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Modelling financial crime population dynamics: optimal control and cost-effectiveness analysis

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Abstract

This work is designed to formulate and analyse a mathematical model for population dynamics of financial crime with optimal control measures. Necessary conditions for the existence and stability of financial crime steady states are derived. The financial crime reproduction number is determined. Based on construction of suitable Lyapunov functionals, crime-free equilibrium point of the formulated model is shown to be globally asymptotically stable when the crime reproduction number is below unity, while a unique crime-present equilibrium is proved to be globally asymptotically stable whenever the crime reproduction number exceeds unity. Sensitivity analysis is carried out to determine the relative importance of model parameters in financial crime spread. Furthermore, optimal control theory is employed to assess the impact of two time-dependent optimal control strategies, including public enlightenment campaign (preventive) and corrective measure, on the financial crime dynamics in a population. The cost-effectiveness analysis is carried out to determine the least costly and most effective strategy of the singular and combined implementations of the intervention strategies, when the available resources to combat the spread of financial crime are limited.

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References

  1. Jung J, Lee J (2017) Contemporary financial crime. J Public Adm Gov 7(2):88–97. https://doi.org/10.5296/jpag.v7i2.11219

    Article  Google Scholar 

  2. Gottschalk P (2010) Categories of financial crime. J Financ Crime 17(4):441–4587. https://doi.org/10.1108/13590791011082797

    Article  Google Scholar 

  3. Pickett KS, Pickett JM (2002) Financial crime investigation and control. Wiley, New York

    MATH  Google Scholar 

  4. Thieme HR (2003) Mathematics in population biology. Princeton University Press, Princeton

    Book  Google Scholar 

  5. Zhao H, Feng Z, Castillo-Chávez C (2014) The dynamics of poverty and crime. J Shangai Normal Univ 43(5):486–495

    Google Scholar 

  6. Nuño JC, Herrero MA, Primicero M (2008) A triangle model of criminality. Physica A 387:2926–2936

    Article  Google Scholar 

  7. Nuño JC, Herrero MA, Primicero M (2010) Fighting cheaters: how and how much to invest. Eur J Appl Math 21:459–478. https://doi.org/10.1017/S0956792510000094

    Article  MathSciNet  MATH  Google Scholar 

  8. Shukla JB, Goyal A, Agrawal K et al (2013) Role of technology in combating social crimes: a modeling study. Eur J Appl Math 24:501–514. https://doi.org/10.1017/S0956792513000065

    Article  MATH  Google Scholar 

  9. Livni J, Stone L (2015) The stabilizing role of the Sabbath in pre-monarchic Israel: a mathematical model. J Biol Phys 41:203–221. https://doi.org/10.1007/s10867-014-9373-9

    Article  Google Scholar 

  10. González-Parra G, Chen-Charpentier B, Kojouharov HV (2018) Mathematical modeling of crime as a social epidemic. J Interdiscip Math 21(3):623–643. https://doi.org/10.1080/09720502.2015.1132574

    Article  Google Scholar 

  11. Athithan S, Ghosh M, Li X-Z (2018) Mathematical modeling and optimal control of corruption dynamics. Asian Eur J Math 11(6):1–12. https://doi.org/10.1142/S1793557118500900

    Article  MathSciNet  MATH  Google Scholar 

  12. Chaharborj FS, Pourghahramani B, Chaharborj SS (2017) A dynamic economic model of criminal activity in the criminal law. Int J Basic Appl Sci 6(4):73–76

    Article  Google Scholar 

  13. Nyabadza F, Ogbogbo CP, Mushanyu J (2017) Modelling the role of correctional services on gangs: insights through a mathematical model. R Soc Open Sci 4:170511. https://doi.org/10.1098/rsos.170511

    Article  MathSciNet  Google Scholar 

  14. Roslan UAM, Zakaria S, Alias A, Malik SM (2018) A mathematical model on the dynamics of poverty, poor and crime in west malaysia. Far East J Math Sci 107(2):309–319. https://doi.org/10.17654/MS107020309

    Article  Google Scholar 

  15. Sooknanan J, Bhatt B, Comissiong DMG (2016) A modified predator–prey model for the interaction of police and gangs. R Soc Open Sci 3:160083. https://doi.org/10.1098/rsos.160083

    Article  MathSciNet  Google Scholar 

  16. Korobeinikov A (2004) Lyapunov functions and global properties for SEIS epidemic models. Math Med Biol 21:75–83

    Article  Google Scholar 

  17. van den Driessche P, Wang L, Zou X (2007) Modeling diseases with latency and relapse. Math Biosci Eng 4(2):205–219. https://doi.org/10.3934/mbe.2007.4.205

    Article  MathSciNet  MATH  Google Scholar 

  18. Hethcote HW (2000) The mathematics of infectious diseases. SIAM Rev 42(4):599–653

    Article  MathSciNet  Google Scholar 

  19. van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29–48. https://doi.org/10.1016/S0025-5564(02)00108-6

