Dynamical analysis of Hyper-SIR rumor spreading model

• Published in: Applied mathematics and computation Vol. 446; p. 127887
• Main Authors: Zhang, Ziyu, Mei, Xuehui, Jiang, Haijun, Luo, Xupeng, Xia, Yang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.06.2023
• Subjects: Higher-order information interactions; Hyper-SIR; Hypergraph; Rumor prevailing equilibrium; Hypergraph; Higher-order information interactions; Rumor prevailing equilibrium; Hyper-SIR
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2023.127887

•For describing the influence of higher-order interactions in the rumor propagation, hypergraph theory is introduced in this paper.•The spreading rate in Hyper-SIR model based on higher-order group interactions is related to the size of groups, and the rumor propagation is not just spread by the point-to-point form. Besides, some new properties are founded.•Uniform immunization and targeted immunization strategies are proposed to control rumor propagation process. These strategies have a significant application in rumor spreading model. 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.