A Fractional Order Model for Rumor Spreading in Mobile Social Networks from A Stochastic Process

In this manuscript, a fractional order model for rumor spreading in mobile social networks (MSNs) is derived from an underlying physical stochastic process, which can be regarded as a heterogeneous-network-based fractional order epidemic model. In the model, the fractional derivative appears because of the time for denying the rumor is power law distributed. Then, the basic reproduction number R0 depended on the fractional derivative order is calculated. If $R_{0}\lt 1$, the rumor-free equilibrium is global asymptotically stable, the rumors will disappear. If $R_{0}\gt 1$, the rumor-endemic equilibrium is local stable, then the rumors will become endemic. Further, the numerical simulation based on the Digg2009 data set demonstrate the effectiveness of the proposed model.