Spreading Dynamics of a CPFB Group Booking Preferential Information Model on Scale-Free Networks

With the development of the Internet, online shopping has become a popular way of life in contemporary society. In recent years, online group booking has become an important strategy for e-commerce to promote commodities. In order to study the impact of the products’ discount rate, customer’s repurchase intention and the heterogeneity of the networks on the spreading of group booking preferential information, we present a novel
$CPFB$
(customer-participant-forwarder-beneficiary) group booking preferential information spreading model based on scale-free networks. The dynamic propagation of preferential information in group booking online is analyzed in detail by the mean-field theory. The basic reproductive number
$R_{0} $
and the two equilibriums are obtained. Then, locally asymptotical stability of equilibriums is discussed based on the Routh–Hurwitz criterion. The global asymptotic stability of the group booking free equilibrium, the permanence of preferential information spreading and the global attractivity of the group booking equilibrium is proved in detail. Theoretical results show that the basic reproductive number
$R_{0} $
depends mainly on the discount rate and the topology of the underlying networks. And the size of the repurchase intention rate
$\eta $
can promote the spreading of preferential information about online group booking, but do not affect the size of the basic reproductive number
$R_{0} $
. Finally, numerical simulations confirm the analytical results of the theories.