  We study 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, including effects of the actual networks, and give insight in the
parameter regime transitions of the ABM. We relate the ABM and the hierarchy of
models to a population-level compartmental ODE model that we proposed
previously for the spread of political revolutions [1], which is shown to be
mathematically consistent with the proposed ABM and provides a way to analyze
the global behaviour of the ABM. This consistency with the linear threshold ABM
also provides further justification a posteriori for the compartmental model of
[1]. Extending concepts from epidemiological modelling, we define a basic
reproduction number $R_0$ for the linear threshold ABM and apply it to predict
ABM behaviour on empirical networks. In small-scale numerical tests we
investigate experimentally the differences in spreading behaviour that occur
under the linear threshold ABM model when applied to some empirical online and
offline social networks, searching for quantitative evidence that political
revolutions may be facilitated by the modern online social networks of social
media.
