, we defined a “stage” of patterned dendrograms to assess changes in the data structure over time. The “stage” is analyzed assuming data that changes over time, such as population, plant reproduction, and pollutant concentration. As the dendrogram becomes more complex, the number of stages increases. Finally, the effectiveness was confirmed by analyzing, evaluating and comparing the data of the 23 wards of Tokyo using the “pattern” and “stage” defined in this paper.

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