Effects of higher-order interactions and impulsive vaccination for rumor propagation

This paper introduces a rumor propagation model with saturation incidence, based on hypergraph theory. Hypergraphs can capture the higher-order interactions between nodes in a social network, where the node degree is substituted with hyperdegree. First, the threshold for rumor spreading model is obtained, the global asymptotically stable of the rumor-free equilibrium, and the global attractive and global asymptotically stable of the rumor-prevailing equilibrium are proved. Then, we incorporate impulsive vaccination into the model to represent the guided effect, simulating the periodic educational activities organized by official institutions to counteract rumor dissemination. By employing the comparison theorem, the paper demonstrates the global attractiveness of the rumor-free periodic solution and the persistence of the model. Finally, through numerical simulations, the paper compares the effects of higher-order and pairwise interactions on rumor spreading, validating the theoretical conclusions. The results indicate that higher-order interactions can promote rumor spreading, while impulsive vaccination can effectively decrease the scale of rumor spreading.