Social contagion model induced by the effect of distinct social contexts

Almost all existing mathematical models of social contagion have been based on the assumption that the contagion probability is controlled by the number of exposures exerted by affected neighbors. However, recent empirical studies in several social contagion processes have revealed that the contagion probability is tightly controlled by the number of distinct social contexts formed by affected neighbors, rather than the actual number of exposures. Inspired by these empirical results, we propose a social contagion model with susceptible–adopted–susceptible dynamics in multi-relational networks. We incorporate the effect of distinct social contexts into our model by assuming that the contagion probability is determined by the number of layers to which an individual is exposed. Our model exhibits a rich variety of phase transitions containing continuous, discontinuous, and double transitions. We identify three universal classes of collective dynamics in the model and determine the conditions for the transitions between these classes. The bifurcation analysis shows that the transition conditions are dependent on the transmission probabilities of other layers and the probabilities of being adopted by one-layer and two-layer exposures, respectively. The theoretical results derived from Microscopic Markov-Chain Approach and mean-field theory are in good agreement with numerical simulations.