Networked SIRS model with Kalman filter state estimation for epidemic monitoring in Europe

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Abstract Background Metapopulation models, which consider epidemic spread across interconnected regions, can provide more accurate epidemic predictions with respect to country-specific models. Still, their added complexity and data requirements raise questions about their tangible benefits over simpler, localized models. Aim Our goal is to develop and validate networked metapopulation SIRS models, integrated with an Extended Kalman Filter (EKF), for predicting influenza-like illness (ILI) across Europe, which enables accurate forecasts, missing data imputation, and actionable insights. Methods We constructed two different metapopulation SIRS models: a detailed network-based model, including inter-country travel dynamics, and a simpler mean-field model, aggregating average regional data. Both were calibrated based on decade-long data of European mobility and ILI incidence, using EKF to estimate disease dynamics and forecast epidemic progression. The forecasting performance was benchmarked against isolated country-specific models. Results Network models outperformed isolated models in forecasting ILI progression, particularly during critical periods such as wave onsets and peaks, and maintained reliability during COVID-19-affected seasons. The full network model provided up to 25% improvement in peak predictions and demonstrated robustness in imputing missing data, even when up to 40% of the input data was unavailable. The models are fully interpretable and align with epidemiological dynamics across borders. Conclusion Our findings unveil the advantages of metapopulation models for epidemic forecasting in interconnected regions. Our framework, combining network models with EKF, offers improved accuracy, resilience to missing data, and enhanced interpretability. Our methodology provides a versatile tool for global public health applications, adaptable to other diseases and geographic scales.

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