In this paper, we study the propagation characteristics of rumors in an institution and develop the rumor dissemination model inside the institution. Different from the traditional model, a person in the proposed model can make a judgement about the message and decide to propagate it or refute it, and most people inside the institution can refute the rumor spreaders and propagate the genuine messages to uninformed people when they have confirmed the message is a rumor. Then, we split all the people into two institutions (inside and outside). Since the rumors and genuine messages from the institution can have a non-negligible impact on people outside the institution, we put forward a new double-institution rumor propagation model , and the model considers the impact of messages on the inside and outside of the institution simultaneously. Based on the two proposed models, the basic reproduction numbers are obtained respectively, and the local and global stability of the rumor-free equilibrium points are discussed separately. We numerically simulate the propagation of rumors in small-world networks. The simulation is carried out to verify the validity of the proposed model, and our model is closer to the reality than traditional models.
