A spatial model for conflict incorporating within- and between-actor effects

Abstract

The application of ecological models to human conflict scenarios has given rise to a number of models which describe antagonistic relationships between adversaries. Recent work demonstrates that the spatial disaggregation of such models is not only well-motivated but also gives rise to interesting dynamic behaviour, particularly with respect to the spatial distribution of resources. One feature which is largely absent from previous models, however, is the ability of an adversary to coordinate activity across its various locations. Most immediately, this corresponds to the notion of ‘support’ — the reallocation of resources from one site to another according to need — which plays an important role in real-world conflict. In this paper, we generalise a spatially-disaggregated form of the classic Richardson model of conflict escalation by adding a cross-location interaction term for the within-adversary dynamics at each location. We explore the model analytically, giving conditions for the stability of the balanced equilibrium state. We then also carry out a number of numerical simulations which correspond to stylised real-world conflict scenarios. Potential further applications of the model, and its implications for policy, are then discussed.