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Calatayud J, Jornet M, Mateu J. Spatio-temporal stochastic differential equations for crime incidence modeling. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT : RESEARCH JOURNAL 2023; 37:1839-1854. [PMID: 36619700 PMCID: PMC9810525 DOI: 10.1007/s00477-022-02369-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 12/15/2022] [Indexed: 06/17/2023]
Abstract
We propose a methodology for the quantitative fitting and forecasting of real spatio-temporal crime data, based on stochastic differential equations. The analysis is focused on the city of Valencia, Spain, for which 90247 robberies and thefts with their latitude-longitude positions are available for a span of eleven years (2010-2020) from records of the 112-emergency phone. The incidents are placed in the 26 zip codes of the city (46001-46026), and monthly time series of crime are built for each of the zip codes. Their annual-trend components are modeled by Itô diffusion, with jointly correlated noises to account for district-level relations. In practice, this study may help simulate spatio-temporal situations and identify risky areas and periods from present and past data.
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Affiliation(s)
- Julia Calatayud
- Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain
| | - Marc Jornet
- Departament de Matemàtiques, Universitat de València, 46100 Burjassot, Spain
| | - Jorge Mateu
- Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain
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Calatayud J, Jornet M, Mateu J. Modeling noisy time-series data of crime with stochastic differential equations. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT : RESEARCH JOURNAL 2023; 37:1053-1066. [PMID: 36340619 PMCID: PMC9628327 DOI: 10.1007/s00477-022-02334-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/25/2022] [Indexed: 05/09/2023]
Abstract
We develop and calibrate stochastic continuous models that capture crime dynamics in the city of Valencia, Spain. From the emergency phone, data corresponding to three crime events, aggressions, stealing and women alarms, are available from the year 2010 until 2020. As the resulting time series, with monthly counts, are highly noisy, we decompose them into trend and seasonality parts. The former is modeled by geometric Brownian motions, both uncorrelated and correlated, and the latter is accommodated by randomly perturbed sine-cosine waves. Albeit simple, the models exhibit high ability to simulate the real data and show promising for crimes-interaction identification and short-term predictive policing.
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Affiliation(s)
- Julia Calatayud
- Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain
| | - Marc Jornet
- Departament de Matemàtiques, Universitat de València, 46100 Burjassot, Spain
| | - Jorge Mateu
- Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain
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Mema E, Spain ES, Martin CK, Hill JO, Sayer RD, McInvale HD, Evans LA, Gist NH, Borowsky AD, Thomas DM. Social influences on physical activity for establishing criteria leading to exercise persistence. PLoS One 2022; 17:e0274259. [PMID: 36260559 PMCID: PMC9581432 DOI: 10.1371/journal.pone.0274259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Accepted: 08/25/2022] [Indexed: 11/19/2022] Open
Abstract
Despite well-documented health benefits from exercise, a study on national trends in achieving the recommended minutes of physical activity guidelines has not improved since the guidelines were published in 2008. Peer interactions have been identified as a critical factor for increasing a population's physical activity. The objective of this study is for establishing criteria for social influences on physical activity for establishing criteria that lead to exercise persistence. A system of differential equations was developed that projects exercise trends over time. The system includes both social and non-social influences that impact changes in physical activity habits and establishes quantitative conditions that delineate population-wide persistence habits from domination of sedentary behavior. The model was generally designed with parameter values that can be estimated to data. Complete absence of social or peer influences resulted in long-term dominance of sedentary behavior and a decline of physically active populations. Social interactions between sedentary and moderately active populations were the most important social parameter that influenced low active populations to become and remain physically active. On the other hand, social interactions encouraging moderately active individuals to become sedentary drove exercise persistence to extinction. Communities should focus on increasing social interactions between sedentary and moderately active individuals to draw sedentary populations to become more active. Additionally, reducing opportunities for moderately active individuals to engage with sedentary individuals through sedentary social activities should be addressed.
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Affiliation(s)
- Ensela Mema
- New Jersey Center for Science, Technology and Mathematics (NJCSTM), Kean University, Union, New Jersey, United States of America
| | - Everett S. Spain
- Department of Behavioral Sciences and Leadership, United States Military Academy, West Point, NY, United States of America
| | - Corby K. Martin
- Body Composition and Metabolism, Pennington Biomedical Research Center, Baton Rouge, LA, United States of America
| | - James O. Hill
- Department of Nutrition Sciences, University of Alabama-Birmingham, Birmingham, AL, United States of America
| | - R. Drew Sayer
- Department of Nutrition Sciences, University of Alabama-Birmingham, Birmingham, AL, United States of America
| | - Howard D. McInvale
- Special Projects Department, The MITRE Corporation, Huntsville, AL, United States of America
| | - Lee A. Evans
- Department of Mathematical Sciences, United States Military Academy, West Point, NY, United States of America
| | - Nicholas H. Gist
- Department of Physical Education, United States Military Academy, West Point, NY, United States of America
| | | | - Diana M. Thomas
- Department of Mathematical Sciences, United States Military Academy, West Point, NY, United States of America
- * E-mail:
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Optimal control model for criminal gang population in a limited-resource setting. INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL 2022; 11:835-850. [PMID: 35845845 PMCID: PMC9274643 DOI: 10.1007/s40435-022-00992-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Revised: 05/26/2022] [Accepted: 06/12/2022] [Indexed: 11/29/2022]
Abstract
In this present paper, the principles of optimal control theory is applied to a non-linear mathematical model for the population dynamics of criminal gangs with variability in the sub-population. To decrease (minimize) the progression rate of susceptible populations with no access to crime prevention programs from joining criminal gangs and increase (maximize) the rate of arrested and prosecution of criminals, we incorporate time-dependent control functions. These two functions represent the crime prevention strategy for the susceptible population and case finding control for the criminal gang population, in a limited-resource setting. Furthermore, we present a cost-effectiveness analysis for crime control intervention-related benefits to ascertain the most cost-effective and efficient optimal control strategy. The optimal control functions presented herein are solved by employing the Runge-Kutta Method of order four. Numerical results are demonstrated for different scenarios to exemplify the impact of the controls on the criminal gangs’ population.
