A sentinel-triggered competing dynamical strategy for misinformation containing in higher-order social networks

The widespread dissemination of misinformation in social networks poses significant threats to cybersecurity, social stability, and the credibility of information. Conventional approaches to misinformation containment often neglect the higher-order interaction structures among users (i.e., multiple users' communications) and the dynamic characteristics of real-world propagation. To address this issue, we propose a sentinel-triggered competing dynamical strategy that integrates local sensitivity monitoring with competing spreading dynamics on higher-order social networks. In this strategy, a certain proportion of nodes are designated as sentinels that continuously monitor their neighbours for evidence of misinformation. Once the local prevalence of misinformation surpasses a predefined threshold, they are activated to broadcast the truth, thereby initiating a competing Susceptible-Infected-Susceptible (SIS) spreading process against the misinformation. Theoretical analysis using the mean-field approximation reveals a first-order phase transition from a persistent misinformation state to complete suppression, identifying the critical conditions for the eradication of misinformation. Both theoretical predictions and numerical simulations show that when the proportion of sentinel nodes exceeds a critical value and activation thresholds are low, misinformation is rapidly suppressed; otherwise, misinformation persists. These findings highlight the importance of balancing sentinel density and activation sensitivity under varying levels of misinformation virulence to achieve optimal containment. Furthermore, by defining a cost function, we find that there exists an optimal proportion of sentinel nodes that can achieve an effective balance between cost control and propagation loss. This study offers theoretical support and practical guidance for mitigating the spread of misinformation.