SHI1I2R competitive information spreading model in online and offline two-layer networks in emergencies

Previous research on information propagation has primarily focused on either online social networks or offline social networks. Additionally, there remains a gap in understanding the propagation of competitive information in emergency scenarios. This paper introduces an SHI1I2R information spreading model to investigate the dynamics of competitive information dissemination and interactions in online and offline two-layer networks during emergencies. To enhance the accuracy of information propagation modeling, we depart from the conventional assumption of constant spreading and decay rates and instead propose nonlinear spreading and interest decay rates within the SHI1I2R model. Employing a microscopic Markov chain approach, we conduct theoretical analysis and derive the spreading threshold of information in two-layer networks. Subsequently, we perform numerical simulations to validate the effectiveness of the SHI1I2R model and explore the factors influencing information propagation. Our findings indicate that information spreads more rapidly and extensively in two-layer networks compared to one-layer networks. Furthermore, the final scale of information dissemination and the speed of propagation follow the order: random network > small-world network > scale-free network > regular network.