The outbreak of COVID-19 disrupts the life of many people in the world. The state of Arizona in the U.S. emerges as one of the country’s newest COVID-19 hot spots. Accurate forecasting for COVID-19 cases will help governments to implement necessary measures and convince more people to take personal precautions to combat the virus. It is difficult to accurately predict the COVID- 19 cases due to many human factors involved. This paper aims to provide a forecasting model for COVID-19 cases with the help of human activity data from the Google Community Mobility Reports. To achieve this goal, a specific partial differential equation (PDE) is developed and validated with the COVID-19 data from the New York Times at the county level in the state of Arizona in the U.S. The proposed model describes the combined effects of transboundary spread among county clusters in Arizona and human activities on the transmission of COVID-19. The results show that the prediction accuracy of this model is well acceptable (above 94%). Furthermore, we study the effectiveness of personal precautions such as wearing face masks and practicing social distancing on COVID-19 cases at the local level. The localized analytical results can be used to help to slow the spread of COVID- 19 in Arizona. To the best of our knowledge, this work is the first attempt to apply PDE models on COVID-19 prediction with the Google Community Mobility Reports.

中文翻译：

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使用带有Google Mobility数据的偏微分方程预测亚利桑那州的COVID-19

COVID-19的爆发破坏了世界上许多人的生活。美国亚利桑那州已成为该国最新的COVID-19热点之一。对COVID-19病例的准确预测将有助于政府实施必要的措施，并说服更多的人采取个人预防措施来对抗这种病毒。由于涉及许多人为因素，因此很难准确预测COVID-19病例。本文旨在借助Google Community Mobility Reports中的人类活动数据为COVID-19病例提供预测模型。为实现此目标，开发了特定的偏微分方程（PDE），并使用了美国亚利桑那州县级《纽约时报》的COVID-19数据进行了验证。提出的模型描述了亚利桑那州各县之间跨界传播与人类活动对COVID-19传播的综合影响。结果表明，该模型的预测准确性是可以接受的（超过94％）。此外，我们研究了个人预防措施的有效性，例如戴着口罩和在地方一级对COVID-19病例进行社交疏远。本地化的分析结果可用于帮助缓解COVID-19在亚利桑那州的扩散。据我们所知，这项工作是首次尝试通过Google社区移动性报告将PDE模型应用于COVID-19预测。我们研究了个人预防措施（例如戴口罩和在地方一级对COVID-19病例进行社交疏远）的有效性。本地化的分析结果可用于帮助缓解COVID-19在亚利桑那州的扩散。据我们所知，这项工作是首次尝试通过Google社区移动性报告将PDE模型应用于COVID-19预测。我们研究了个人预防措施（例如戴着口罩和在地方一级对COVID-19病例进行社交疏远）的有效性。本地化的分析结果可用于帮助缓解COVID-19在亚利桑那州的扩散。据我们所知，这项工作是首次尝试通过Google社区移动性报告将PDE模型应用于COVID-19预测。