Abstract
A complex contagion is an infectious process in which individuals may require multiple transmissions before changing state. These are used to model behaviours if an individual only adopts a particular behaviour after perceiving a consensus among others. We may think of individuals as beginning inactive and becoming active once they are contacted by a sufficient number of active partners. Here we study the dynamics of the Watts threshold model (WTM). We adapt techniques developed for infectious disease modelling to develop an analyse analytic models for the dynamics of the WTM in configuration model networks and a class of random clustered (triangle-based) networks. We derive conditions under which cascades happen with an arbitrarily small initial proportion active. We also observe hybrid phase transitions when cascades are not possible for small initial conditions, but occur for large enough initial conditions.