Spatio-temporal Modelling of H5N1 Avian Influenza Outbreaks in Europe (2021-2024)

Abstract. Highly Pathogenic Avian Influenza (HPAI), particularly the H5N1 strain, poses a significant ongoing threat to animal health, biodiversity and food security across Europe. Understanding where and when avian influenza risks intensify is essential for targeted surveillance and rapid response. This study develops a data-driven spatio-temporal framework that integrates geospatial, ecological and climatic datasets to explain and forecast the dynamics of H5N1 outbreaks between 2021 and 2024. Weekly country-level outbreak counts (208 weeks, 37 countries) were analysed using a hierarchical endemic-epidemic model with an assumption of Negative Binomial distribution. Environmental covariates, bird-species densities, and human population metrics were incorporated into endemic and autoregressive components. Model performance was evaluated using rolling one-step-ahead forecasts assessed by proper scoring rules (logarithmic score and ranked probability score) and calibration diagnostics. The proposed framework substantially outperformed a regression-only Negative Binomial baseline, reducing mean logS by approximately 29% and RPS by 49%, while exhibiting improved probabilistic calibration. Results indicate that H5N1 transmission is structured by ecological drivers and local persistence mechanisms rather than purely seasonal effects. Anseriformes, Charadriiformes and Pelecaniformes densities were identified as the key migratory bird families contributing to the viral spread. The endemic-epidemic model achieved high forecast accuracy, with majority of the of observed weekly outbreak counts falling within central predictive intervals (RPS = 0.76, logS = 0.61). Overall, the proposed framework provides a scalable approach for integrating ecological and spatial information into early-warning systems for HPAI surveillance.