Spatio-temporal modelling of civil violence: Four frameworks for obtaining policy-relevant insights

Mathematical modelling of civil violence can be accomplished in different ways. In this thesis, four modelling frameworks are investigated, each of which leads to different insights into the spatio-temporal properties of civil violence. These frameworks vary with respect to the extent in which empirical data is used in generating model assumptions, and the extent in which simplifying assumptions distance the model from the real world. An overarching objective is to compare the insights and underlying assumptions of each framework, and to consider how they might be consolidated to aid policy decision-making. Within each framework, novel contributions both to the mathematical modelling of social systems, and to the theoretical understanding of civil violence are made. First, a novel data-driven approach for analysing local patterns of geographic diffusion in event data is presented, and applied to offences associated with the 2011 London riots. Second, by considering the decision-making of individuals, thereby taking an agent-based perspective, and using existing theory to construct model assumptions, a parametric statistical model of discrete choice is derived that more closely inspects the targets chosen by rioters, and how these choices might have changed over time. The application of this model to the policy domain is explored by considering police deployment strategies. Third, focusing on the interaction between two adversaries, and employing stochastic point process models, a series of multivariate and nonlinear Hawkes processes are proposed and used to explore spatio-temporal dependency during the Naxal insurgency in India. Fourth, a novel spatially-explicit differential equation-based model of conflict escalation between two adversaries is derived. A bifurcation is identified that results from the spatial disaggregation of the model. Implications for the interpretation of the model in the real world and potential applications are discussed