Local and Global Intervention for Public Opinion Evolution Based on a Memory-Decaying SIS-FJ Model

The evolution of public opinion on social media is marked by elevated diffusion efficiency, heightened interactivity, and considerable influence. Failure to effectively control the dissemination of negative public opinion or the polarization of group opinions can readily impact public cognition and the management of social risks. Existing research has not sufficiently captured the coupled dynamics of information diffusion and opinion interaction, nor has it adequately modeled the cognitive mechanisms underpinning the evolution of public opinion. Furthermore, the evolutionary logic and quantitative assessment of intervention strategies remain underexplored. Building upon the bidirectional SIS (Susceptible–Infected–Susceptible)-FJ (Friedkin–Johnsen) coupling framework, this study introduces an exponential decay mechanism for historical opinions and develops a memory-decaying SIS-FJ model. This model not only aligns more closely with the cognitive principle of memory decay in a physical sense, but also mathematically resolves the non-convergence problem of opinions in the traditional FJ model caused by fixed initial opinion weights. On this foundation, we propose two intervention strategies: local intervention targeting hub nodes and global intervention centered on authoritative nodes. Experimental findings demonstrate that both approaches can effectively regulate public opinion evolution. Specifically, global intervention accelerates opinion convergence, whereas local intervention affords greater flexibility in modulating the intensity of intervention. This study can provide a methodological reference for the management of public opinion on social media platforms.