Mathematical home burglary model with stochastic long crime trips and patrolling: Applied to Mexico City

Abstract

Mathematical models for predicting the geographical distribution of areas with high rates of home burglary and numerical experiments to evaluate the effectiveness of police patrol routing strategies in reducing crime can support security policymakers in planning more effective patrol routes. We give an overview of the model formulated by Jones et al. (2010) to study the effects of the presence of law enforcement on the formation of home-burglary hotspots. We propose an extension of the model to contemplate that a small proportion of burglars travel far away from their awareness space to burgle houses. We incorporate these trips in the form of long-range stochastic jumps that are biased towards more attractive sites. Simulations suggest that hotspots lose attractiveness as police more influences via deterrence on burglars’ decision making about returning home rather than burglarizing a house. The results indicate that a higher proportion of burglars making long crime journeys might counteract the deterrent effect form the police presence. A case study is carried out to predict at the zone and citywide levels the distribution of areas with the highest home burglary rates in Mexico City. The L-BFGS method is applied to get the values for the parameters in both the Jones et al. model and our model; we use data from home burglaries reported, patrol zones and prison admissions. The minimum of the objective function is slightly lower for our model than for the Jones et al. model. Results obtained through numerical simulations using our model better fit the spatial statistical distribution of home-burglary hotspots for the entire city than for the zones.