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Fractional Order Mathematical Model of Serial Killing with Different Choices of Control Strategy. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6030162] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag–Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam’s stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams–Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.
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Martinez-Vaquero LA, Dolci V, Trianni V. Evolutionary dynamics of organised crime and terrorist networks. Sci Rep 2019; 9:9727. [PMID: 31278354 PMCID: PMC6611905 DOI: 10.1038/s41598-019-46141-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Accepted: 06/18/2019] [Indexed: 11/09/2022] Open
Abstract
Crime is pervasive into modern societies, although with different levels of diffusion across regions. Its dynamics are dependent on various socio-economic factors that make the overall picture particularly complex. While several theories have been proposed to account for the establishment of criminal behaviour, from a modelling perspective organised crime and terrorist networks received much less attention. In particular, the dynamics of recruitment into such organisations deserve specific considerations, as recruitment is the mechanism that makes crime and terror proliferate. We propose a framework able to model such processes in both organised crime and terrorist networks from an evolutionary game theoretical perspective. By means of a stylised model, we are able to study a variety of different circumstances and factors influencing the growth or decline of criminal organisations and terrorist networks, and observe the convoluted interplay between agents that decide to get associated to illicit groups, criminals that prefer to act on their own, and the rest of the civil society.
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Affiliation(s)
- Luis A Martinez-Vaquero
- Institute of Cognitive Sciences and Technologies, National Research Council of Italy, via San Martino della Battaglia 44, 00185, Rome, Italy.
- Lab of Socioecology and Social Evolution, Department of Biology, KU Leuven, Naamsestraat 59, 3000, Leuven, Belgium.
| | - Valerio Dolci
- INFN Roma1, Rome, Italy
- Physics Department, Sapienza University of Rome, Rome, Italy
| | - Vito Trianni
- Institute of Cognitive Sciences and Technologies, National Research Council of Italy, via San Martino della Battaglia 44, 00185, Rome, Italy
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Galam S, Javarone MA. Modeling Radicalization Phenomena in Heterogeneous Populations. PLoS One 2016; 11:e0155407. [PMID: 27166677 PMCID: PMC4863968 DOI: 10.1371/journal.pone.0155407] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Accepted: 04/28/2016] [Indexed: 11/18/2022] Open
Abstract
The phenomenon of radicalization is investigated within a mixed population composed of core and sensitive subpopulations. The latest includes first to third generation immigrants. Respective ways of life may be partially incompatible. In case of a conflict core agents behave as inflexible about the issue. In contrast, sensitive agents can decide either to live peacefully adjusting their way of life to the core one, or to oppose it with eventually joining violent activities. The interplay dynamics between peaceful and opponent sensitive agents is driven by pairwise interactions. These interactions occur both within the sensitive population and by mixing with core agents. The update process is monitored using a Lotka-Volterra-like Ordinary Differential Equation. Given an initial tiny minority of opponents that coexist with both inflexible and peaceful agents, we investigate implications on the emergence of radicalization. Opponents try to turn peaceful agents to opponents driving radicalization. However, inflexible core agents may step in to bring back opponents to a peaceful choice thus weakening the phenomenon. The required minimum individual core involvement to actually curb radicalization is calculated. It is found to be a function of both the majority or minority status of the sensitive subpopulation with respect to the core subpopulation and the degree of activeness of opponents. The results highlight the instrumental role core agents can have to hinder radicalization within the sensitive subpopulation. Some hints are outlined to favor novel public policies towards social integration.
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Affiliation(s)
- Serge Galam
- CEVIPOF – Centre for Political Research, CNRS and Sciences Po, Paris, France
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D'Orsogna MR, Perc M. Statistical physics of crime: a review. Phys Life Rev 2014; 12:1-21. [PMID: 25468514 DOI: 10.1016/j.plrev.2014.11.001] [Citation(s) in RCA: 193] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2014] [Revised: 10/20/2014] [Accepted: 11/03/2014] [Indexed: 11/28/2022]
Abstract
Containing the spread of crime in urban societies remains a major challenge. Empirical evidence suggests that, if left unchecked, crimes may be recurrent and proliferate. On the other hand, eradicating a culture of crime may be difficult, especially under extreme social circumstances that impair the creation of a shared sense of social responsibility. Although our understanding of the mechanisms that drive the emergence and diffusion of crime is still incomplete, recent research highlights applied mathematics and methods of statistical physics as valuable theoretical resources that may help us better understand criminal activity. We review different approaches aimed at modeling and improving our understanding of crime, focusing on the nucleation of crime hotspots using partial differential equations, self-exciting point process and agent-based modeling, adversarial evolutionary games, and the network science behind the formation of gangs and large-scale organized crime. We emphasize that statistical physics of crime can relevantly inform the design of successful crime prevention strategies, as well as improve the accuracy of expectations about how different policing interventions should impact malicious human activity that deviates from social norms. We also outline possible directions for future research, related to the effects of social and coevolving networks and to the hierarchical growth of criminal structures due to self-organization.
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Affiliation(s)
- Maria R D'Orsogna
- Department of Mathematics, California State University at Northridge, Los Angeles, CA 91330, USA; Department of Biomathematics, UCLA, Los Angeles, CA 90095, USA.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia; Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia; CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia.
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