arXiv subjects

Martin J. Kühn

Publications and source records attributed to Martin J. Kühn.

13 recordsLinked to original sources

arXiv2026

MEmilio -- A high performance Modular EpideMIcs simuLatIOn software for multi-scale and comparative simulations of infectious disease dynamics

Epidemic and pandemic preparedness with rapid outbreak response rely on timely, trustworthy evidence. Mathematical models are crucial for supporting timely and reliable evidence generation for public health decision-making with models spanning approaches from compartmental and metapopulation models to detailed agent-based simulations. Yet, the accompanying software ecosystem remains fragmented across model types, spatial resolutions, and computational targets, making models harder to compare, extend, and deploy at scale. Here we present MEmilio, a modular, high-performance framework for epidemic simulation that harmonizes the specification and execution of diverse dynamic epidemiological models within a unified and harmonized architecture. MEmilio couples an efficient C++ simulation core with coherent model descriptions and a user-friendly Python interface, enabling workflows that run on laptops as well as high-performance computing systems. Standardized representations of space, demography, and mobility support straightforward adaptations in resolution and population size, facilitating systematic inter-model comparisons and ensemble studies. The framework integrates readily with established tools for uncertainty quantification and parameter inference, supporting a broad range of applications from scenario exploration to calibration. Finally, strict software-engineering practices, including extensive unit and continuous integration testing, promote robustness and minimize the risk of errors as the framework evolves. By unifying implementations across modeling paradigms, MEmilio aims to lower barriers to reuse and generalize models, enable principled comparisons of implicit assumptions, and accelerate the development of novel approaches that strengthen modeling-based outbreak preparedness.

q-bio.PE↗

arXiv2026

A full software stack for epidemic disease management: Unlocking the joint potential of software technology and supercomputing

Infectious diseases remain a major threat to human societies. During the recent COVID-19 pandemic, mathematical modeling and extensive computer simulations proved highly effective in supporting public health experts and decision makers. Despite these advances, the full potential of modern modeling approaches and digital technologies has not yet been realized. Many critical tasks -- including expert consultations, model execution, scenario analyses, report preparation, and result communication -- still relied heavily on manual, human-driven processes with each manual interaction introducing avoidable delays and limiting responsiveness during rapidly evolving outbreaks. Pandemic preparedness should opt for automated workflows and seamlessly integrated software modules that can improve pandemic mitigation capabilities by substantially reducing response times. For this step, we require robust and flexible computational infrastructure capable of supporting heterogeneous hardware and continuously evolving infectious-disease models. In addition, data sources need to be dynamically integrated. Managing such demands needs infrastructure that supports automated high-performance computing (HPC) workflows. Beyond computational performance, software infrastructure must ensure secure user and data management to comply with data-protection regulations and provide clear, transparent presentation of results to both decision makers and the public. Meeting the aforementioned challenges requires tight integration of state-of-the-art scientific software with modern, scalable infrastructure that can leverage supercomputing resources when necessary. For rapid deployment in future epidemic or pandemic scenarios, adherence to the FAIR principles for research software is critical to ensure reusability and sustainability.

cs.CE↗

arXiv2026

Efficient numerical computation of traveler states in explicit mobility-based metapopulation models: Mathematical theory and application to epidemics

Metapopulation models are powerful tools for capturing the spatio-temporal spread of infectious diseases. Models that explicitly account for traveler origins and destinations, such as Lagrangian metapopulation models, enable a detailed representation of mobility and traveling subpopulations. However, in densely connected networks, tracking these subpopulations leads to quadratic growth in system size with the number of spatial patches. While specific approaches reducing the effort of traveler state estimation have been proposed, these approaches are either model-specific or heuristic. Here, we introduce a Runge-Kutta (RK) stage-aligned computation of traveler states that leverages the precomputed intermediate stage values of explicit RK methods under the assumption of localized homogeneous mixing. We prove that the resulting numerical solution is identical to that of the standard Lagrangian formulation when solved with the corresponding RK method. For compartments without inflows, we further show that the exact same results can be obtained using a simple algebraic scaling based on the initial traveler share. When embedded in a recently proposed metapopulation framework that combines local dynamics with discrete mobility, the stage-aligned approach eliminates the need for heuristic traveler approximations. In contrast to the standard Lagrangian formulation, the resulting method enables efficient simulations by reducing the global ODE system to linear scaling in the number of patches, while the remaining quadratic interactions are handled through highly efficient algebraic updates. Numerical experiments confirm the theoretical results, demonstrating optimal convergence order. Benchmarks on fully connected networks with up to 1025 patches, 1024 local travel connections, and six age groups achieve speedups of up to 76 and 50 for first- and fourth-order Runge-Kutta methods, respectively.

