Mathematical model offers new strategies to prevent urban burglary

As with most crime, the highest rates of burglary occur in urban communities since large metropolitan areas generally boast more concentrated wealth. Big cities also allow burglars to maintain anonymity and evade authority while offering ample opportunities for discreet disposal of stolen property. Burglars observe their target cities with the careful attention of urban planners, taking note of public spaces, roadways, building architecture, behavior patterns, and tenant schedules. Although law enforcement is making concerted efforts to address and prevent burglary, frequent offenses in major metropolises continue to unsettle city-dwellers.

Existing mathematical models typically examine burglaries in residential, suburban environments, where similarly-structured houses with predictable lattice alignments are hotspots for repeated criminal activity. Some are agent-based, others utilize differential equations, and still others account for the effect of police presence. These models suggest that residential burglars prefer revisiting previously-burgled houses--or those with similar architecture--because they are already familiar with layout, security features, and availability of goods. Thus, if a home or its neighboring residence is robbed, repeat or near-repeat victimization heightens that home's attractiveness. While this phenomenon--upon which most models are based--occurs throughout the world, it is much more common in suburban districts. Flexible models that include alternate patterns of victimization are especially desirable when considering urban burglary.

A new approach has been presented based on a nonlinear model of urban burglary dynamics that accounts for the deterring effect of police presence. The new model emphasizes timing of criminal activity rather than spatial spreading and location. The work is inspired by age-dependent population models, which study a population's evolution in time based on the physiological ages of its individuals. A burglar's age is the amount of time since his most recent offense, while a house's age is the amount of time since it was last burglarized. The likelihood of robbery acts as a function of a burglar's age, and a house's susceptibility is a function of that house's age. When a burglar commits a crime, the ages of both the house and the burglar reset to zero. These details add a level of heterogeneity to the populations of houses and burglars.

When preparing their model, the authors ignore demographic turnover and assume that both the total number of burglars and burgled houses remain constant, i.e., a closed population of burglars acts on a specific geographic area. They also presume that a house's victimization age directly correlates with its status as a desirable target. Other considerations include the belief that all burglars will eventually commit another robbery (as long as vulnerable targets still exist) and the possibility of burglars working together (co-offending). In the authors' model, a lower house vulnerability leads to a higher degree of co-offending. The aforementioned assumptions imply a predator-prey type relationship between burglars and vulnerable homes.

Because this model is simpler than most previous models, it yields both numerical simulations and explicit results for further study. It also allows the authors to explore model adjustments, such as the introduction of space into the system via a meta-population approach or consideration of the burglars' physiological age or experience. Fundamentally, however, testing possible police configurations and strategies is of utmost importance, so the model can fit with real data and be relevant to police departments.