In the process of rumor spreading, controlling and killing rumor problem is of great importance on social networks. In this paper, we present a new SEIR (susceptible-exposed-infected-removed) rumor spreading model with hesitating mechanism. By using mean-field theory, the equilibrium of the model and the basic reproduction number R 0 are obtained. The global stability of the rumor-free equilibrium and the permanence are proved in detail, and the global attractivity of the rumor-prevailing equilibrium is proved by using a monotone iterative technique. Furthermore, the modified model with feedback mechanism on social networks is introduced. The feedback mechanism cannot change the basic reproductive number but it can reduce the continuous level and the spread of rumor. Numerical simulations confirm the analytical results.

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