A Hierarchy of Linear Threshold Models for the Spread of Political Revolutions on Social Networks

摘要

We study a linear threshold agent-based model (ABM) for the spread ofpolitical revolutions on social networks using empirical network data. Wepropose new techniques for building a hierarchy of simplified ordinarydifferential equation (ODE) based models that aim to capture essential featuresof the ABM, including effects of the actual networks, and give insight in theparameter regime transitions of the ABM. We relate the ABM and the hierarchy ofmodels to a population-level compartmental ODE model that we proposedpreviously for the spread of political revolutions [1], which is shown to bemathematically consistent with the proposed ABM and provides a way to analyzethe global behaviour of the ABM. This consistency with the linear threshold ABMalso provides further justification a posteriori for the compartmental model of[1]. Extending concepts from epidemiological modelling, we define a basicreproduction number $R_0$ for the linear threshold ABM and apply it to predictABM behaviour on empirical networks. In small-scale numerical tests weinvestigate experimentally the differences in spreading behaviour that occurunder the linear threshold ABM model when applied to some empirical online andoffline social networks, searching for quantitative evidence that politicalrevolutions may be facilitated by the modern online social networks of socialmedia.