Dynamic behavior of an I2S2R rumor propagation model on weighted contract networks

Rumor, a typical social phenomenon in real life, has a considerably huge negative impact on the construction of a harmonious society. With the rapid development of Internet, different groups in the network exert more and more impact on rumor spreading with different level of influence. Therefore, the rumor propagation model of the unauthorized network may not be appropriate for describing the difference between the existing influence. In this paper, a novel I2S2R rumor spreading model in weighted contract networks is proposed. By analyzing the corresponding mean-field equations of this model, the basic reproduction number R₀ is calculated by the next generation matrix method. For the model with fixed weighted networks, by deriving the equation, the unique positive equilibrium of the system in fixed weighted networks is obtained. And meanwhile, the global stability of the rumor-free equilibrium and the persistence of the rumor equilibrium are studied. As for the model with adaptive weighted networks, we perform the stability of the equilibrium point by numerical simulations. Finally, several sensitive parameters which can prove the government effectively curb rumor spreading are obtained.