Spreading dynamics of an online social rumor model with psychological factors on scale-free networks

Abstract Considering people’s psychological factors such as hesitation and forgetting, and the heterogeneity of online social networks, a novel S H P R S (susceptible–hesitating–propagating–resisted–susceptible) rumor spreading model on scale-free networks is proposed in this paper. The spreading dynamics of rumor is analyzed in detail through the mean-field theory. First, the basic reproductive number R 0 is derived by the next generation matrix method and equilibriums are obtained. Both the existence of rumor equilibriums and the dynamic behaviors of model are determined by the basic reproductive number R 0 . Then, the global stability of the rumor-free equilibrium E 0 and the permanence of rumor spreading are studied in detail. Furthermore, we studied the global attractivity of the rumor-prevailing equilibrium. Finally, numerical simulations are performed to confirm the analytical results.

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