The competitive diffusion of rumor and anti-rumor in multiple layer networks considering time delay and triple debunking mechanisms

Abstract The investigation of rumor propagation mechanisms is crucial for the development of effective rumor control strategies. Most of the existing research are devoted to separately analyzing the influence of user or media debunking mechanisms on rumor propagation in single-layer networks, and few propagation models comprehensively consider the two kinds of debunking mechanisms on the propagation process. In addition, researchers tend to assume that different entities have a uniform time-delay effect in the propagation process. To fill these gaps, this work constructs a novel spreading dynamics model, called KLM-SIDR-XY, to systematically explore the interaction relationships and competitive propagation process of rumor and anti-rumor in a multiple layer network. The proposed model considers the time delay effect and triple debunking mechanisms of different entities in the propagation process, and the debunking individuals and behaviors are separately discussed to make it more comprehensive and realistic. Then, the mean field equation is introduced to calculate the basic regeneration number of the proposed model, and the Lyapunov stability theory is introduced to analyze the local and global stability of the proposed model with and without considering the time delay effect. Finally, we conduct several simulation experiments to discuss the effects of different parameters on the stability of KLM-SIDR-XY model, and aim to find out the vital factors affecting the rumor propagation process. Numerical simulations reveal that during the initial stage of rumor propagation, individuals are more likely to spread rumor due to the time delay in debunking mechanisms. The effect of time delay on the rumor and anti-rumor propagation process shows a tendency towards decreasing marginal effects, while the earlier intervention measures are taken to address the spread process of rumor, the more substantive and significant effects can be achieved. In addition, triple debunking mechanisms affect the duration and peak value of rumor and anti-rumor, which effectively controls the spread of rumor and increases the propagation scale of anti-rumor.