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Fractional-order crime propagation model with non-linear transmission rate

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  • Bansal, Komal
  • Mathur, Trilok
  • Agarwal, Shivi

Abstract

Various studies present different mathematical models of ordinary and fractional differential equations to reduce delinquent behavior and encourage prosocial growth. However, these models do not consider the non-linear transmission rate, which depicts reality better than the linear transmission rate, as the relationship between non-criminals and criminals is not linear. In light of this, a novel fractional-order mathematical crime propagation model with a non-linear Beddington–DeAngelis transmission rate is proposed that divides the entire population into three clusters. The present study also compares the crime transmission models for various transmission rates, followed by an analytical investigation. The model shows two equilibrium points (criminal-free and crime-persistence equilibrium). The criminal-free equilibrium is locally and globally asymptotically stable when the criminal generation number is less than one. The crime-persistence equilibrium point does not appear until the criminal generation number exceeds one. In addition, this research investigates the incidence of transcritical bifurcation at the criminal-free equilibrium point. Furthermore, numerical simulations are performed to demonstrate the analytical results. In summary, the finding of this research suggests that as the order of derivative increases, the population approaches equilibrium more swiftly, and criminals decline with time for the different order of derivative.

Suggested Citation

  • Bansal, Komal & Mathur, Trilok & Agarwal, Shivi, 2023. "Fractional-order crime propagation model with non-linear transmission rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923002229
    DOI: 10.1016/j.chaos.2023.113321
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    1. Tripathi, Jai Prakash & Bugalia, Sarita & Burdak, Kavita & Abbas, Syed, 2021. "Dynamical analysis and effects of law enforcement in a social interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Jin-Zhu Zhang & Zhen Jin & Quan-Xing Liu & Zhi-Yu Zhang, 2008. "Analysis of a Delayed SIR Model with Nonlinear Incidence Rate," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-16, January.
    3. Freeman, Scott & Grogger, Jeffrey & Sonstelie, Jon, 1996. "The Spatial Concentration of Crime," Journal of Urban Economics, Elsevier, vol. 40(2), pages 216-231, September.
    4. Chunjin Wei & Lansun Chen, 2008. "A Delayed Epidemic Model with Pulse Vaccination," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-12, March.
    5. Randi Hjalmarsson & Matthew J. Lindquist, 2012. "Like Godfather, Like Son: Exploring the Intergenerational Nature of Crime," Journal of Human Resources, University of Wisconsin Press, vol. 47(2), pages 550-582.
    6. Xu, Rui & Ma, Zhien, 2009. "Stability of a delayed SIRS epidemic model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2319-2325.
    7. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    8. Wang, Shoou-Jiun & Batta, Rajan & Rump, Christopher M., 2005. "Stability of a crime level equilibrium," Socio-Economic Planning Sciences, Elsevier, vol. 39(3), pages 229-244, September.
    9. Komal Bansal & Sugandha Arora & Kocherlakota Satya Pritam & Trilok Mathur & Shivi Agarwal, 2022. "Dynamics Of Crime Transmission Using Fractional-Order Differential Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-16, February.
    10. Alfred Blumstein & Richard Larson, 1969. "Models of a Total Criminal Justice System," Operations Research, INFORMS, vol. 17(2), pages 199-232, April.
    11. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    12. Baba, Isa Abdullahi & Abdulkadir, Rabiu Aliyu & Esmaili, Parvaneh, 2020. "Analysis of tuberculosis model with saturated incidence rate and optimal control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    13. Pritam, Kocherlakota Satya & Sugandha, & Mathur, Trilok & Agarwal, Shivi, 2021. "Underlying dynamics of crime transmission with memory," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Mendes, Renio S., 2013. "Scaling laws in the dynamics of crime growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2672-2679.
    15. Nuño, Juan C. & Herrero, Miguel A. & Primicerio, Mario, 2008. "A triangle model of criminality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2926-2936.
    16. María J. Quinteros & Marcelo J. Villena & Abdellatif Ben Makhlouf, 2022. "On the Dynamics and Stability of the Crime and Punishment Game," Complexity, Hindawi, vol. 2022, pages 1-14, March.
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