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

COVID-19大流行明确了传染病爆发的时空动态可以遵循哪些复杂模式。采取干预措施控制和缓解疫情的业务决策需要对疾病传播进行快速风险评估。拟议的项目将提供和使用基于计算数据的评估和预测工具，在多个空间尺度上评估和预测传染病的传播。我们的研究团队在COVID-19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提供了坚实的方法论基础。重要的是，这些方法并不局限于COVID-19，而是可以适用于描述不同疾病的传播。将使用的所有数据源在项目期间都是安全的，并且团队过去已经使用过。   从小规模的聚集性感染到扩散性演变，控制传染波需要在地方（例如县或市的特定地区）以及更大规模（例如区域或国家）上采取干预措施。本项目将使用高空间分辨率的传染病传播数学模型，并利用报告的监测和流动数据加以丰富，以描述正在发生的疫情，并进行短期预测。该项目的目的是在几个空间尺度上描述疾病传播的时间，在空间分辨率上有很大的提高。第一个空间尺度由完善的数学模型提供（Barbarossa小组，使用德国联邦州一级的数据（每周预测，见）。下一个更精细的级别将在县一级（Landkreise）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县）的地区级别。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的社会经济和人口特征。其次，这种复杂模型的自适应需要数据有效的模型拟合和处理不完整知识的能力。第三，我们需要根据完全数据驱动的方法评估性能。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，并将联合收割机机械模型预测（Barbarossa小组）与Pipa小组的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.