math.NA↗

arXiv2026

On the Effect of Missing Transmission Chain Information in Agent-Based Models: Outcomes of Superspreading Events and Workplace Transmission

Agent-based models (ABMs) have emerged as distinguished tools for epidemic modeling due to their ability to capture detailed human contact patterns and can, thus, support decision-makers in times of outbreaks and epidemics. However, as a result of missing correspondingly resolved data transmission events are often modeled based on simplified assumptions. In this article, we present a framework to assess the impact of these simplifications on epidemic prediction outcomes, considering superspreading and workplace transmission events. We couple the VADERE microsimulation model with the large-scale MEmilio-ABM and compare the outcomes of four outbreak events after 10 days of simulation in a synthetic city district generated from German census data. In a restaurant superspreading event, where up to four households share tables, we observe 17.2 % more infections on day 10 after the outbreak. The difference increases to 46.0 % more infections when using the simplified initialization in a setting where only two households share tables. We observe similar outcomes (41.3 % vs. 9.3 % more infections) for two workplace settings with different mixing patterns between teams at work. In addition to the aggregated difference, we show differences in spatial dynamics and transmission trees obtained with complete or reduced outbreak information. We observe differences between simplified and fully detailed initializations that become more pronounced when the subnetworks in the outbreak setting are mixing less. In consequence and aside from classical calibration of models, the significant outcome differences should drive us to develop a more profound understanding of how and where simplified assumptions about transmission events are adequate.

physics.soc-ph↗

arXiv2026

Graph Neural Network Surrogates to leverage Mechanistic Expert Knowledge towards Reliable and Immediate Pandemic Response

During the COVID-19 crisis, mechanistic models have guided evidence-based decision making. However, time-critical decisions in a dynamical environment limit the time available to gather supporting evidence. We address this bottleneck by developing a graph neural network (GNN) surrogate of an age-structured and spatially resolved mechanistic metapopulation simulation model. This combined approach complements classical modeling approaches which are mostly mechanistic and purely data-driven machine learning approaches which are often black box. Our design of experiments spans outbreak and persistent-threat regimes, up to three contact change points, and age-structured contact matrices on a spatial graph with 400 nodes representing German counties. We benchmark multiple GNN layers and identify an ARMAConv-based architecture that offers a strong accuracy-runtime trade-off. Across horizons of 30-90 day simulation and prediction, allowing up to three contact change points, the surrogate model attains 10-27 \% mean absolute percentage error (MAPE) while delivering (near) constant runtime with respect to the forecast horizon. Our approach accelerates evaluation by up to 28,670 times compared with the mechanistic model, allowing responsive decision support in time-critical scenarios and straightforward web integration. These results show how GNN surrogates can translate complex metapopulation models into immediate, reliable tools for pandemic response.

cs.LG↗

arXiv2026

Differentially private federated learning for localized control of infectious disease dynamics

In times of epidemics, swift reaction is necessary to mitigate epidemic spreading. For this reaction, localized approaches have several advantages, limiting necessary resources and reducing the impact of interventions on a larger scale. However, training a separate machine learning (ML) model on a local scale is often not feasible due to limited available data. Centralizing the data is also challenging because of its high sensitivity and privacy constraints. In this study, we consider a localized strategy based on the German counties and communities managed by the related local health authorities (LHA). For the preservation of privacy to not oppose the availability of detailed situational data, we propose a privacy-preserving forecasting method that can assist public health experts and decision makers. ML methods with federated learning (FL) train a shared model without centralizing raw data. Considering the counties, communities or LHAs as clients and finding a balance between utility and privacy, we study a FL framework with client-level differential privacy (DP). We train a shared multilayer perceptron on sliding windows of recent case counts to forecast the number of cases, while clients exchange only norm-clipped updates and the server aggregated updates with DP noise. We evaluate the approach on COVID-19 data on county-level during two phases. As expected, very strict privacy yields unstable, unusable forecasts. At a moderately strong level, the DP model closely approaches the non-DP model: R2 around 0.94 (vs. 0.95) and mean absolute percentage error (MAPE) of 26 % in November 2020; R2 around 0.88 (vs. 0.93) and MAPE of 21 % in March 2022. Overall, client-level DP-FL can deliver useful county-level predictions with strong privacy guarantees, and viable privacy budgets depend on epidemic phase, allowing privacy-compliant collaboration among health authorities for local forecasting.

cs.LG↗

arXiv2025

Memory- and compute-optimized geometric multigrid GMGPolar for curvilinear coordinate representations -- Applications to fusion plasma

