Global stability analysis and control law design for rumor propagation models

This study develops a compartmental dynamical model to elucidate rumor propagation mechanisms in social contact. The model categorizes individuals into three distinct groups: ignorant, spreaders, and wise individuals who can identify and counter misinformation. By introducing a standard incidence rate and two key reproduction numbers Rw and Rv, we establish a complete global stability analysis for all system equilibria. Our results uncover two fundamental mechanisms for rumor control: increasing Rw induces a phase transition from rumor persistence to extinction, while reducing Rv below a critical threshold can drive rumor collapse, albeit with a potential trade-off in wise individual density. Furthermore, we demonstrate that targeted interventions, including limiting contact between ignorant individuals and spreaders and enhancing fact-checking initiatives, can effectively suppress rumor dissemination. Notably, strengthening debunking capabilities not only curbs rumor spread but also amplifies the wise population, creating a positive feedback loop for sustainable rumor containment. These findings provide actionable strategies for mitigating the societal impact of misinformation.