Riots originating during, or in the aftermath of, sports events can incur significant costs in damages, as well as large-scale panic and injuries. A mathematical description of sports riots is therefore sought to better understand their propagation and limit these physical and financial damages. In this work, we present an agent-based modelling framework that describes the qualitative features of populations engaging in riotous behaviour. Agents, pertaining to either a 'rioter' or a 'bystander' sub-population, move on an underlying lattice and can either be recruited or defect from their respective subpopulation. In particular, we allow these individual-level recruitment and defection processes to vary with local population density. This agent-based modelling framework provides the unifying link between multi-population stochastic models and density-dependent reaction processes. Furthermore, the continuum description of this ABM framework is shown to be a system of nonlinear reaction-diffusion equations and faithfully agrees with the average ABM behaviour from individual simulations. Finally, we determine the unique correspondence between the underlying individual-level recruitment and defection mechanisms with their population-level counterparts, providing a link between local-scale effects and macroscale rioting phenomena.
Agent-based modelling of sports riots