A temporal network-based model for assessing inter-city epidemic risk: evidence from a self-reported influenza-like illness outbreak in Shanxi Province, China

Assessing spatiotemporal transmission risk is essential for epidemic prevention and control, yet conventional approaches often do not capture dynamic inter-city transmission patterns well. This study developed a temporal network framework to assess transmission risk during self-reported influenza-like illness outbreak in Shanxi Province, China.

Data on daily newly infected cases in 11 prefecture-level cities in Shanxi Province from 1 December 2022 to 13 January 2023 were obtained from a large-scale questionnaire survey, together with demographic, transport, and geographical distance data. The epidemic period was divided into five time intervalss according to the temporal trend in daily new cases. Pearson correlation coefficients between cities were calculated for each time intervals. An improved gravity model integrating infection burden, population size, transport connectivity, geographical distance, and inter-city epidemic correlation was then used to construct temporal transmission networks. Threshold sensitivity analysis was performed, and global network indicators and node-level centrality measures were analysed.

The outbreak showed marked spatiotemporal heterogeneity, with high-risk clustering concentrated in central and south-eastern Shanxi. Network density and clustering coefficient increased during the growth and peak stages and declined during the later stage, indicating that inter-city spatiotemporal associations first intensified and then weakened. Threshold sensitivity analysis showed smooth variation in network density, supporting the robustness of network construction. Taiyuan ranked highest across major centrality measures and accounted for approximately 53% of total betweenness centrality, identifying it as the dominant transmission bridge. Jinzhong also showed high centrality, whereas Datong and Shuozhou remained peripheral. Xinzhou showed relatively high in-degree, suggesting greater vulnerability to imported transmission.

The findings indicate clear regional aggregation and phase-dependent evolution of epidemic transmission in Shanxi Province. Temporal changes in global network structure indicate that epidemic spread was closely associated with changing inter-city connectivity. Core hub cities, especially Taiyuan and Jinzhong, should be prioritised for targeted interventions, while cities vulnerable to imported risk, such as Xinzhou, require strengthened surveillance. This framework provides a useful basis for regional epidemic risk assessment and city-specific prevention strategies. Future studies should integrate temporal network analysis with dynamic epidemic models and weighted transmission information to improve mechanistic interpretation and predictive performance.

Not applicable. (As this study is not a clinical trial.).