Disentangling the Role of Heterogeneity and Hyperedge Overlap in Explosive Contagion on Higher-Order Networks

We introduce group-based compartmental modeling (GBCM), a mean-field framework for irreversible contagion in higher-order networks that captures structural heterogeneity and correlations across group sizes. Validated through numerical simulations, GBCM analytically disentangles the role of each interaction order to the global epidemic dynamics, revealing how heterogeneity and inter-order correlations jointly shape the onset of outbreaks and the emergence of explosive dynamics. Crucially, we show that inter-order correlations drive the system along distinct pathways to explosive contagion - emerging universally across both irreversible and reversible spreading processes.