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This paper introduces a novel hybrid mathematical modeling approach that effectively couples Partial Differential Equations (PDEs) with Ordinary Differential Equations (ODEs), exemplified through the simulation of epidemiological processes. The hybrid model aims to integrate the spatially detailed representation of disease dynamics provided by PDEs with the computational efficiency of ODEs. In the presented epidemiological use-case, this integration allows for the rapid assessment of public health interventions and the potential impact of infectious diseases across large populations. We discuss the theoretical formulation of the hybrid PDE-ODE model, including the governing equations and boundary conditions. The model's capabilities are demonstrated through detailed simulations of disease spread in synthetic environments and real-world scenarios, specifically focusing on the regions of Lombardy, Italy, and Berlin, Germany. Results indicate that the hybrid model achieves a balance between computational speed and accuracy, making it a valuable tool for policymakers in real-time decision-making and scenario analysis in epidemiology and potentially in other fields requiring similar modeling approaches.
Respiratory viral infections (RVIs) are common reasons for healthcare consultations. The inpatient management of RVIs consumes significant resources. From 2009 to 2014, we assessed the costs of RVI management in 4776 hospitalized children aged 0–18 years participating in a quality improvement program, where all ILI patients underwent virologic testing at the National Reference Centre followed by detailed recording of their clinical course. The direct (medical or non-medical) and indirect costs of inpatient management outside the ICU (‘non-ICU’) versus management requiring ICU care (‘ICU’) added up to EUR 2767.14 (non-ICU) vs. EUR 29,941.71 (ICU) for influenza, EUR 2713.14 (non-ICU) vs. EUR 16,951.06 (ICU) for RSV infections, and EUR 2767.33 (non-ICU) vs. EUR 14,394.02 (ICU) for human rhinovirus (hRV) infections, respectively. Non-ICU inpatient costs were similar for all eight RVIs studied: influenza, RSV, hRV, adenovirus (hAdV), metapneumovirus (hMPV), parainfluenza virus (hPIV), bocavirus (hBoV), and seasonal coronavirus (hCoV) infections. ICU costs for influenza, however, exceeded all other RVIs. At the time of the study, influenza was the only RVI with antiviral treatment options available for children, but only 9.8% of influenza patients (non-ICU) and 1.5% of ICU patients with influenza received antivirals; only 2.9% were vaccinated. Future studies should investigate the economic impact of treatment and prevention of influenza, COVID-19, and RSV post vaccine introduction.
Collaborative comparisons and combinations of epidemic models are used as policy-relevant evidence during epidemic outbreaks. In the process of collecting multiple model projections, such collaborations may gain or lose relevant information. Typically, modellers contribute a probabilistic summary at each time-step. We compared this to directly collecting simulated trajectories. We aimed to explore information on key epidemic quantities; ensemble uncertainty; and performance against data, investigating potential to continuously gain information from a single cross-sectional collection of model results. Methods We compared July 2022 projections from the European COVID-19 Scenario Modelling Hub. Five modelling teams projected incidence in Belgium, the Netherlands, and Spain. We compared projections by incidence, peaks, and cumulative totals. We created a probabilistic ensemble drawn from all trajectories, and compared to ensembles from a median across each model’s quantiles, or a linear opinion pool. We measured the predictive accuracy of individual trajectories against observations, using this in a weighted ensemble. We repeated this sequentially against increasing weeks of observed data. We evaluated these ensembles to reflect performance with varying observed data. Results. By collecting modelled trajectories, we showed policy-relevant epidemic characteristics. Trajectories contained a right-skewed distribution well represented by an ensemble of trajectories or a linear opinion pool, but not models’ quantile intervals. Ensembles weighted by performance typically retained the range of plausible incidence over time, and in some cases narrowed this by excluding some epidemic shapes. Conclusions. We observed several information gains from collecting modelled trajectories rather than quantile distributions, including potential for continuously updated information from a single model collection. The value of information gains and losses may vary with each collaborative effort’s aims, depending on the needs of projection users. Understanding the differing information potential of methods to collect model projections can support the accuracy, sustainability, and communication of collaborative infectious disease modelling efforts. Data availability All code and data available on Github: https://github.com/covid19-forecast-hub-europe/aggregation-info-loss
The recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method's learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available.
Aims: Interpretation of continuous EEG is a demanding task that requires the expertise of trained neurologists. However, these experts are not always available in many medical centers. As part of the 2023 George B. Moody PhysioNet Challenge, we developed a deep learning based method for analyzing EEG data of comatose patients and predicting prognosis following cardiac arrest. Methods: Our approach is a two-step pipeline that consists of a prediction model and a decision-making strategy. The prediction model is a residual neural network (ResNet-18) that extracts features and makes a prediction based on a short 5-minute EEG recording. In the second step, a majority vote over multiple predictions made for several EEG recordings of a patient determines the final prognosis. Results: Based on 10-fold cross-validation on the training set, we achieved a true positive rate (TPR) of 0.41 for predicting poor outcome while keeping the false positive rate below 0.05 at 72 hours after recovery of spontaneous circulation. On the official challenge leaderboard, our team ZIB_Visual scored 0.426 TPR. Conclusion: Our approach, while simple to implement and execute, faced overfitting challenges during the official competition phase. In this paper, we discuss our implementation and potential improvements to address these issues.
Implantable Cardiac Monitor (ICM) devices are demonstrating as of today, the fastest-growing market for implantable cardiac devices. As such, they are becoming increasingly common in patients for measuring heart electrical activity. ICMs constantly monitor and record a patient's heart rhythm and when triggered - send it to a secure server where health care professionals (denote HCPs from here on) can review it. These devices employ a relatively simplistic rule-based algorithm (due to energy consumption constraints) to alert for abnormal heart rhythms. This algorithm is usually parameterized to an over-sensitive mode in order to not miss a case (resulting in a relatively high false-positive rate) and this, combined with the device's nature of constantly monitoring the heart rhythm and its growing popularity, results in HCPs having to analyze and diagnose an increasingly growing amount of data. In order to reduce the load on the latter, automated methods for ECG analysis are nowadays becoming a great tool to assist HCPs in their analysis. While state-of-the-art algorithms are data-driven rather than rule-based, training data for ICMs often consist of specific characteristics that make its analysis unique and particularly challenging. This study presents the challenges and solutions in automatically analyzing ICM data and introduces a method for its classification that outperforms existing methods on such data. It does so by combining high-frequency noise detection (which often occurs in ICM data) with a semi-supervised learning pipeline that allows for re-labeling of training episodes, and by using segmentation and dimension reduction techniques that are robust to morphology variations of the sECG signal (which are typical to ICM data). As a result, it performs better than state-of-the-art techniques on such data with e.g. F1 score of 0.51 vs. 0.38 of our baseline state-of-the-art technique in correctly calling Atrial Fibrilation in ICM data. As such, it could be used in numerous ways such as aiding HCPs in the analysis of ECGs originating from ICMs by, e.g., suggesting a rhythm type.
Mathematical world knowledge is a fundamental component of Wikidata. However, to date, no expertly curated knowledge graph has focused specifically on contemporary mathematics. Addressing this gap, the Mathematical Research Data Initiative (MaRDI) has developed a comprehensive knowledge graph that links multimodal research data in mathematics. This encompasses traditional research data items like datasets, software, and publications and includes semantically advanced objects such as mathematical formulae and hypotheses. This paper details the abilities of the MaRDI knowledge graph, which is based on Wikibase, leading up to its inaugural public release, codenamed Bravo, available on https://portal.mardi4nfdi.de.