A SEIR-UD model with reinforcement effect for the interaction between rumors and rumor-induced behaviors

Given the significant impact of interactive rumor and rumor-induced behavior propagation on societal stability and individual well-being, understanding the dynamics of their interaction is crucial. To this end, this paper introduces the SEIR-UD model, which encapsulates the reinforcing dynamics between rumors and behaviors, illustrated through real-world instances. Subsequently, mean-field equations describing the system of rumor-behavior interactive spreading (RBIS) are derived. It deeply analyzes the propagation threshold of RBIS and the influences of reinforcement effect on the local and global stability of rumor-behavior free/existence equilibriums (RBFE/RBEE). Finally, the RBIS event triggered by COVID-19 in 2020 is taken as an example to evaluate the proposed model, and investigate the roles of reinforcement effect, intervention strategies, and intensities on the evolutionary process of RBIS. The findings reveal that the SEIR-UD model closely mirrors real-world data trends in RBIS scenarios, surpassing models that overlook RBIS dynamics. Furthermore, the increase of reinforcement effect tends to have obvious positive impacts on the maximum influence of RBIS, while is not much pronounced on final RBIS size. Moreover, interventions targeting both rumors and behaviors, especially when intensified, are effective in diminishing RBIS’s peak impact and hastening the transition to a stable state.