Higher-order dynamics and optimal control of SEIR rumor propagation models in homogeneous and heterogeneous networks

Higher-order interactions play a critical role in driving the rapid propagation of rumors. We propose a susceptible–exposed–infected–removed (SEIR) model that incorporates group interactions as higher-order terms. Detailed analysis reveals the emergence of bistability in both homogeneous and heterogeneous networks and shows that the bistable region expands as group interactions intensify. By utilizing group interactions as the bifurcation parameter, we derive explicit bifurcation conditions for both network types. For heterogeneous networks, we establish global stability criteria and propose an effective control strategy. Numerical simulations demonstrate the significant influence of group interactions on the bistable region. This study advances the theoretical understanding of rumor propagation dynamics and provides a practical strategy for controlling rumor propagation.