Henrik Zunker

Henrik Zunker, René Schmieding, Jan Hasenauer et al.

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.

Agatha Schmidt, Henrik Zunker, Alexander Heinlein et al.

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 a spatially and demographically resolved mechanistic metapopulation simulator. This combined approach advances classical 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 400-node spatial graph. We benchmark multiple GNN layers and identify an ARMAConv-based architecture that offers a strong accuracy-runtime trade-off. Across 30-90 day horizons and up to three contact change points, the surrogate 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.

Raouf Kerkouche, Henrik Zunker, Mario Fritz et al.

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: $R^2= 0.94$ (vs. 0.95) and mean absolute percentage error (MAPE) of 26 % in November 2020; $R^2= 0.88$ (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.