Beyond mean-field age-structured models: degree heterogeneity and cross-country variability in epidemic risk.

Age structure is a fundamental determinant of infectious disease transmission, but most applications of age-specific contact matrices remain within mean-field compartmental frameworks based on population-averaged mixing. Such models describe average contact rates between age groups but do not explicitly represent variability in individual contact numbers or the network topology generated by age-dependent interactions. In this study, we combined age-stratified contact matrices with stochastic network-based epidemic simulations to investigate how demographic composition and contact structure shape epidemic dynamics across countries. Using the contact matrices developed by Prem et al. (Prem et al. 2017 PLoS Comput. Biol. 13, e1005697 (doi:10.1371/journal.pcbi.1005697)), we constructed age-structured contact networks under a unified transmission rate, enabling cross-country comparisons that isolate structural effects from pathogen-specific differences. Stochastic susceptible-infected-recovered simulations on the generated networks revealed marked cross-country variation in final epidemic size and age-specific infection burden, even under identical epidemiological parameters. Countries with youthful populations and strong cross-age connectivity showed larger epidemic sizes, whereas countries with more stratified or ageing contact structures exhibited more constrained transmission. We further used an edge-based compartmental model as an analytical approximation to interpret the simulation results, derive R0 and assess the consistency between network simulations and theoretical expectations. The results show that R0 alone does not uniquely determine final epidemic size, because degree heterogeneity and age-specific network connectivity strongly influence epidemic outcomes. Analyses of school- and workplace-contact removal further demonstrated that intervention effectiveness depends on country-specific demographic and contact structures. This framework provides a data-driven approach for evaluating structure-dependent epidemic risks and highlights the importance of incorporating age-dependent network topology into epidemic modelling and intervention assessment.