The spread of infectious pathogens in socially structured populations is shaped by variability in host behavior and resource access, which can burden certain individuals with transmission potentials far above the population average. Additionally, infector-infectee pairs in social systems may also have more similar transmission potentials than expected by chance, as risk factors assort among individuals who frequently interact. Epidemic models indicate that transmission heterogeneity can alter the size and frequency of local outbreaks, while assortativity in transmission potential can affect the probability that an outbreak will grow into a major epidemic. However, the joint impact of transmission heterogeneity and assortativity in real-world populations remains poorly understood, due to the difficulty of capturing the multifaceted ways in which populations can be organized. As a result, we lack a predictive understanding of epidemic thresholds in social systems, and particularly in human populations. In this talk I will present work to quantify the net impact of transmission heterogeneity and assortativity on epidemic risk by modeling autocorrelation of individual reproductive numbers along chains of transmission. Outbreaks can be orders of magnitude larger when individual reproductive numbers are autocorrelated, and self-exciting superspreading events can sustain epidemics even when the average reproductive number in the wider population is less than one. Applying this framework for statistical inference, we find significant autocorrelation in empirical transmission trees previously reported in the literature for a range of pathogens including SARS, SARS-CoV-2, and Ebola. We demonstrate that the critical threshold for control in social-epidemic systems is dynamic and can shift in response to control measures, with the potential to drive persistence beyond canonical elimination points predicted by asocial models. Our results quantify the conditions under which populations of social organisms may collectively amplify or suppress transmission of infectious agents, providing a mathematical foundation to predict the spread and control of contagion in complex adaptive systems.