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The spread of rumors has a great impact on social order, people’s psychology, and life. In recent years, the application of rumor-spreading models in complex networks has received extensive attention. Taking the management and control of rumors by relevant departments in real life into account, the SIDRQ rumor-spreading model that combines forgetting mechanism, immune mechanism, and suspicion mechanism and guides on a uniform network is established in this paper. Then, the basic reproductive number of the system and the unique existence of the solution are discussed, and the stability of the system is analyzed using the basic reproductive number, Lyapunov function, and Lienard and Chipart theorem; furthermore, the basic reproductive number may not be able to deduce the stability of the system and a counterexample is given. Finally, the influence of different parameters on the spread of rumors is studied, and the validity of the theoretical results is verified.

Dynamics of the Rumor-Spreading Model with Control Mechanism in Complex Network