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The COVID-19 outbreak has called for renewed attention to the need for sound statistical analyses to monitor mortality patterns and trends over time. Excess mortality has been suggested as the most appropriate indicator to measure the overall burden of the pandemic in terms of mortality. As such, excess mortality has received considerable interest since the outbreak of COVID-19 began. Previous approaches to estimate excess mortality are somewhat limited, as they do not include sufficiently long-term trends, correlations among different demographic and geographic groups, or autocorrelations in the mortality time series. This might lead to biased estimates of excess mortality, as random mortality fluctuations may be misinterpreted as excess mortality. We propose a novel approach that overcomes the named limitations and draws a more realistic picture of excess mortality. Our approach is based on an established forecasting model that is used in demography, namely, the Lee-Carter model. We illustrate our approach by using the weekly age- and sex-specific mortality data for 19 countries and the current COVID-19 pandemic as a case study. Our findings show evidence of considerable excess mortality during 2020 in Europe, which affects different countries, age, and sex groups heterogeneously. Our proposed model can be applied to future pandemics as well as to monitor excess mortality from specific causes of death.

The future development of population size and structure is of importance since planning in many areas of politics and business is conducted based on expectations about the future makeup of the population. Countries with both decreasing mortality and low fertility rates, which is the case for most countries in Europe, urgently need adequate population forecasts to identify future problems regarding social security systems as one determinant of overall macroeconomic development. This contribution proposes a stochastic cohort-component model that uses simulation techniques based on stochastic models for fertility, migration and mortality to forecast the population by age and sex. We specifically focused on quantifying the uncertainty of future development as previous studies have tended to underestimate future risk.The model is applied to forecast the population of Germany until 2045. The results provide detailed insight into the future population structure, disaggregated into both sexes and age groups. Moreover, the uncertainty in the forecast is quantified as prediction intervals for each subgroup.

Data Quality is, in essence, understood as the degree to which the data of interest satisfies the requirements, is free of flaws, and is suited for the intended purpose. Data Quality is usually measured utilizing several criteria, which may differ in terms of assigned importance, depending on, e.g., the data at hand, stakeholders, or the intended use.

Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number ( R t ) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in R t until August 2020. Implications of state-specific R t on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

School-level infection control measures in Germany during the early Coronavirus Disease 2019 (COVID-19) pandemic differed across the 16 federal states and lacked a dependable evidence base, with available evidence limited to regional data restricted to short phases of the pandemic. This study aimed to assess the (a) infection risks in students and staff; (b) transmission risks and routes in schools; (c) effects of school-level infection control measures on school and population infection dynamics; and (d) contribution of contacts in schools to population cases. For this retrospective observational study, we used German federal state (NUTS-2) and county (NUTS-3) data from public health and education agencies from March 2020 to April 2022. We assessed (a) infection risk as cumulative risk and crude risk ratios and (b) secondary attack rates (SARs) with 95% confidence interval (CI). We used (c) multiple regression analysis for the effects of infection control measures such as reduced attendance, mask mandates, and vaccination coverage as absolute reduction in case incidence per 100,000 inhabitants per 14 days and in percentage relative to the population, and (d) infection dynamic modelling to determine the percentage contribution of school contacts to population cases. We included (a) nationwide NUTS-2 data from calendar weeks (W) 46-50/2020 and W08/2021-W15/2022 with 3,521,964 cases in students and 329,283 in teachers; (b) NUTS-3 data from W09-25/2021 with 85,788 student and 9,427 teacher cases; and (c) detailed data from 5 NUTS-3 regions from W09/2020 to W27/2021 with 12,814 cases (39% male, 37% female; median age 14, range 5 to 63), 43,238 contacts and 4,165 secondary cases for students (for teachers, 14,801 [22% male, 50% female; median age 39, range 16 to 75], 5,893 and 472). Infection risk (a) for students and teachers was higher than the population risk in all phases of normal presence class and highest in the early 2022 omicron wave with 30.6% (95% CI 30.5% to 32.6%) of students and 32.7% (95% CI 32.6% to 32.8%) of teachers infected in Germany. SARs (b) for students and staff were below 5% in schools throughout the study period, while SARs in households more than doubled from 13.8% (95% CI 10.6% to 17.6%) W21-39/2020 to 28.7% (95% CI 27% to 30.4%) in W08-23/2021 for students and 10.9% (95% CI 7% to 16.5%) to 32.7% (95% CI 28.2% to 37.6%) for staff. Most contacts were reported for schools, yet most secondary cases originated in households. In schools, staff predominantly infected staff. Mandatory surgical mask wearing during class in all schools was associated with a reduction in the case incidence of students and teachers (c), by 56/100,000 persons per 14 days (students: 95% CI 47.7 to 63.4; teachers: 95% CI 39.6 to 71.6; p < 0.001) and by 29.8% (95% CI 25% to 35%, p < 0.001) and 24.3% (95% CI 13% to 36%, p < 0.001) relative to the population, respectively, as were reduced attendance and higher vaccination coverage. The contribution of contacts in schools to population cases (d) was 2% to 20%, lowest during school closures/vacation and peaked during normal presence class intervals, with the overall peak early during the omicron wave. Limitations include underdetection, misclassification of contacts, interviewer/interviewee dependence of contact-tracing, and lack of individual-level confounding factors in aggregate data regression analysis. In this study, we observed that open schools under hygiene measures and testing strategies contributed up to 20% of population infections during the omicron wave early 2022, and as little as 2% during vacations/school closures; about a third of students and teachers were infected during the omicron wave in early 2022 in Germany. Mandatory mask wearing during class in all school types and reduced attendance models were associated with a reduced infection risk in schools.

