Online-Offline Higher-Order Rumor Propagation Model Based on Quantum Cellular Automata Considering Social Adaptation

With the development of the Internet, the influence of rumors is more widespread. Studying the propagation law of rumors is an effective way to reduce the damage of rumors. We therefore propose a new two-layer rumor propagation model, which simultaneously introduces simplicial complexes into the online and offline network layers and considers the social adaptation of individuals. We derive the basic regeneration number, the rumor-free equilibrium, and the rumor-prevalence equilibrium using mean-field theory, and verify their accuracy through extensive computer simulations. The results show that the inclusion of higher-order interactions in both layers leads to richer dynamical phenomena. Specifically, higher-order interactions lead to bistable states, discontinuous transitions, and the coexistence of multiple rumor-prevalence equilibria, and increasing the infection parameter within a certain range reduces the outbreak size of rumors in another layer. In addition, a higher speed and degree of social adaptation, a stronger strength of coupled propagation enhancement effect, and a weaker strength of coupled recovery enhancement effect significantly increase the spread speed and size of rumors. Finally, we present and analyze two intervention strategies: improving public media literacy and building a truth space. We find that both intervention strategies can reduce the spread size and speed of rumors, but the synergy of two intervention strategies is more effective.