Hyper-S2IR: a model for characterizing higher-order interactions and dynamics in public opinion dissemination

Traditional public opinion diffusion models generally assume interactions between individuals as binary pair-wise effects, which struggle to capture the higher-order complexities of multi-group interactions in social networks—such as group discussions in WeChat and topic reposting on Weibo. Moreover, these models fail to adequately depict the nonlinear trust accumulation mechanisms and individual heterogeneity inherent in the diffusion process. Therefore, the paper proposes a hypergraph-based Hyper-S2IR model for disseminating public opinion. The “Goebbels effect” is operationalized by leveraging the hypergraph structure: a susceptible node’s risk of infection is proportional to its hyperdegree, mathematically representing the cumulative exposure to information from multiple sources within different hyperedges. Our model introduces two types of communicators ( HI 1 and HI 2 ) with different motivations and capabilities, thereby systematically depicting the inherent heterogeneity of the communication group. Through theoretical derivation, we derive a novel basic reproduction number R 0 that explicitly incorporates the hyperdegree distribution of the hypergraph. This R 0 provides a threshold for dissemination dynamics: When R 0 > 1, the public opinion will continue to spread and converge to a stable public opinion prevalence equilibrium point; when R 0 < 1, the public opinion will gradually disappear. Critically, the expression for R 0 reveals how higher-order group interactions, encoded in the hyperdegree, fundamentally alter the spreading threshold compared to traditional pairwise networks. Numerical simulations verify the theoretical conclusions and demonstrate that the hypergraph structure significantly accelerates the spread and expands the scale of public opinion compared to traditional network structures. This work provides theoretical support and a quantitative basis for analyzing public opinion dissemination mechanisms and formulating intervention strategies.