Abstract
In this paper, a hyper susceptible-infected-recovered (Hyper-SIR) rumor propagation model is proposed based on hypergraph, which can describe the higher-order information interactions among nodes in the networks. Notably, hyperdegree is substitute for degree to model rumor spreading, and some reasonable results are obtained. Firstly, the threshold of Hyper-SIR rumor propagation model is acquired. Then, the stability of rumor-free/prevailing equilibrium is discussed by employing Lyapunov stability theory and LaSalle’s invariance principle. Moreover, uniform immunization and targeted immunization strategies are introduced to control the propagation of rumors. Besides, sensitivity analysis shows the different effects of parameters between Hyper-SIR model and SIR model. Finally, the numerical simulations are displayed and the results show Hyper-SIR model reaches equilibrium faster than general SIR model.
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