SEIAR rumor spreading model with antagonistic states in hypernetworks

Rumors pose serious harm to society, often affecting public safety and social stability as they spread. Most existing studies on rumor propagation models are based on binary relationships within ordinary graphs, constructing complex network information propagation models. However, these models struggle to capture the multi-dimensional, multi-attribute, and multi-relational complex interaction characteristics of real-world social networks. This paper proposes an SEIAR (Susceptible-Exposed-Informed-Antagonistic-Removed) rumor propagation model, built upon hypergraph theory, which effectively captures complex interaction relationships. The model builds on the SEIR framework by introducing a debunking state, enabling a more comprehensive reflection of the dynamic characteristics of rumor propagation and debunking behavior. Using mean-field theory, the dynamic equations of the SEIAR model are derived, along with an analytical expression for its basic reproduction number R0, and a stability analysis is conducted. The study shows that when R0≤1, the rumor-free equilibrium state of the model is locally and globally stable, ultimately leading to the disappearance of the rumor. When R0>1, the rumor persists and continues to spread. Numerical simulations using the Runge-Kutta method were performed to validate the effectiveness of the theoretical findings. Subsequently, the model was validated using actual rumor datasets, and the results showed that the model can effectively simulate the rumor propagation process in real social networks. In addition, this paper systematically analyzes the impact of factors such as the influence of debunkers, information control strength and control time, individual interests, information timeliness, and network structure on rumor propagation, and compares the propagation characteristics of different models through simulation. The model presented in this paper broadens the perspective of information propagation research, providing a detailed depiction of the rumor propagation mechanism that includes a debunking state, and offers significant theoretical support for developing rumor control strategies.