Impact of individual activity on behavior adoption in complex networks: A two-layer generalized SAR model analysis

The correlation between an individual's activity level and the propagation of behavior is inherently intertwined on a social platform. Simultaneously, individuals with varying activity levels are subject to social reinforcement during the information accumulation process. In this paper, we develop a two-layer generalized Susceptible-Adopted-Recovered (SAR) model to simulate the cumulative effect of information reliability influenced by individual's activity and social reinforcement. Furthermore, we investigate how the accumulation of information reliability affects individual behavioral adoption. We provide a theoretical analysis of the mathematical model of the two-layer network based on edge-based compartmental theory and mean field theory. Subsequently, numerical simulations are performed to validate the model's effectiveness and offer insights for the advancement of information dissemination strategies. The results show that the proportion of active nodes in the network and their active intensities have a significant effect on behavioral propagation. The increase of them can reduce the outbreak threshold of behavioral adoption and expand the scale of behavioral adoption. Additionally, the intensity of local social reinforcement of information reliability has a more significant positive effect on behavioral adoption than global social reinforcement. Moreover, the information threshold of behavioral adoption in the Scale-Free (SF) network is larger than that in the Erdös-Rényi(ER) network.