Johannes Bracher

Respiratory diseases cause considerable morbidity in autumn and winter and are a priority in public health monitoring. In Germany, they are subject to a number of surveillance systems, including both pathogen-specific and syndromic indicators. In this paper we present a collaborative multi-target and multi-model real-time forecasting system rolled out during the 2024/25 season, and discuss differences to earlier efforts carried out during the COVID-19 pandemic. We focus on general practitioner consultations for acute respiratory infections (ARI) and hospitalizations for severe acute respiratory infections (SARI), where a total of eight models were run to generate nowcasts and forecasts. In addition, we consider confirmed cases of seasonal influenza and respiratory syncytial virus (RSV) where one forecasting model each was available. As all indicators were subject to retrospective revisions, forecasting models were combined with a nowcasting step. For the SARI and ARI indicators, we combined the available models into an ensemble and conducted detailed quantitative evaluations. Nowcasts overall showed convincing performance, even though for some models Christmas break effects led to an upward bias in early January. Forecasts were overall well-calibrated and most models outperformed simple benchmark models. When taking into account age-stratified targets, most observed performance differences to a persistence baseline were statistically significant. Anticipating the peak timing and magnitude, however, proved to be challenging, with many models predicting too flat curves with a too early turnaround (e.g., in late January rather than mid-February for SARI). The combined ensemble forecast was among the best-performing approaches, but unlike in previous related projects did not consistently outperform individual models. We conclude by discussing learnings on the organization of collaborative forecasting projects in post-COVID-19 times. Author summary: Nowcasting and short-term forecasting are key tasks in epidemic modelling, and have received increasing attention from public health agencies in recent years. So-called Forecast Hubs have become a standard format to structure and coordinate modelling efforts. By collecting time-stamped predictions in standardized formats, they facilitate meaningful model comparisons and the generation of combined ensemble forecasts, which have often been found to be more robust. In this paper, we present the setup of a multi-model and multi-pathogen Forecasting Hub set up in Germany, along with detailed evaluation results for the 2024/25 season. Nowcasting models (i.e., models correcting recent incidence values for reporting delays) showed reliable performance. Forecasting models, on the other hand, mostly outperformed simple reference models, but struggled to anticipate peak timing and magnitude correctly. This paper adds to a growing body of evidence on the real-time performance of epidemic forecasts.

Time-varying effective reproductive numbers of infectious diseases are commonly estimated using renewal equation models. In the widely applied R package EpiEstim and various related tools, this approach is combined with a Poisson distributional assumption. This has been criticized on various occasions, mostly on grounds of general model realism or a desire to estimate dispersion parameters. Here, we argue that an important issue arising from the Poisson assumption is that inference about the effective reproductive number becomes overconfident in the presence of overdispersion. The extent to which standard errors are underestimated follows from theory on generalized linear models in a straightforward manner. We therefore recommend to replace the Poisson assumption by quasi-Poisson or negative binomial extensions, and contrast their respective properties. We illustrate our arguments in detailed simulation studies and three case studies on Ebola, pandemic influenza, and COVID-19.

Wastewater-based epidemiology provides a low-cost, scalable view of community infection dynamics, but converting these signals into actionable epidemiological insights remains difficult. Mechanistic models offer interpretability, yet, assumptions such as a constant transmission rate limit realism over long simulation horizons and heterogeneous settings. We present a susceptible-exposed-infectious-recovered (SEIR) universal differential equation (UDE) that links wastewater viral loads to case counts and embeds neural networks to represent time-varying parameters. Parameter and prediction uncertainties are quantified using an ensemble method. We assessed the method using newly collected data for Bonn, Germany, as well as published data for five cities in Rhineland-Palatinate, Germany. The proposed approach produces realistic out-of-sample projections of case counts over an up to 50-week test horizon, and it learns city-specific mappings to prevalence that generalise within each location. Compared to SEIR models with fixed transmission rates, the UDE captures non-stationary drivers (policy, behaviour, seasonality) without sacrificing epidemiological structure, while propagating observation and model uncertainty into the projections. Accordingly, the approach facilitates a scalable interpretation and exploitation of wastewater data for the monitoring of infectious diseases.

Background: Up-to-date real-time disease surveillance data can provide critical public health insights, however reporting delays can create downward bias in the latest data. Nowcasting methods designed to correct for this bias remain underused in public health practice due to their complexity, lack of tailored documentation, or technical barriers. Methodological advances in nowcasting are also hampered by the absence of standardised benchmarks for evaluating new methods. Methods: To address these needs, we developed a family of nowcasting methods and an accompanying R package, baselinenowcast . We validated our method against the baseline method that was used in the German COVID-19 Nowcast Hub and on which our approach was based. Using this data, we conducted an analysis to compare different specifications of our method which were designed to address common issues in epidemiology such as weekday patterns in reporting and the ability to share estimates across different strata. We used our approach on norovirus surveillance data from the United Kingdom Health Security Agency (UKHSA) and compared the performance of three of our method specifications against three methods evaluated in a previous study. Results: Our baseline method improved estimates compared to unadjusted data across all case studies. We found that the optimal choice of baseline method specification depends on context but that our default method specification performed well in a range of settings. Applied to UKHSA norovirus data, our method helped us understand the performance of the model currently used in public health practice. Conclusions: Our method and software can be used both as a straightforward nowcasting method and provides a benchmark for nowcasting model development. Plain Language Summary: Reporting delays in public health surveillance systems can create a misleading impression of declining trends in recent data. While a number of “nowcasting” methods have been developed to correct for this bias, widespread adoption in public health practice has yet to be realized. Currently, there is no simple method to perform nowcasting that both meets the needs of public health practice and can be used as a benchmark for further methodological advancement. To address these two gaps, we developed a family of baseline nowcasting methods and an accompanying software package. Using data from COVID-19 in Germany and norovirus in England, we evaluated the performance of our default method against other methods used in previous studies and assessed the performance of our different method specifications designed specifically for common problems in epidemiology such as weekday patterns in reporting and sharing estimates across different strata. Our findings indicate that our baseline methods improve performance over unadjusted data or more ad-hoc baseline nowcasting approaches, provide an interpretable and accessible nowcasting solution for public health practice, and are useful as a standard benchmark for enhanced understanding of more advanced methods.

