Stability of a crime level equilibrium

Wang, Shoou-Jiun; Batta, Rajan; Rump, Christopher M.

doi:10.1016/j.seps.2004.01.001

Cited by 10 publications

(2 citation statements)

References 23 publications

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“…For example, Freedman et al [19] developed a model that depicts that crime is concentrated in places where the possible monetary benefit from committing a crime (the probability of not being convicted due to the reward of the crime) exceeds the cost of criminal opportunity. Wang et al [20] generalized this approach allowing for the cost of an opportunity to be heterogeneous across future criminals and depending on the level of crime in a given society and estimated the amount of group crime activity in equilibrium. Another study focused on sanction policies that reduce crime through general or specific deterrence [21,22].…”

Section: Introductionmentioning

confidence: 99%

Curtailing crime dynamics: A mathematical approach

Kwofie

Dogbatsey

Moore

2023

Front. Appl. Math. Stat.

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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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Section: Introductionmentioning

confidence: 99%

Curtailing crime dynamics: A mathematical approach

Kwofie

Dogbatsey

Moore

2023

Front. Appl. Math. Stat.

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“…For example, Freedman and colleagues [29] developed a model explaining how crime becomes concentrated in certain neighborhoods, where the expected monetary return from committing a crime (the probability of not being arrested times the reward of the crime) exceeds the opportunity costs for crime. Wang et al [30] generalized this approach – by allowing opportunity costs to be heterogeneous across potential criminals and depend on the level of crime in a particular neighborhood – and derived the equilibrium amount of criminal activity in a neighborhood.…”

Section: Introductionmentioning

confidence: 99%

Modeling the Underlying Dynamics of the Spread of Crime

2014

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The spread of crime is a complex, dynamic process that calls for a systems level approach. Here, we build and analyze a series of dynamical systems models of the spread of crime, imprisonment and recidivism, using only abstract transition parameters. To find the general patterns among these parameters—patterns that are independent of the underlying particulars—we compute analytic expressions for the equilibria and for the tipping points between high-crime and low-crime equilibria in these models. We use these expressions to examine, in particular, the effects of longer prison terms and of increased incarceration rates on the prevalence of crime, with a follow-up analysis on the effects of a Three-Strike Policy.

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Fractional-order crime propagation model: a comparison between logistic and exponential growth

Bansal,

Mathur

2024

Ricerche mat

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Stability of a crime level equilibrium

Cited by 10 publications

References 23 publications

Curtailing crime dynamics: A mathematical approach

Curtailing crime dynamics: A mathematical approach

Modeling the Underlying Dynamics of the Spread of Crime

Fractional-order crime propagation model: a comparison between logistic and exponential growth

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