Underlying dynamics of crime transmission with memory

Pritam, Kocherlakota Satya; Sugandha,; Mathur, Trilok; Agarwal, Shivi

doi:10.1016/j.chaos.2021.110838

Cited by 17 publications

(8 citation statements)

References 39 publications

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“…Paper [23] put forward a model of crime transmission to study the spread of crime, imprisonment, and recidivism. One of the main findings of this work is that the long-run effect of increasing the length of prison terms has no effect on changing the fraction of criminally active people in the population, which contrasts findings from [24] who propose a model of crime transmission inherited with memory property. ey show the progression of the flow of population by classifying into three systems based on involvement in crime and imprisonment by considering the criminal history of an individual.…”

Section: Literature Reviewcontrasting

confidence: 89%

On the Dynamics and Stability of the Crime and Punishment Game

Quinteros

Villena

2022

Complexity

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We study the dynamics and stability of the economics of crime and punishment game from an evolutionary perspective. Specifically, we model the interaction between agents and controllers as an asymmetric game exploring the dynamics of the classic static model using a replicator dynamics equation, given exogenous levels of monitoring and criminal sanctions. The dynamics show five possible equilibria, from which three are stable. Our results show that a culture of honest agents is never stable; however when the penalty is high enough, the system will neutrally tend to an equilibrium of honest agents and a monitoring firm. By contrast, when the probability of detecting wrongdoing is small, the system, in some cases, will remain in a transient state, in which it is impossible to predict the proportion of honest agents.

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Section: Literature Reviewcontrasting

confidence: 89%

On the Dynamics and Stability of the Crime and Punishment Game

Quinteros

Villena

2022

Complexity

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“…Regarding the mentioned dependence of the equilibrium solution (x * 2 , y * 2 , z * 2 ) on the new parameter λ, a simple inspection of Eqs. ( 15) and (12) shows that for large λ we have the following dependencies: z * 2 ∝ λ, y * 2 ∝ λ and x * 2 ∝ λ 2 . Since λ is the rate of increase of violent crimes (x) due to the presence of legal guns in the civilian' hands (y), the last results show that the civilian gun ownership leads to a fast increase of violent crimes, despite the slower growth of legal and illegal firearms.…”

Section: Resultsmentioning

confidence: 91%

“…In other words, if the state wants to fight homicides, evidences show that removing criminals from circulation with incarceration is the best option [22]. 15) and (12). The parameters are α = 0.5, β = 0.8, γ = 2.5, δ = 0.8, ǫ = 5.0, θ = 0.5 and ν = σ = 2.0 (all parameters are given in unities year −1 ).…”

Section: Resultsmentioning

confidence: 99%

“…Mathematical models can be useful to analyze some aspects of the evolution of crimes due to legal and/or illegal firearms. Indeed, we can cite some recent works [11,12,13,14,15]. In order to study specifically the impact of legal firearms on the evolution of violent crimes, i.e., crimes commited by civilians using legal guns, we propose an extension of the model presented in [11].…”

Section: Introductionmentioning

confidence: 99%

“…The lines are given by Eqs. (15) and(12). The parameters are α = 0.5, β = 0.8, γ = 2.5, δ = 0.8, ǫ = 5.0, θ = 0.5 and ν = σ = 2.0 (all parameters are given in unities year −1 ).…”

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confidence: 99%

See 2 more Smart Citations

Modeling the impact of civilian firearm ownership in the evolution of violent crimes

Crokidakis

2022

Preprint

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We propose a simple mathematical model to describe the evolution of violent crimes. For such purpose, we built a model based on ordinary differential equations that take into account the number of violent crimes and the number of legal and illegal guns. The dynamics is governed by probabilities, modeling for example the police action, the risk perception regarding crimes that leads to increase of ownership of legal guns, and so on. Our analytical and numerical results show that, in addition to the rise of criminality due to the presence of illegal guns, the increase of legal guns leads to a fast increase of violent crimes, suggesting that the access of firearms by civilians is not a good option regarding the control of crimes.

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Comparative Study of the Fractional-Order Crime System as a Social Epidemic of the USA Scenario

Partohaghighi

Kumar

Akgül

2022

Int. J. Appl. Comput. Math

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Fractional derivatives are considered significant mathematical tools to design the fractional-order models of real phenomena. In this investigation, we are going to design and compare the non-integer models of the crime system by using three fractional-order operators called Atangana-Baleanu-Caputo, Caputo, and Caputo-Fabrizio derivatives for the first time. We use the real initial conditions for the subgroups of USA. To get the approximate solutions of the suggested models some numerical methods are derived. To see the performance of the numerical methods different values of the fractional orders are considered. The differences between the solutions under the used operators for each state variable are provided through some figures.

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Underlying dynamics of crime transmission with memory

Cited by 17 publications

References 39 publications

On the Dynamics and Stability of the Crime and Punishment Game

On the Dynamics and Stability of the Crime and Punishment Game

Modeling the impact of civilian firearm ownership in the evolution of violent crimes

Comparative Study of the Fractional-Order Crime System as a Social Epidemic of the USA Scenario

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