Social contagions on interconnected networks of heterogeneous populations

Recently, the dynamics of social contagions ranging from the adoption of a new product to the diffusion of a rumor have attracted more and more attention from researchers. However, the combined effects of individual's heterogenous adoption behavior and the interconnected structure on the social contagions processes have yet to be understood deeply. In this paper, we study theoretically and numerically the social contagions with heterogeneous adoption threshold in interconnected networks. We first develop a generalized edge-based compartmental approach to predict the evolution of social contagion dynamics on interconnected networks. Both the theoretical predictions and numerical results show that the growth of the final recovered fraction with the intralayer propagation rate displays double transitions. When increasing the initial adopted proportion or the adopted threshold, the first transition remains continuous within different dynamic parameters, but the second transition gradually vanishes. When decreasing the interlayer propagation rate, the change in the double transitions mentioned above is also observed. The heterogeneity of degree distribution does not affect the type of first transition, but increasing the heterogeneity of degree distribution results in the type change of the second transition from discontinuous to continuous. The consistency between the theoretical predictions and numerical results confirms the validity of our proposed analytical approach.