Demographic aging puts social insurance systems under immense pressure as frailty risks increase with age. The statutory long-term care insurance in Germany (GPV), whose society has been aging for decades due to low fertility and decreasing mortality, faces massive future pressure. The present study presents a stochastic outlook on long-term care insurance in Germany until 2045 by forecasting the future number of frail persons who could claim insurance services by severity level with theory-based Monte Carlo simulations. The simulations result in credible intervals for age-, sex- and severity-specifc care rates as well as the numbers of persons for all combinations of age, sex and severity by defnition of the GPV on an annual basis. The model accounts for demographic trends through time series analysis and considers all realistic epidemiological developments by simulation. The study shows that increases in the general prevalence of disabilities, especially for severe disabilities, caused by the demographic development in Germany are unavoidable, whereas the infuence of changes in agespecifc care risks does not afect the outcome signifcantly. The results may serve as a basis for estimating the future demand for care nurses and the fnancial expenses of the GPV.

Demographic aging results in a growing number of older people in need of care in many regions all over the world. Germany has witnessed steady population aging for decades, prompting policymakers and other stakeholders to discuss how to fulfill the rapidly growing demand for care workers and finance the rising costs of long-term care. Informed decisions on this matter to ensure the sustainability of the statutory long-term care insurance system require reliable knowledge of the associated future costs. These need to be simulated based on well-designed forecast models that holistically include the complexity of the forecast problem, namely the demographic transition, epidemiological trends, concrete demand for and supply of specific care services, and the respective costs. Care risks heavily depend on demographics, both in absolute terms and according to severity. The number of persons in need of care, disaggregated by severity of disability, in turn, is the main driver of the remuneration that is paid by long-term care insurance. Therefore, detailed forecasts of the population and care rates are important ingredients for forecasts of long-term care insurance expenditures. We present a novel approach based on a stochastic demographic cohort-component approach that includes trends in age- and sex-specific care rates and the demand for specific care services, given changing preferences over the life course. The model is executed for Germany until the year 2050 as a case study.

Regional fertility forecasts are important for long-term planning in a variety of fields that include future birth numbers in their forecast, such as school or kindergarten planning. They are one of the major components of regional population forecasts as well. Therefore, it is important to construct reliable forecasts that are based on sophisticated models that cover the high complexity of future regional fertility. We suggest a novel forecast model for forecasting regional age-specific fertility rates that covers long-term trends by time series models, demographic and regional correlations by principal component analysis, and future uncertainty by Monte Carlo simulation. The model is applied to all German NUTS-3 regions (districts/Kreise) simultaneously, where we forecast all regional age-specific fertility rates through the period of 2022–2045. The results from the simulations are presented via median predictions with 75% prediction intervals of the regional total fertility rates. The simulation shows strong regional heterogeneities in long-term fertility trends that are associated with the historical background of Germany, housing supply for families, opportunities for education, and the strength of labor markets, inter alia.

Substantiated knowledge of future demographic changes that is derived from sound statistical and mathematical methods is a crucial determinant of regional planning. Of the components of demographic developments, migration shapes regional demographics the most over the short term. However, despite its importance, existing approaches model future regional migration based on deterministic assumptions that do not sufficiently account for its highly probabilistic nature. In response to this shortcoming in the literature, our paper uses age- and gender-specific migration data for German NUTS-3 regions over the 1995–2019 period and compares the performance of a variety of forecasting models in backtests. Using the best-performing model specification and drawing on Monte Carlo simulations, we present a stochastic forecast of regional migration dynamics across German regions until 2040 and analyze their role in regional depopulation. The results provide evidence that well-known age-specific migration patterns across the urban-rural continuum of regions, such as the education-induced migration of young adults, are very likely to persist, and to continue to shape future regional (de)population dynamics.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.