SEIDR: modeling the competitive propagation of rumor and anti-rumor in complex networks with emotional infection theory

Social networks have become the best medium for the unbridled dissemination of rumor, which arises with the crisis of environment and has serious negative functions on social stability and people’s daily life. At present, a series of models have been constructed to study the spreading dynamics of rumor. However, most of existing researches ignore the competitive relationships between rumor and anti-rumor, and the emotional tendencies that may occurs during the propagation process of rumor. In this work, we construct a Susceptible-Exposed-Infectious-Debunker-Recovered (SEIDR) model by adopting the emotional infection theory of users and the competitive mechanism between rumor and anti-rumor. Furthermore, we investigate the influence of debunking behaviors and varying emotional intensities on the propagation of rumor. Then, the stability behaviors of rumor-free and epidemic equilibriums are calculated according to Routh–Hurwitz stability criterion. Finally, numerical examples are carried out to describe the influence of different parameters and verify the validity of theoretical results.