Abstract
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.
Highlights
Rumors refer to unconfirmed information and are spread in certain ways. e rumor-spreading model can be traced back to the 1960s
Later researchers called the rumor-spreading model in the name of the author for the D-K model. e D-K model analyzes the problem of rumors based on a random process and divides people in the process of spreading rumors into three categories: people who have never heard of rumors, people who spread rumors, and people who have heard rumors but did not spread them
It is found that the D-K model and the M-K model are only applicable to rumor propagation models in small-scale social networks, but social networks in daily life are large in scale and have the characteristics of small world and scalefree
Summary
Rumors refer to unconfirmed information and are spread in certain ways. e rumor-spreading model can be traced back to the 1960s. From the analysis of the research work on the rumorspreading model, it can be seen that compared with infectious diseases, rumor spreading has specific complex network characteristics. Mathematical models play an important role in the study of the spread of rumors, and the spread of rumors in society can be seen as a network communication behavior that obeys a certain law. Most previous works assume that rumors spread in a closed system and the population size in OSNs (Open Systems Network Support) is constant These models can only simulate the rumorspreading process in a closed system for which rumors spread over a relatively short period of time. An SIDRQ rumor propagation model is proposed to describe the dynamic model with suspicion mechanism, immune mechanism, forgetting mechanism, and guiding mechanism.
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