Rumor spreading and control in both homogeneous and heterogeneous networks with guidance mechanism

In this paper, we study the influence of authoritative institutions on rumor propagation and establish an IHSQR model, where Q represents the guided individuals. We consider the homogeneous and heterogeneous network models, respectively. By analyzing the conditions for the global asymptotically stable of equilibria in these models, we show their behavior under various scenarios. For the homogeneous network model, a case study of the Haze rumor is given, which verifies the effectiveness of the model. For the heterogeneous network model, we introduce optimal control to determine the minimum guidance strength and cost. The results show that the guiding role has a significant impact on rumor spread. Specifically, the stronger the guiding role, the smaller the size of rumor spreading. Therefore, to control the spread of rumors, authoritative institutions can play an important guiding role in managing and mitigating rumor propagation.