The COVID-19 pandemic has led to an unprecedented world-wide effort to gather data, model, and understand the viral spread. Entire societies and economies are desperate to recover and get back to normality. However, to this end accurate models are of essence that capture both the viral spread and the courses of disease in space and time at reasonable resolution. Here, we combine a spatially resolved county-level infection model for Germany with a memory-based integro-differential approach capable of directly including medical data on the course of disease, which is not possible when using traditional SIR-type models. We calibrate our model with data on cumulative detected infections and deaths from the Robert-Koch Institute and demonstrate how the model can be used to obtain county- or even city-level estimates on the number of new infections, hospitality rates and demands on intensive care units. We believe that the present work may help guide decision makers to locally fine-tune their expedient response to potential new outbreaks in the near future.

中文翻译：

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Covid-19 的基于内存的中尺度建模

COVID-19 大流行在全球范围内引发了前所未有的努力，以收集数据、建模和了解病毒传播。整个社会和经济都迫切希望恢复并恢复正常。然而，为此，准确的模型至关重要，它能够以合理的分辨率在空间和时间上捕捉病毒传播和疾病进程。在这里，我们将德国的空间分辨县级感染模型与基于记忆的整合差分方法相结合，该方法能够直接包含有关疾病过程的医学数据，这在使用传统的 SIR 类型模型时是不可能的。我们使用来自罗伯特-科赫研究所的累积检测到的感染和死亡数据来校准我们的模型，并演示如何使用该模型来获得县级甚至市级对新感染数量的估计，招待费率和重症监护病房的需求。我们相信，目前的工作可能有助于指导决策者在不久的将来在当地微调他们对潜在新疫情的权宜之计反应。