Networked SIRS Model with Kalman Filter State Estimation for Epidemic Monitoring in Europe

Background: Metapopulation models, which consider epidemic spread across interconnected regions, can provide more accurate epidemic predictions compared to isolated models for the corresponding regions. Still, their added complexity and data requirements raise questions about their tangible benefits over simpler, localized models. Methods: We develop and validate two networked compartmental metapopulation models for predicting influenza-like illness across Europe: a detailed network-based model, including international travel dynamics, and a simpler mean-field model, aggregating average regional data. The network is constructed using public mobility data and complemented with population densities at border regions. Incidence data of influenza-like illnesses from 28 countries are integrated using an Extended Kalman filter. Results: We show that networked epidemic models effectively capture epidemic dynamics across regions and epidemic phases. The models enable accurate forecasts, missing data imputation, and actionable insights: network models outperform isolated models in forecasting epidemic progression, particularly during critical periods such as wave onsets and peaks, and maintain reliability in scenarios with missing data. Conclusions: The findings unveil and quantify the advantages of metapopulation models for epidemic forecasting in interconnected regions, and pave the way to the integration of mobility and epidemic surveillance to improve the monitoring and prediction of spreading diseases.