Frontiers in Applied Mathematics and Statistics (Jan 2023)
Curtailing crime dynamics: A mathematical approach
Abstract
IntroductionCrime and criminal activities have huge influences on society and societal development. The social makeup of the society has a significant impact on the propagation of crime within a population. It is a well-known reality that crime spreads across society like an infectious disease, despite the fact that there are many elements that might affect this dynamic. So, understanding crime and the factors influencing its spread are essential in formulating policies to reduce the prevalence and impacts of crime.MethodsWe formulate a deterministic mathematical model using a system of nonlinear ordinary differential equations incorporating education programs as tools to assess the population-level impact on the spread of crime. The model has a global asymptotically stable crime-free equilibrium whenever a certain criminological threshold, known as the effective reproduction number RE, is less than unity.Results and discussionThe model is fitted with prison data reported from July 2021 to June 2022 by the State of Illinois in The United States. The simulations are carried out to assess the population-level impact of the widespread use of the intervention programs and the compliance rate in the State of Illinois. We hypothetically fixed the efficacy of the intervention programs at 25% while varying the compliance rate (by the general public). With no compliance, a high level of active criminal population was recorded. As the compliance rates were significantly improved, the active population level decreased. The global sensitivity analysis is performed primarily to determine the parameters with the most effect on the spread of crime in the State of Illinois. The results demonstrate that the effective community contact rate, βc, for the criminally active individuals is the main driver of crime in the State of Illinois.
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