Dynamic analysis of a fractional-order rumor spreading model with double time delay under higher-order interactions

Although traditional network-based models also explore higher-order interactions, they are limited in capturing the complex impacts of multibody interactions, making it difficult to characterize the reinforcement effect in rumor propagation. With this in mind, firstly, this study introduces the simplicial complexes, a higher-order mathematical tool, to model rumor propagation. Secondly, the fractional-order derivatives are employed to more accurately capture the memory effect and anomalous diffusion phenomenon in the rumor propagation process under higher-order interactions. Then propagation thresholds and the existence of model solutions are investigated. Moreover, the proposed model exhibits bistability, and the Hopf bifurcation is analysed by choosing time delay as the threshold. Numerical simulations suggest that fractional-order rumor spreading models with higher-order interactions are more consistent with actual data than network-based models and integer-order models.