    Article  MathSciNet  MATH  Google Scholar 

  20. LaSalle JP (1976) The stability of dynamical systems. In: Regional conference series in applied mathematics. SIAM, Philadelphia, Pa

  21. Okuonghae D, Gumel AB, Ikhimwin BO, Iboi E (2018) Mathematical assessment of the role of early latent infections and targeted control strategies on syphilis transmission dynamics. Acta Biotheor. https://doi.org/10.1007/s10441-018-9336-9

    Article  Google Scholar 

  22. Obabiyi OS, Olaniyi S (2019) Global stability analysis of malaria transmission dynamics with vigilant compartment. Electron J Differ Equ 2019(09):1–10

    MathSciNet  MATH  Google Scholar 

  23. Karamzadeh OAS (2011) One-line proof of the AM-GM inequality. Math Intell 33(2):3. https://doi.org/10.1007/s00283-010-9197-9

    Article  MATH  Google Scholar 

  24. Chitnis N, Hyman JM, Cushing JM (2008) Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol 70(5):1272–1296. https://doi.org/10.1007/s11538-008-9299-0

    Article  MathSciNet  MATH  Google Scholar 

  25. Olaniyi S, Obabiyi OS (2014) Qualitative analysis of malaria dynamics with nonlinear incidence function. Appl Math Sci 8(74):3889–3904. https://doi.org/10.12988/ams.2014.45326

    Article  Google Scholar 

  26. Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF (1962) The mathematical theory of optimal processes. Wiley, New York

    MATH  Google Scholar 

  27. Gaoue OG, Jiang J, Ding W, Agusto FB, Lenhart S (2016) Optimal harvesting strategies for timber and non-timber forest products in tropical ecosystems. Theor Ecol. https://doi.org/10.1007/s12080-015-0286-4

    Article  Google Scholar 

  28. Hugo A, Makinde OD, Kumar S, Chibwana FF (2017) Optimal control and cost effectiveness analysis for Newcastle disease eco-epidemiological model in Tanzania. J Biol Dyn 11(1):190–209. https://doi.org/10.1080/17513758.2016.1258093

    Article  MathSciNet  Google Scholar 

  29. Olaniyi S (2018) Dynamics of Zika virus model with nonlinear incidence and optimal control strategies. Appl Math Inf Sci 12(5):969–982. https://doi.org/10.18576/amis/120510

    Article  Google Scholar 

  30. Olaniyi S, Okosun KO, Adesanyan SO, Areo EA (2018) Global stability and optimal control analysis of malaria dynamics in the presence of human travelers. Open Infect Dis 10:166–186. https://doi.org/10.2174/1874279301810010166

    Article  Google Scholar 

  31. Bonyah E, Khan MA, Okosun KO, Gómez-Aguilar JF (2019) On the co-infection of dengue fever and Zika virus. Optim Control Appl Meth. https://doi.org/10.1002/oca.2483

    Article  MathSciNet  MATH  Google Scholar 

  32. Fleming WH, Richel RW (1975) Deterministic and stochastic optimal control. Springer, New York

    Book  Google Scholar 

  33. Magombedze G, Chiyaka C, Mukandavire Z (2011) Optimal control of malaria chemotherapy. Nonlinear Anal Model Control 16(4):415–434

    Article  MathSciNet  Google Scholar 

  34. Lenhart S, Workman JT (2007) Optimal control applied to biological models. Chapman & Hall, London

    Book  Google Scholar 

  35. Alhassan A, Momoh AA, Abdullahi AS, Kadzai MTY (2017) Optimal control strategies and cost effectiveness analysis of a malaria transmission model. Math Theory Model 7(6):123–138

    Google Scholar 

  36. Berhe HW, Makinde OD, Theuri DM (2018) Optimal control and cost-effectiveness analysis for dysentery epidemic model. Appl Math Inf Sci 12(6):1183–1195. https://doi.org/10.18576/amis/120613

    Article  MathSciNet  Google Scholar 

  37. Oke SI, Matadi MB, Xulu SS (2018) Cost-effectiveness analysis of optimal control strategies for breast cancer treatment with ketogenic diet. Far East J Math Sci 109(2):303–342. https://doi.org/10.17654/MS109020303

    Article  Google Scholar 

  38. Okosun KO, Rachid O, Marcus N (2013) Optimal control strategies and cost-effectiveness analysis of a malaria model. BioSystems 111:83–101. https://doi.org/10.1016/j.biosystems.2012.09.008

    Article  Google Scholar 

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Acknowledgements

The authors express thanks to the editor and anonymous reviewers whose insightful suggestions enhanced the original manuscript.

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Akanni, J.O., Akinpelu, F.O., Olaniyi, S. et al. Modelling financial crime population dynamics: optimal control and cost-effectiveness analysis. Int. J. Dynam. Control 8, 531–544 (2020). https://doi.org/10.1007/s40435-019-00572-3

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  • DOI: https://doi.org/10.1007/s40435-019-00572-3

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