Spreading Dynamics of a Word-of-Mouth Model on Scale-Free Networks

Nowadays, human behaviors are known to spread through social contact. Word-of-mouth (WOM) communication has also become a prevalent strategy for product sales on the internet and most consumers attribute a higher importance to WOM communication. Mathematical modeling is an important approach to study WOM communication in online social networks. In order to investigate the characteristics of WOM communication and heterogeneity of online social networks, a
$SIALS$
(susceptible-infected-acknowledged-loath) model is presented on scale-free networks. The spreading dynamics of WOM are analyzed in detail by using the theory of mean field. The basic reproductive number
$R_{0} $
is calculated by the next generation matrix method and two equilibriums are derived. The theoretical analysis indicates that the basic reproductive number depends mainly on the transmission of WOM and the topology of the underlying networks. Furthermore, the global stability of the WOM-disappearance equilibrium is proved. The permanence of WOM information spreading and the global attractivity of the WOM-prevailing equilibrium are also studied in detail. Finally, numerical simulations confirm the analytical results.