Competitive information spreading model in two-layer networks considering dual debunking mechanisms and time lag effects

With the widespread use of social media in modern society, the impact of rumor propagation on public opinion and social stability has become increasingly prominent. Investigating the dynamics of rumor propagation is crucial for developing effective rumor control strategies and mitigating the harmful effects of rumors. However, existing studies primarily focus on the effects of individual or media debunking mechanisms within a single-layer network framework, often assuming uniform time lag effects across different propagating entities and processes. To address these gaps, this paper aims to comprehensively examine both debunking mechanisms, along with different types of time lag effects arising from information collection, transmission, and clarification processes, to investigate how rumors and counter-rumors interact and spread within two-layer networks. We first develop a new rumor spreading model, the XYZ-SIDR model, which consists of seven states: susceptible, debunking, and removed media, as well as susceptible, infected, debunking, and removed individuals. We then calculate the basic reproduction number and establish the local and global asymptotic stability of the model’s equilibrium points. Similarly, we construct and analyze an SIDR spreading system without the media debunking mechanism, which serves as a comparison to understand the impact of the media debunking mechanism on rumor propagation. Additionally, we examine the XYZ-SIDR spreading system with different time lags, allowing us to explore the influence of time lags on rumor propagation. Finally, the stability of the XYZ-SIDR model is verified using numerical simulations, key factors influencing rumor propagation are explored, and a comparative analysis of the XYZ-SIDR model with the SIDR and SIR models is conducted.