Tokamak fusion reactors are actively studied as a means of realizing energy production from plasma fusion. However, due to the substantial cost and time required to construct fusion reactors and run physical experiments, numerical experiments are indispensable for understanding plasma physics inside tokamaks, supporting the design and engineering phase, and optimizing future reactor designs. Geometric multigrid methods are optimal solvers for many problems that arise from the discretization of partial differential equations. It has been shown that the multigrid solver GMGPolar solves the 2D gyrokinetic Poisson equation in linear complexity and with only small memory requirements compared to other state-of-the-art solvers. In this paper, we present a completely refactored and object-oriented version of GMGPolar which offers two different matrix-free implementations. Among other things, we leverage the Sherman-Morrison formula to solve cyclic tridiagonal systems from circular line solvers without additional fill-in and we apply reordering to optimize cache access of circular and radial smoothing operations. With the Give approach, memory requirements are further reduced and speedups of four to seven are obtained for usual test cases. For the Take approach, speedups of 16 to 18 can be attained. In an additionally experimental setup of using GMGPolar as a preconditioner for conjugate gradients, this speedup could even be increased to factors between 25 and 37.

cs.MS↗

arXiv2025

A nonstandard numerical scheme for a novel SECIR integro-differential equation-based model allowing nonexponentially distributed stay times

Ordinary differential equations (ODE) are a popular tool to model the spread of infectious diseases, yet they implicitly assume an exponential distribution to describe the flow from one infection state to another. However, scientific experience yields more plausible distributions where the likelihood of disease progression changes accordingly with the duration spent in a particular state of the disease. Furthermore, transmission dynamics depend heavily on the infectiousness of individuals. The corresponding nonlinear variation with the time individuals have already spent in an infectious state requires more realistic models. The previously mentioned items are particularly crucial when modeling dynamics at change points such as the implementation of nonpharmaceutical interventions. In order to capture these aspects and to enhance the accuracy of simulations, integro-differential equations (IDE) can be used. In this paper, we propose a generalized model based on IDEs with eight infection states. The model allows for variable stay time distributions and generalizes the concept of ODE-based models as well as IDE-based age-of-infection models. In this, we include particular infection states for severe and critical cases to allow for surveillance of the clinical sector, avoiding bottlenecks and overloads in critical epidemic situations. On the other hand, a drawback of IDE-based models is that efficient numerical solvers are not as widely available. We extend a recently introduced nonstandard numerical scheme. This scheme is adapted to our more advanced model and we prove important mathematical and biological properties. Furthermore, we validate our approach numerically by demonstrating the convergence rate. Eventually, we also show that our novel model is intrinsically capable of better assessing disease dynamics upon the introduction of nonpharmaceutical interventions.

math.NA↗

arXiv2025

Revisiting the Linear Chain Trick in epidemiological models: Implications of underlying assumptions for numerical solutions

In order to simulate the spread of infectious diseases, many epidemiological models use systems of ordinary differential equations (ODEs) to describe the underlying dynamics. These models incorporate the implicit assumption, that the stay time in each disease state follows an exponential distribution. However, a substantial number of epidemiological, data-based studies indicate that this assumption is not plausible. One method to alleviate this limitation is to employ the Linear Chain Trick (LCT) for ODE systems, which realizes the use of Erlang distributed stay times. As indicated by data, this approach allows for more realistic models while maintaining the advantages of using ODEs. In this work, we propose an advanced LCT SECIR-type model incorporating eight infection states with demographic stratification. We review key properties of the corresponding LCT model and demonstrate that predictions derived from a simple ODE-based model can be significantly distorted, potentially leading to wrong political decisions. Our findings demonstrate that the influence of distribution assumptions on the behavior at change points and on the prediction of epidemic peaks is substantial, while the assumption has no effect on the final size of the epidemic. With respect to prior findings in literature, we demonstrate that the influence of the number of subcompartments on the timing and size of the epidemic peak is nontrivial and that a general statement cannot be obtained. We, then, show how these age-resolved LCT SECIR-type models capture the spread of SARS-CoV-2 in Germany in 2020. Eventually, we study the implications on the time-to-solution for different LCT models using fixed and adaptive step-size Runge-Kutta methods and provide computational performance for these models in the MEmilio software framework, also using distributed memory parallelism to speed up ensemble runs.

math.DS↗

arXiv2025

Agent-based modeling for realistic reproduction of human mobility and contact behavior to evaluate test and isolation strategies in epidemic infectious disease spread

