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

Abstract

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 R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> 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.