The competitive diffusion of knowledge and rumor in a multiplex network: A mathematical model

The competition between rumor and knowledge has received significant attention from the global world. How to spread knowledge to better contain rumor has also become an important practical issue. In this study, we build a multi-compartment model in a multiplex network to study the competitive diffusion of knowledge and rumor. Two factors are emphasized in the model: penetration of knowledge into rumor, and spreading channel difference between knowledge and rumor. The model is further improved with the information-infected states divided into two sub-states: information-accepted and information-sharing. The mean-field method is adopted to analyze the model and then verified by the numerical results in both ER random networks and BA scale-free networks. The consistent results in ER and BA networks show that both rumor and knowledge thresholds are increased by the intensity of competition between them, and the rumor-knowledge competition goes through four phases: "no rumor and no knowledge", "rumor outbreak and no knowledge" (rumor wins), "no rumor and knowledge outbreak" (knowledge wins), and "rumor vs knowledge" (rumor competes and coexists with knowledge), where the thresholds of rumor and knowledge act as the boundary of different phases. The different results in ER and BA networks show that rumor and knowledge are generally easier to break out in BA networks. But the BA rumor threshold may exceed the ER rumor threshold with the increase of rumor-knowledge competition, making rumor instead become difficult to break out in ER networks than that in BA networks, which infers that the hub nodes play very important roles in knowledge spreading. Based on the results, two types of management on rumor-knowledge competition are explored to control rumor and accelerate knowledge. Interestingly, critical values are discovered in both types of management, highlighting the importance of strengthening knowledge sharing and penetrating knowledge into rumor spreaders and listeners. The results reveal the management complexity of rumor-knowledge competition under different conditions.