Shaping contagion with group synergy in hypergraphs

Higher-order interactions—simultaneous contacts among groups of three or more—are increasingly recognized as drivers of complex contagion phenomena that escape the explanatory scope of classical pairwise models. To elucidate how these interactions shape epidemic spreading, we introduce a hypergraph SIS framework combining first-order (pairwise) and second-order (triadic) transmission, parametrized by the average degrees k̄ and k̄△ and a synergy weight α. Through extensive simulations and mean-field analysis on random hypergraphs, we identify four distinct regimes: (i) when k̄△≪k̄, contagion behaves as simple, continuous spreading driven by pairwise links; (ii) for k̄△≈k̄, one- and two-body pathways coexist, yielding bistability, hysteresis, and non-monotonic prevalence curves that mark an activation threshold for group contagion; (iii) when k̄△>k̄, increasing α inverts outbreak and extinction thresholds-making epidemics harder to start but easier to sustain, and producing memory effects; and (iv) in the extreme k̄△≫k̄ limit, synergistic channels dominate, monotonically lowering epidemic thresholds and amplifying infection density even from minimal seeds. We further demonstrate that negative degree-triangle correlation-where highly connected nodes participate in fewer triangles-maximizes infection prevalence by freeing hubs from local clustering. Our findings provide quantitative structure-function relationships for contagion on hypergraphs and suggest that effective interventions or promotions require not only tuning transmission parameters but also engineering the density and organization of group interactions to selectively suppress or leverage synergistic spreading.