John Lang, PhD Candidate
Department of Applied Mathematics, University of Waterloo
A Hierarchy of Linear Threshold Models for the Spread of Political Revolutions on Social Networks
We formulate a linear threshold agent-based model (ABM) for the spread of political revolutions on social networks using empirical network data. We propose new techniques for building a hierarchy of simplified ordinary differential equation (ODE) based models that aim to capture essential features of the ABM and give insight in the parameter regime transitions of the ABM. Specifically, we relate the ABM to a previously developed one-dimensional population-level ordinary differential equation (ODE) model. We then present two new effective ways to incorporate network structure into the ODE model that enhance the ability of the ODE model to approximate the dynamical evolution of ABM. We show numerically that these ODE approximations often perform as well as or better than a higher-order model. In small-scale numerical tests we investigate experimentally the differences in spreading behaviour that occur under the ABM when applied to some empirical (modern) online social networks versus (traditional) offline social networks, searching for quantitative evidence that political revolutions may be facilitated by the modern online social networks of social media.