Deep learning-based parameter estimation of high spatial resolution mathematical models for the spread and control of COVID-19 in Germany

新冠肺炎大流行清楚地表明了传染病暴发的时空动态可能遵循哪些复杂的模式。控制和减轻暴发的干预措施的业务决策要求对疾病传播的快速风险评估。拟议的项目将提供和使用基于计算数据的传染病在多个空间尺度上传播的评估和预测工具。我们的研究小组在新冠肺炎大流行的第一年开发和应用的数学技术为拟议的科学项目奠定了坚实的方法学基础。重要的是，这些方法并不局限于新冠肺炎，而是可以被改编成描述不同疾病的传播。将使用的所有数据源在项目时间内都是安全的，并且团队过去已经使用过。 的范围从小的感染聚集性到扩散演化，控制传染病浪潮需要在地方(例如，一个县或城市的特定地区)以及在更大的(例如，区域或全国)范围内采取干预措施。这一项目将使用高空间分辨率的传染病传播数学模型，丰富了报告的监测和流动数据，以描述正在发生的疫情并实现短期预测。该项目旨在描述在几个空间尺度上传播的时间疾病，空间分辨率有了很大提高。第一个空间尺度是由成熟的数学模型(Barbarossa Group)提供的，该模型使用德国联邦各州的数据(每周预报，见)。下一个更精细的级别将在县(Landkreise)级别使用相同的疾病动力学模型。具有最高空间分辨率的最精细级别将在奥斯纳布吕克县(以及项目第二阶段后期的奥尔登堡)的县级别上。为此，挑战有三个方面。首先，必须调整数学(机械)模型，以考虑多个空间尺度和相互作用的地理区域上的社会经济和人口特征。其次，这种复杂模型的适应需要数据高效的模型拟合和处理不完全知识的能力。第三，我们需要根据完全由数据驱动的方法来评估性能。为了应对这些挑战，我们将使用机器学习工具来估计模型参数，并将机械模型预测(Barbarossa组)与PIPA组完全数据驱动的贝叶斯回归相结合。

The COVID-19 pandemic has made clear which complex patterns the spatio-temporal dynamics of an infectious disease outbreak can follow. Operational decisions for intervention measures to control and mitigate an outbreak require a rapid risk assessment of the disease spread. The proposed project will provide and use computational data-based evaluation and prediction tools of infectious disease spread on multiple spatial scales. Mathematical techniques developed and applied by our research groups during the first year of the COVID-19 pandemic constitute a solid methodological basis for the proposed scientific project. Importantly, the methods do not restrict to COVID-19 but can be adapted to describe the spread of different diseases. All data sources that will be used are secured for the project time and have been already used by the team in the past.   Ranging from small clusters of infection to diffuse evolution, controlling an infectious wave calls for intervention measures on a local (e.g. a specific district of a county or a city) as well as on a larger (e.g. regional or national) scale. Mathematical models for the spread of infectious diseases on high spatial resolution, enriched with reported surveillance and mobility data, will be used in this project to describe an ongoing outbreak and to enable short term forecasts. The project is designed to describe the temporal disease spread on several spatial scales with a large improvement in spatial resolution. The first spatial scale is provided by well-established mathematical models (Barbarossa group, that use data on the level of Federal States of Germany (weekly forecast, see ). The next finer level will use the same disease dynamics models on the level of counties (Landkreise). The finest level with the highest spatial resolution will be on the level of districts of the counties of Osnabrück (and Oldenburg in the later second phase of the project). To this end the challenge is threefold. Firstly, the mathematical (mechanistic) models must be adapted to account for socio-economic and demographic features over multiple spatial scales and interacting geographic areas. Secondly, the adaptation of such complex models requires data efficient model fitting and the ability to deal with incomplete knowledge. Thirdly, we need to assess the performance against a fully data driven approach. To tackle these challenges, we will use machine learning tools to estimate model parameters and combine mechanistic models predictions (Barbarossa group) with fully data-driven Bayesian regression by the Pipa group.