Multi-scale higher-order contagion dynamics in complex networks

Real-world social contagions exhibit significant multi-scale features, where behavioral adoption is driven by both microscopic synergistic pressure within tight-knit groups and mesoscopic prevalence across diverse social circles, yet existing studies treat these mechanisms in isolation. Here, we propose a unified multi-scale higher-order contagion model integrating micro-local clustering and meso-structural diversity, and develops a dynamic message passing method to accurately analyze system dynamics. We rigorously derive tricritical points defining the topological boundary between second-order and first-order phase transitions, beyond which significant bistability and hysteresis emerge. While the higher-order effects have a limited impact on the forward threshold, they significantly lower the backward threshold, thereby expanding the active region of propagation. Crucially, structural diversity dually regulates contagion through a competition mechanism between single-component size fragmentation and component quantity gain. This leads to a significant non-monotonic U-shaped variation of the steady-state density with the structural diversity, proving the existence of an optimal structural diversity capable of minimizing the infection scale.