Stability analysis and control models for rumor spreading in online social networks

Abstract

This paper establishes a novel Susceptible-Infected-Removed (SIR) rumor spreading model for online social networks (OSNs). The model utilizes the node degree to describe the dynamic changes of the number of rumor spreaders and it can be regarded as an extension of the traditional SIR model. Stability analysis of the model reveals that the spreader in social networks has a basic reproduction number. If the basic reproduction number is less than 1, then rumors will disappear. Otherwise, rumors will persist. According to this result, we can predict the trend of rumor spreading. Then we propose an immune-structure SIR model to explore the control method of rumor spreading. Stability analysis and numerical simulation of the model indicate that immunizing susceptible individual is an effective method to control rumors. Further, the immune-structure model explains that the network structure decides the choice of immune methods. Our findings offer some new insights to control the spread of rumors on OSNs.