Disentangling the role of heterogeneity and hyperedge overlap in explosive contagion on higher-order networks

Higher-order networks are used to model complex contagion processes in social groups of varying sizes, where heterogeneity and microscopic group arrangements can critically influence the dynamics. However, existing frameworks fail to fully capture the interplay between these features. Here, we introduce group-based compartmental modeling (GBCM), a mean-field framework for irreversible contagion that incorporates heterogeneity and captures correlations across group sizes. Validated through numerical simulations, GBCM analytically disentangles the contributions of different interaction orders to global epidemic dynamics. Our results reveal how heterogeneity and inter-order correlations shape epidemic thresholds and demonstrate that high heterogeneity in group membership drives rapid infection growth, leading to abrupt phase transitions. This provides an explanation for the emergence of explosive contagion in higher-order networks.