The Purposed Next-Generation of Epidemiological Crime Models

After decades of rising crime in the United States, the crime rate has unexpectedly plummeted—a trend that has continued until very recently. Although crime was a topic of interest long before this phenomenon occurred, the drop has provided opportunities for researchers to explore the determinants of crime and the effectiveness of different preventative methods. In recent years, there have been several constructions and analyses of mathematical models of crime utilizing various methods, including agent-based modeling, ordinary and partial differential equations, and optimization.

Epidemiology is the medical study of infections, their distribution, and prevention/control of diseases or other health-related matters. It is said that crime can spread like an infectious disease. This means that criminal behavior does not start on its own but is disseminated through social contagion, dependent on the social environment—including the justice system. There are several advantages to using this modeling method. Firstly, the data collected and observed in these models directly illustrate exposure to social environmental factors. Another benefit of epidemiological methods involves

Researchers may face problems when studying crime reproduction within a society as the interactions between criminals and ordinary people involve complexity derived from intangible variables like sociological, economic, and geographical factors. Fortunately, a recent paper titled, Mathematical Modeling of Crime as a Social Epidemic, proposes an analogy between the spread of epidemic disease and the reproduction of crime. In the paper, the Malthusian rate of crime is evaluated by the basic reproduction number, R0.

This is a commonly used technique in epidemiological studies, and R0 is a threshold parameter for predicting whether a disease can be controlled. The application of this analogy and the mathematical models described vary across multiple articles (CITATION). Each has unique methods and advantages. By understanding the intuition in each proposed model, we aim to incorporate their strengths and create our unique epidemiological model of crime. This modeling method focuses more on crime transmission rather than the causal relationship between psychological factors and crime reproduction—enhancing its feasibility.

This is where our group comes in, and why our project is essential. The epidemiological model we introduce assumes crime is an infectious process similar to the spread of a disease. It aims to evaluate the general pattern of crime stabilization. Using the population model we constructed and the next-generation matrix method, we will compute a theoretical formula of the basic reproduction number, R0. A sensitivity analysis of R0 will be conducted to identify which parameter will help stabilize criminality.

Our research proposes the challenge of fitting real-world data into this model due to the difficulty of accounting for certain variables discussed. These difficulties include having data that includes the number of free criminals, susceptibles, etc., within the population. To overcome these challenges, we will implement the controlled variable method to fix some parameters, hoping to reveal complications or inspirations in our model. Using the sensitivity analysis we will develop, we aim to improve existing policies.

Did you like this example?

900

47