Many models of disease and rumor spreading phenomena average the behavior of individuals in a population in order to obtain a coarse description of expected system behavior. For these types of models, we determine how close the coarse population-level approximation is to its corresponding agent-based system and discuss the accuracy of the population-level approximation. We apply these theoretical results to real social network data to see how well they describe the contagious nature of social phenomena. Specifically, we consider hashtag adoption data collected from the Twitter social network. To assimilate the Twitter data to a simple contagion model, we developed and implemented statistical learning methods to construct an adaptive state estimator for systems described by nonlinear stochastic differential equations.

We found that the static network structure alone is not sufficient for explaining hashtag adoption among users in the Twitter social network, and our result suggest that a user-centric model would be more appropriate for this task. We propose a model for individual social media users, termed a genotype, which is a per-topic summary of a user's interest, activity and susceptibility to adopt new information. We show that the genotype framework is capable of accurately quantifying the adoption behavior of individual users with respect to hashtag topics.