Social contagions with heterogeneous credibility

An individual's credibility is strongly affected by their social status. Assuming that a person's level of credibility correlates with their degree from a microscopic perspective, we propose a non-Markovian model to understand how the heterogeneity of credibility levels affects social contagions within a population. To describe the model, we develop a heterogeneous edge-based compartmental theory. Through extensive numerical simulations, we find that the growth pattern of the final adoption size versus the information transmission probability is discontinuous, and that in ER networks the final adoption size increases when hubs have high levels of credibility. When hubs in an ER network have low levels of credibility, the growth pattern is continuous. We also study social contagions on SF networks and find that the growth pattern versus information transmission probability is always continuous. On both ER and SF networks, the final adoption size versus the heterogeneity parameter exhibits a discontinuous pattern. The results of our theory agree well with those of numerical simulations.