Agent-based models have proven to be useful tools in supporting decision-making processes in different application domains. The advent of modern computers and supercomputers has enabled these bottom-up approaches to realistically model human mobility and contact behavior. The COVID-19 pandemic showcased the urgent need for detailed and informative models that can answer research questions on transmission dynamics. We present a sophisticated agent-based model to simulate the spread of respiratory diseases. The model is highly modularized and can be used on various scales, from a small collection of buildings up to cities or countries. Although not being the focus of this paper, the model has undergone performance engineering on a single core and provides an efficient intra- and inter-simulation parallelization for time-critical decision-making processes. In order to allow answering research questions on individual level resolution, nonpharmaceutical intervention strategies such as face masks or venue closures can be implemented for particular locations or agents. In particular, we allow for sophisticated testing and isolation strategies to study the effects of minimal-invasive infectious disease mitigation. With realistic human mobility patterns for the region of Brunswick, Germany, we study the effects of different interventions between March 1st and May 30, 2021 in the SARS-CoV-2 pandemic. Our analyses suggest that symptom-independent testing has limited impact on the mitigation of disease dynamics if the dark figure in symptomatic cases is high. Furthermore, we found that quarantine length is more important than quarantine efficiency but that, with sufficient symptomatic control, also short quarantines can have a substantial effect.

cs.MA↗

arXiv2025

Risk-mediated dynamic regulation of effective contacts de-synchronizes outbreaks in metapopulation epidemic models

Metapopulation epidemic models help capture the spatial dimension of infectious disease spread by dividing heterogeneous populations into separate but interconnected communities, represented by nodes in a network. In the event of an epidemic, an important research question is, to what degree spatial information (i.e., regional or national) is relevant for mitigation and (local) policymakers. This study investigates the impact of different levels of information on nationwide epidemic outcomes, modeling the reaction to the measured hazard as a feedback loop reducing contact rates in a metapopulation model based on ordinary differential equations (ODEs). Using COVID-19 and high-resolution mobility data for Germany of 2020 as a case study, we found two markedly different regimes depending on the maximum contact reduction $ψ_{\rm max}$: mitigation and suppression. In the regime of (modest) mitigation, gradually increasing $ψ_{\rm max}$ from zero to moderate levels delayed and spread out the onset of infection waves while gradually reducing the peak values. This effect was more pronounced when the contribution of regional information was low relative to national data. In the suppression regime, the feedback-induced contact reduction is strong enough to extinguish local outbreaks and decrease the mean and variance of the peak day distribution, thus regional information was more important. When suppression or elimination is impossible, ensuring local epidemics are desynchronized helps to avoid hospitalization or intensive care bottlenecks by reallocating resources from less-affected areas.

q-bio.PE↗

arXiv2024

Hybrid metapopulation agent-based epidemiological models for efficient insight on the individual scale: a contribution to green computing

Emerging infectious diseases and climate change are two of the major challenges in 21st century. Although over the past decades, highly-resolved mathematical models have contributed in understanding dynamics of infectious diseases and are of great aid when it comes to finding suitable intervention measures, they may need substantial computational effort and produce significant CO2 emissions. Two popular modeling approaches for mitigating infectious disease dynamics are agent-based and population-based models. Agent-based models (ABMs) offer a microscopic view and are thus able to capture heterogeneous human contact behavior and mobility patterns. However, insights on individual-level dynamics come with high computational effort that scales with the number of agents. On the other hand, population-based models using e.g. ordinary differential equations (ODEs) are computationally efficient even for large populations due to their complexity being independent of the population size. Yet, population-based models are restricted in their granularity as they assume a (to some extent) homogeneous and well-mixed population. To manage the trade-off between computational complexity and level of detail, we propose spatial- and temporal-hybrid models that use ABMs only in an area or time frame of interest. To account for relevant influences to disease dynamics, e.g., from outside, due to commuting activities, we use population-based models, only adding moderate computational costs. Our hybridization approach demonstrates significant reduction in computational effort by up to 98% -- without losing the required depth in information in the focus frame. Concluding, hybrid epidemiological models can provide insights on the individual scale where necessary, using aggregated models where possible, thereby making a contribution to green computing.

q-bio.PE↗

arXiv2023

ESID: Exploring the Design and Development of a Visual Analytics Tool for Epidemiological Emergencies

Visual analytics tools can help illustrate the spread of infectious diseases and enable informed decisions on epidemiological and public health issues. To create visualisation tools that are intuitive, easy to use, and effective in communicating information, continued research and development focusing on user-centric and methodological design models is extremely important. As a contribution to this topic, this paper presents the design and development process of the visual analytics application ESID (Epidemiological Scenarios for Infectious Diseases). ESID is a visual analytics tool aimed at projecting the future developments of infectious disease spread using reported and simulated data based on sound mathematical-epidemiological models. The development process involved a collaborative and participatory design approach with project partners from diverse scientific fields. The findings from these studies, along with the guidelines derived from them, played a pivotal role in shaping the visualisation tool.

cs.HC↗