Dynamics analysis of an online gambling spreading model on scale-free networks

Abstract

Abstract Nowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new SHGD (susceptible–hesitator–gambler–disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive number R 0 $R_{0}$ is got and analyzed. The basic reproductive number R 0 $R_{0}$ is related to anti-gambling policy and the network topology. Then, gambling-free equilibrium E 0 $E_{0}$ and gambling-prevailing equilibrium E + $E_{ +} $ are obtained. The global stability of E 0 $E_{0}$ is analyzed. The global attractivity of E + $E_{ +} $ and the persistence of online gambling phenomenon are studied. Finally, the theoretical results are verified by some simulations.

Keywords

• SHGD model
• Heterogeneity
• Psychological factors
• Anti-gambling policy
• Stability
• Persistence