Modeling the competitive propagation of rumors and counter-rumors in two-layer complex networks with nonlinear spreading and decay rates

Abstract

Prior investigations into the propagation of rumors have predominantly focused on either online or offline social networks, neglecting the concurrent dissemination of rumors and counter-rumors. Hence, to investigate how rumors and counter-rumors spread and interact in online and offline two-layer networks, and to devise an optimal control strategy for rumors, we propose a nonlinear SEIDR spreading model that incorporates the effects of social reinforcement and interest decay. By constructing mean-field equations, we present the mathematical expression of the SEIDR model and further define and compute the basic reproduction number of rumors. Subsequently, three theorems related to the final scale of rumors are introduced. Finally, we investigate the primary factors influencing rumor propagation via Monte Carlo simulations, yielding the following key findings: (i) The final scale of rumors exhibits a positive correlation with the social reinforcement effect and the second-order moment of the network, while displaying a negative correlation with the interest decay effect and the average degree of the network. (ii) The final scale of rumors ranks in the order of: random network > scale-free network > small-world network > regular network. (iii) Notably, the speed of rumor propagation aligns with the order: scale-free network > random network > small-world network > regular network.