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Counts of SARS-CoV-2-related deaths have been key numbers for justifying severe political, social and economical measures imposed by authorities world-wide. A particular focus thereby was the concomitant excess mortality (EM), i.e. fatalities above the expected all-cause mortality (AM). Recent studies, inter alia by the WHO, estimated the SARS-CoV-2-related EM in Germany between 2020 and 2021 as high as 200 000. In this study, we attempt to scrutinize these numbers by putting them into the context of German AM since the year 2000. We propose two straightforward, age-cohort-dependent models to estimate German AM for the ‘Corona pandemic’ years, as well as the corresponding flu seasons, out of historic data. For Germany, we find overall negative EM of about −18 500 persons for the year 2020, and a minor positive EM of about 7000 for 2021, unveiling that officially reported EM counts are an exaggeration. In 2022, the EM count is about 41 200. Further, based on NAA-test-positive related death counts, we are able to estimate how many Germans have died due to rather than with CoViD-19; an analysis not provided by the appropriate authority, the RKI. Through 2020 and 2021 combined, our due estimate is at no more than 59 500. Varying NAA test strategies heavily obscured SARS-CoV-2-related EM, particularly within the second year of the proclaimed pandemic. We compensated changes in test strategies by assuming that age-cohort-specific NAA-conditional mortality rates during the first pandemic year reflected SARS-CoV-2-characteristic constants.
Die Geometrie unseres Anschauungsraumes – die euklidische Geometrie – ist für einen allgemeinbildenden Mathematikunterricht elementar. Seitens der Mathematiklehrkraft stellt grundsätzlich ihr Fachwissen das Fundament des Unterrichtens dar. Als Teil ihres Professionswissens sollten Mathematiklehrkräfte prinzipiell über ein Fachwissen verfügen, das in Bezug zur akademischen Mathematik den unterrichtlichen Anforderungen der schulischen Mathematik gerecht wird.
Die im Rahmen der Dissertation entwickelte Theorie des metrisch-normalen euklidischen Raumes charakterisiert sich in ihrer perspektivischen Dualität, der mathematischen Stringenz eines axiomatisch-deduktiven Vorgehens auf der einen und der Berücksichtigung der fachdidaktischen Anforderungen an Mathematiklehrkräfte auf der anderen Seite; sie hebt sich darin von bestehenden Theorien ab.
In the last years, the public interest in epidemiology and mathematical modeling of disease spread has increased - mainly caused by the COVID-19 pandemic, which has emphasized the urgent need for accurate and timely modelling of disease transmission. However, even prior to that, mathematical modelling has been used for describing the dynamics and spread of infectious diseases, which is vital for developing effective interventions and controls, e.g., for vaccination campaigns and social restrictions like lockdowns. The forecasts and evaluations provided by these models influence political actions and shape the measures implemented to contain the virus.
This research contributes to the understanding and control of disease spread, specifically for Dengue fever and COVID-19, making use of mathematical models and various data analysis techniques. The mathematical foundations of epidemiological modelling, as well as several concepts for spatio-temporal diffusion like ordinary differential equation (ODE) models, are presented, as well as an originally human-vector model for Dengue fever, and the standard (SEIR)-model (with the potential inclusion of an equation for deceased persons), which are suited for the description of COVID-19. Additionally, multi-compartment models, fractional diffusion models, partial differential equations (PDE) models, and integro-differential models are used to describe spatial propagation of the diseases.
We will make use of different optimization techniques to adapt the models to medical data and estimate the relevant parameters or finding optimal control techniques for containing diseases using both Metropolis and Lagrangian methods. Reasonable estimates for the unknown parameters are found, especially in initial stages of pandemics, when little to no information is available and the majority of the population has not got in contact with the disease. The longer a disease is present, the more complex the modelling gets and more things (vaccination, different types, etc.) appear and reduce the estimation and prediction quality of the mathematical models.
While it is possible to create highly complex models with numerous equations and parameters, such an approach presents several challenges, including difficulties in comparing and evaluating data, increased risk of overfitting, and reduced generalizability. Therefore, we will also consider criteria for model selection based on fit and complexity as well as the sensitivity of the model with respect to specific parameters. This also gives valuable information on which political interventions should be more emphasized for possible variations of parameter values.
Furthermore, the presented models, particularly the optimization using the Metropolis algorithm for parameter estimation, are compared with other established methods. The quality of model calculation, as well as computational effort and applicability, play a role in this comparison. Additionally, the spatial integro-differential model is compared with an established agent-based model. Since the macroscopic results align very well, the computationally faster integro-differential model can now be used as a proxy for the slower and non-traditionally optimizable agent-based model, e.g., in order to find an apt control strategy.