外出自粛行動の微分方程式モデル：ベイズ統計モデリングによる都道府県別データの分析

In this paper, we propose a mathematical model to explain the sequential change in the number of people who stay at home under the spread of COVID-19. We collected data on the number of people who stay at home for each prefecture based on the location data of about 80 million cell phones. We built a differential equation model to express the characteristics of data that have multiple peaks where the derivatives change depending on the time period. By applying the differential equation model, we found the following implications: in the case where we assumed a quantity of staying at home request as a decreasing function of time, the total number of people who stayed at home was greater than in the case where we assumed an increasing function of time. Additionally, we examined the fit of the theoretical model by applying it to data collected from Tokyo, Osaka, Hokkaido, and Iwate prefectures from February 1 to July 10, 2020. Further, we benchmarked our model against a state-space model. Our model fits the data as well as the benchmark model.