Time-varying effective reproductive numbers of infectious diseases are commonly estimated using renewal equation models. In the widely applied R package EpiEstim and various related tools, this approach is combined with a Poisson distributional assumption. This has been criticized on various occasions, mostly on grounds of general model realism or a desire to estimate overdispersion parameters. Here we argue that an important issue arising from the Poisson assumption is that inference about the effective reproductive number becomes overconfident in presence of overdispersion. By how much standard errors are underestimated follows in a straightforward manner from theory on generalized linear models. We therefore recommend to replace the Poisson assumption by quasi-Poisson or negative binomial extensions, and contrast their respective properties. We illustrate our arguments in detailed simulation studies and three examples of case studies of Ebola, pandemic influenza and COVID-19.

INAR (integer‐valued autoregressive) and INGARCH (integer‐valued GARCH) models are among the most commonly employed approaches for count time series modeling, but have been studied in largely distinct strands of literature. In this paper, a new class of generalized integer‐valued ARMA (GINARMA) models is introduced which unifies a large number of compound Poisson INAR and INGARCH processes. Its stochastic properties, including stationarity and geometric ergodicity, are studied. Particular attention is given to a generalization of the INAR() model which parallels the extension of the INARCH() to the INGARCH(, ) model. For inference, we consider maximum likelihood, Gaussian quasi‐likelihood, and moment‐based approaches, along with likelihood ratio tests to distinguish between selected instances of our class. Models from the proposed class have a natural interpretation as stochastic epidemic processes, which throughout the article is used to illustrate our arguments. In a case study, different instances, including both established and newly introduced models, are applied to weekly case numbers of measles and mumps in Bavaria, Germany.

In infectious disease surveillance, incidence data are frequently subject to reporting delays and retrospective corrections, making it hard to assess current trends in real time. A variety of probabilistic nowcasting methods have been suggested to correct for the resulting biases. Building upon a recent comparison of eight of these methods in an application to COVID-19 hospitalization data from Germany, the objective of this paper is twofold. Firstly, we investigate how nowcasts from different models can be improved using statistical post-processing methods as employed, e.g., in weather forecasting. Secondly, we assess the potential of weighted ensemble nowcasts, i.e., weighted combinations of different probabilistic nowcasts. These are a natural extension of unweighted nowcast ensembles, which have previously been found to outperform most individual models. Both in post-processing and ensemble building, specific challenges arise from the fact that data are constantly revised, hindering the use of standard approaches. We find that post-processing can improve the individual performance of almost all considered models both in terms of evaluation scores and forecast interval coverage. Improving upon the performance of unweighted ensemble nowcasts via weighting schemes, on the other hand, poses a substantial challenge. Across an array of approaches, we find modest improvement in scores for some and decreased performance for most, with overall more favorable results for simple methods. In terms of forecast interval coverage, however, our methods lead to rather consistent improvements over the unweighted ensembles.

Predictive epidemic modeling can enhance situational awareness during emerging and seasonal outbreaks and has received increasing interest in recent years. A common distinction is between nowcasting, which corrects recent incidence data for reporting delays, and forecasting, which predicts future trends. This paper presents an integrated system for nowcasting and multi-model short-term forecasting of hospitalizations from severe acute respiratory infections (SARI) in Germany (November 2023–September 2024). We propose a modular approach combining a statistical nowcasting model with various data-driven forecasting methods, including a time series model, a gradient boosting approach, and a neural network. These are combined into an ensemble approach, which achieves the best average performance. The resulting forecasts are overall well-calibrated up to four weeks ahead, but struggled to capture the unusual double peak which occurred during the test season. While the presented analysis is retrospective, it serves as a blueprint for a collaborative real-time forecasting platform for respiratory diseases in Germany (the RESPINOW Hub ). We conclude with an outlook on this system, which was launched in the fall of 2024 and covers a broader range of data sources and modeling approaches.

Monitoring influenza activity is a key task of public health agencies worldwide. Intensity thresholds serve to retrospectively classify season peak intensity and to compare current influenza activity to past peak values. The resulting classifications into low, medium, high, or very high intensity inform national-level risk assessment and planning. Moreover, they feed into international summary reports. Two common thresholding approaches, recommended in dedicated WHO guidelines, are the moving epidemic method (MEM) and the WHO method. In both approaches, thresholds correspond to quantiles of a normal distribution fitted to a set of historical observations. While an extensive literature on applications of these methods exists, their statistical properties have not been assessed systematically. In this article, we study them analytically and in a simulation study based on re-sampling of French influenza surveillance data. Moreover, extensions to account for small sample sizes and secular trends are described. Under the default settings, both the MEM and WHO method on average classify more seasons than intended as high or very high intensity. Combining characteristics of both and adding a small-sample correction, better-calibrated thresholds can be achieved. Even these, however, have modest sensitivity and positive predictive values. This concerns especially thresholds for very high intensity.