Global Stability Analysis of Rumor Propagation in Social Networks
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Abstract
Rumor propagation is a typical form of social interaction that has a negative effect on society and human life. The study of rumor dissemination and regulation on social networks is significant and vital. The propagation of rumors is caused by a variety of circumstances. In this study, we take into account how people react to rumors differently depending on their personalities and levels of comprehension. In order to categorize the entire human population, we use the terms susceptible (S), exposed (E), infected (I), and recovered (R).
The dynamics of rumor transmission in social networks are represented by differential equations. The spreading threshold of the SEIR model in social networks is then obtained using the Jacobian matrix and the Next Generation matrix. Then the equilibrium's existence and stability are analyzed. It is established that rumor-free equilibrium E0 is locally asymptotically stable if the basic reproduction number is low, which means rumor has stopped spreading in a population, and unstable if the basic reproduction number is high, which means new rumor is spreading in the population. Finally, in order to validate the analytic findings, numerical simulations of the dynamic model are run on the system using MATLAB.
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References
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