Predicting burglary patterns through math modeling of crime

May 31, 2012

Pattern formation in physical, biological, and sociological systems has been studied for many years. Despite the fact that these subject areas are completely diverse, the mathematics that describes underlying patterns in these systems can be surprisingly similar. Mathematical tools can be used to study such systems and predict their patterns.

One area where the study of pattern formation has been of growing interest is in crime modeling. It has been observed that criminal activity tends to cluster in in urban settings. Analyzing spatio-temporal patterns of urban crime using mathematical modeling can reveal hidden patterns in the process of criminal activity, and potentially help establish methods for prevention.

The authors of a paper published this month in the SIAM Journal on analyzed pattern formation as a model to predict burglaries. The rate of burglaries tends to be higher for houses that have been burglarized before or are close of those that have been burglarized. This leads to the creation of burglary hotspots. Authors Steve Cantrell, Chris Cosner, and Raúl Manásevich propose a model to generate patterns that would describe the specific location of such hotspots.

"Our research provides a mathematically rigorous way of connecting the geographical characteristics of a neighborhood [such as demographics, economics and ecology] to the patterns of burglary that would be seen in the neighborhood," says lead author Steve Cantrell. "Bringing geography into the model is an important step in understanding the model in realistic situations."

"Our work was inspired by models of burglary that were developed by a group of mathematicians and scientists at UCLA," he goes on to explain. The UCLA group analyzed the dynamics of burglary hotspots based on the assumption that criminal agents strike based on a house's "attractiveness value."

The attractiveness value is a measure of how easily a house can be burgled without negative consequences for the burglar. Thus, when a house has been burglarized before, it increases the attractiveness value for the house and those nearby. Criminal agents move toward areas of high attractiveness values. If no additional burglaries occur in the vicinity, the attractiveness decreases.

Mathematical modeling of crime in general, and burglaries in particular, is based on the "broken window effect" or repeat victimization sociological effect, which implies that houses in areas of past burglaries have a higher chance of being burglarized.

Using two discrete models, one modeling the attractiveness of individual houses to burglars and the other modeling burglar movement, the authors of the UCLA study developed a continuum model based on a system of parabolic differential equations. Using this system as a starting point, the authors apply bifurcation theory, or the analysis of a system of ordinary differential equations under varying conditions, such as social or economic conditions of a neighborhood, to extend the scope of analysis. This paper expands on previous analyses and provides a general method to track social, economic or other conditions of a neighborhood over time.

Explore further: Jerusalem stone may answer Jewish revolt questions

More information: Global Bifurcation of Solutions for Crime Modeling Equations, Robert Stephen Cantrell, Chris Cosner, and Raúl Manásevich, SIAM Journal on Mathematical Analysis, 44, pp. 1340-1358 (Online publish date: May 3, 2012)

Related Stories

Can math and science help solve crimes?

Feb 22, 2010

(PhysOrg.com) -- UCLA scientists working with Los Angeles police are using sophisticated mathematics to identify and analyze urban crime patterns.

Fighting violent gang crime with math

Oct 31, 2011

(PhysOrg.com) -- UCLA mathematicians working with the Los Angeles Police Department to analyze crime patterns have designed a mathematical algorithm to identify street gangs involved in unsolved violent crimes. Their research ...

Recommended for you

US state reaches deal to keep dinosaur mummy

8 hours ago

North Dakota reached a $3 million deal to keep a rare fossil of a duckbilled dinosaur on display at the state's heritage center, where it will serve as a cornerstone for the facility's $51 million expansion, officials said ...

Jerusalem stone may answer Jewish revolt questions

11 hours ago

Israeli archaeologists said Tuesday they have discovered a large stone with Latin engravings that lends credence to the theory that the reason Jews revolted against Roman rule nearly 2,000 ago was because ...

Kung fu stegosaur

11 hours ago

Stegosaurs might be portrayed as lumbering plant eaters, but they were lethal fighters when necessary, according to paleontologists who have uncovered new evidence of a casualty of stegosaurian combat. The ...

User comments : 4

Adjust slider to filter visible comments by rank

Display comments: newest first

Riff
not rated yet May 31, 2012
Crime modeling = thought police = profiling = totalitarianism. It's not if, it's when. It's not when, it's now.
kaasinees
2 / 5 (4) May 31, 2012
Before you know it they will arrest you for potential theft because you lost your job and no longer have the means to sustain yourself.
Telekinetic
5 / 5 (2) May 31, 2012
Crime modeling = thought police = profiling = totalitarianism. It's not if, it's when. It's not when, it's now.

Wait till someone breaks in and steals your shit. You'll be spilling all of your thoughts in the police report.
Riff
not rated yet May 31, 2012
I am an alarm technician brainiac.