Social contagion models on adaptive simplicial complexes

Complex networks, composed of nodes and edges connecting them, are successful in modeling various social contagion phenomena, such as epidemic spreading or rumor diffusion in population. Recently, there is extensive interest in studying higher-order interactions which uncover the complex mechanisms of influence and reinforcement in social contagion. Yet, existing models are primarily within the framework of static networks. Here we investigate the susceptible–infected–susceptible model on adaptive simplicial complexes, in which the networks exhibiting high-order structure can change their connectivity with time depending on their dynamical state. By applying mean-field equations, we derive an implicit analytical expression of the invasion threshold in adaptive simplicial complexes, but explicit expressions of the invasion threshold in three prototypical adaptive networks. We further analyze the effects of the transmission rate, the rewiring rate and higher-order interactions on epidemic prevalence and the invasion threshold. Our model can lead to collective phenomena including first-order phase transition, bistability, and hysteresis loops. Our study paves the way to predict and control a wide variety of social contagion processes on networks.