Abstract
Nowadays, pyramid schemes have caused extremely negative effects on people’s lives and seriously damaged the social economy. With the rapid development of network and communication technology, people’s direct or indirect social interaction is more frequent, which makes the phenomenon of pyramid schemes more serious. Therefore, it is necessary to study transmission mechanisms and transmission rules of pyramid schemes. In order to study the influence of government management and social interaction topology on the spreading of pyramid schemes, a novel SHIPR (susceptible-hesitator-involved-punished-resister) pyramid scheme spreading model is proposed on scale-free networks. The spreading dynamics of pyramid schemes are analyzed in detail by mean-field theory. Then, the basic reproduction number $R_{0}$ and equilibria are got. Theoretical analysis shows that the basic reproduction number $R_{0}$ has a great correlation with government crackdown intensity for involved individuals, the coverage rate of government anti-pyramid scheme publicity for susceptible individuals and hesitator, and social interaction topology. Furthermore, the local asymptotic stability of fraud-elimination equilibrium is analyzed based on the Routh-Hurwitz criterion, the global asymptotic stability of the fraud-elimination equilibrium is discussed by the Lyapunov function, the global attractivity of fraud-prevailing equilibrium is proved in detail by comparison principle. Finally, numerical simulations verify the theoretical analysis results.
Highlights
With the development of network and communication technology, people's life and work are more convenient, but various pyramid scheme organizations emerge in endlessly due to the imperfect internet supervision mechanism
The number of people participating in pyramid schemes is growing exponentially, the economic losses caused by pyramid schemes are increasingly serious [4, 5]
Constantin et al [15] studied the main features of legal marketing and analyzed how independent distributors avoid cooperation with illegal pyramid schemes
Summary
With the development of network and communication technology, people's life and work are more convenient, but various pyramid scheme organizations emerge in endlessly due to the imperfect internet supervision mechanism. It is necessary to take effective control measures and establish a pyramid scheme model to study the spreading dynamics of pyramid schemes. Constantin et al [15] studied the main features of legal marketing and analyzed how independent distributors avoid cooperation with illegal pyramid schemes. They have not studied the dynamics behavior of the spread of pyramid schemes. B. Xue et al.: Spreading Dynamics of SHIPR Pyramid Scheme Model on Scale-free Networks to controlling the spread of pyramid schemes and reducing the damage of pyramid schemes to society. Based on the above analysis, considering government management and social interaction topology, we present a novel SHIPR pyramid scheme spreading model on scale-free networks.
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