No abstract

Non-pharmaceutical interventions (NPIs) are important to mitigate the spread of infectious diseases as long as no vaccination or outstanding medical treatments are available. We assess the effectiveness of the sets of non-pharmaceutical interventions that were in place during the course of the Coronavirus disease 2019 (Covid-19) pandemic in Germany. Our results are based on hybrid models, combining SIR-type models on local scales with spatial resolution. In order to account for the age-dependence of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we include realistic prepandemic and recently recorded contact patterns between age groups. The implementation of non-pharmaceutical interventions will occur on changed contact patterns, improved isolation, or reduced infectiousness when, e.g., wearing masks. In order to account for spatial heterogeneity, we use a graph approach and we include high-quality information on commuting activities combined with traveling information from social networks. The remaining uncertainty will be accounted for by a large number of randomized simulation runs. Based on the derived factors for the effectiveness of different non-pharmaceutical interventions over the past months, we provide different forecast scenarios for the upcoming time.

The simulation of the Liquid Composite Moulding process is an important step for the manufacturing of composites with textile reinforcements. However, its fast direct numerical simulation is impossible on the microscale due to computational complexity reasons. We have to resort to the macroscale instead. Here, an essential task is the fast and accurate prediction of the permeability of textile microstructures. For textiles composed of impermeable yarns, we discuss the homogenisation of the Stokes equations. This leads to Darcy's law on the macroscale and gives the permeability via the so-called unit cell problems. These equations are then discretised and solved numerically. For textiles composed of permeable yarns, their dual porosity is accounted for by a fictitious domain approach in form of the Stokes/Brinkman equations. The results of our permeability computations in textiles are validated and compared to experimental data.

Non-pharmaceutical interventions (NPIs) are important to mitigate the spread of infectious diseases as long as no vaccination or outstanding medical treatments are available. We assess the effectiveness of the sets of non-pharmaceutical interventions that were in place during the course of the Coron-avirus disease 2019 (Covid-19) pandemic in Germany. Our results are based on hybrid models, combining SIR-type models on local scales with spatial resolution. In order to account for the age-dependence of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we include realistic pre-pandemic and recently recorded contact patterns between age groups. The implementation of non-pharmaceutical interventions will occur on changed contact patterns, improved isolation, or reduced infectiousness when, e.g., wearing masks. In order to account for spatial heterogeneity, we use a graph approach and we include high-quality information on commuting activities combined with traveling information from social networks. The remaining uncertainty will be accounted for by a large number of randomized simulation runs. Based on the derived factors for the effectiveness of different non-pharmaceutical interventions over the past months, we provide different forecast scenarios for the upcoming time.Mathematics Subject Classification (2010) 00A72 · 65L05 · 68U20