Studying Rumor Immunization On Small-world Networks

Studies about networks indicate that many networks have "small-world effect". Therefore, sometimes small-world networks can accurately describe the structure of networks in the real world. Further, it is meaningful and important to investigate problems concerned with the rumor propagation. Based on those facts, we study the rumor propagation on small-world networks and our work is as follows:1. We modify the rumor model introduced by Moreno and coauthors which describes the rumor propagation on networks. We divide the class of people who lose interest to spread the rumor into two subclasses. One class corresponds to the people who accept the rumor but lose interest to propagate it; the other class corresponds to the people who reject the rumor. In addition, we introduce a new parameter which can represent the credibility of the rumor.2. Based on those modifications, we give mean-field equations about the rumor propagation on small-world networks. Through solving these equations, we find that there is no "rumor-threshold" on small-world networks. Further, the parameter which can represent the credibility of the rumor has inverse relation with the density of individuals who accept the rumor but lose interest to spread it.3. We investigate whether random immunization mechanism and targeted immunization strategy are effective or not in the modified rumor model. Through numerical simulations and analysis, we find that when the average degree of the network is small, random immunization strategy and targeted immunization strategy can successfully control the propagation of the rumor. However, it is not the case when the average degree of the network is large. In this circumstance, we can decrease the rumor credibility and apply random or targeted immunization strategy at the same time. As a consequence, the rumor propagation can be still controlled without immunizing large density of individuals on networks.