SCIR rumor propagation model with the chord mechanism in social networks

Rumors, as a typical social phenomenon in real life, have a negative impact on the harmony of the society. When people hear rumors, they may not resonate with rumors because they do not trust them during the process of rumors transmission. Thus, they will not spread rumors. The essential difference between chord mechanism and spreader mechanism is that spreaders will spread regardless of whether they think it is true or false. The chord needs to believe that the rumor is true in order to keep spreading it, otherwise they become immune to spreading it. Therefore, this paper proposes a new Spreader-Chord-Ignorant-Restorer (SCIR) model, which considers that the trust may affect the level of empathy. Since the level of trust affects the spread of rumors and the extent to which the immune person trusts the rumor is different, the connecting edges from the restorer to the chord and the restorer to the ignorant were added to the model. First, the basic reproductive number [Formula: see text] is derived by the next generation matrix method and thus equilibriums are obtained. Then, the global stability of the rumor-free equilibrium [Formula: see text] and the persistence of rumor propagation are proved in detail during the theoretical analysis.