No abstract

The COVID-19 pandemic has kept the world in suspense for the past months. In most federal countries such as Germany, locally varying conditions demand for state- or county-level decisions. However, this requires a deep understanding of the meso-scale outbreak dynamics between micro-scale agent models and macro-scale global models. Here, we introduce a reparameterized SIQRD network model that accounts for local political decisions to predict the spatio-temporal evolution of the pandemic in Germany at county and city resolution. Our optimized model reproduces state-wise cumulative infections and deaths as reported by the Robert-Koch Institute, and predicts development for individual counties at convincing accuracy. We demonstrate the dominating effect of local infection seeds, and identify effective measures to attenuate the rapid spread. Our model has great potential to support decision makers on a state and community politics level to individually strategize their best way forward.

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.

The COVID-19 pandemic has kept the world in suspense for the past year. In most federal countries such as Germany, locally varying conditions demand for state- or county-level decisions to adapt to the disease dynamics. However, this requires a deep understanding of the mesoscale outbreak dynamics between microscale agent models and macroscale global models. Here, we use a reparameterized SIQRD network model that accounts for local political decisions to predict the spatiotemporal evolution of the pandemic in Germany at county resolution. Our optimized model reproduces state-wise cumulative infections and deaths as reported by the Robert Koch Institute and predicts the development for individual counties at convincing accuracy during both waves in spring and fall of 2020. We demonstrate the dominating effect of local infection seeds and identify effective measures to attenuate the rapid spread. Our model has great potential to support decision makers on a state and community politics level to individually strategize their best way forward during the months to come.

In this contribution, the accuracy and efficiency of various modeling assumptions and numerical settings in thermo-mechanical simulations of powder bed fusion (PBF) processes are analyzed. Thermo-mechanical simulations are used to develop a better understanding of the process and to determine residual stresses and distortions based on the temperature history. In these numerically very complex simulations, modeling assumptions are often made that reduce computational effort but lead to inaccuracies. These assumptions include the omission of the surrounding powder or the use of geometrically linearized material models. The numerical setting, in particular the temporal and spatial discretizations, can further lead to discretization errors. Here, a highly parallelized and adaptive finite element method based on the open source C++ library deal.II is validated and utilized, to investigate some of these modeling assumptions and to identify the required temporal and spatial discretizations for the simulation of PBF of Ti-6Al-4V. The insights initially gained on a simple wall-like geometry are transferred to a larger open rectangular profile where the results of a detailed simulation are compared with those of a more efficient one. The results for the efficient approach show a maximum deviation of $$\approx 8\%$$ ≈ 8 % in the displacements and $$\approx 3.5\%$$ ≈ 3.5 % in the residual stresses while significantly reducing the computational time.