Abstract
Crimes are social ills that make a society unsafe to live in. Since a child is born into a family and a society is made up of different families, we develop a model to study the influence of family background on the spread of crime in the society. Five compartments are considered including: those who can commit crime (S), those who are resistant to committing crime (R), those who are committing crime alone (I), those who are committing crime in group (G) and the criminals who are under rehabilitation (J). The validity of the model was established. Crime reproductive ratio \({\mathcal{C}}_{R}\) was computed and used to derive the necessary and sufficient conditions for crime eradication and persistence. Simulation was conducted using the computer-in-built Runge–Kutta scheme implemented in software maple and the results showed that the effectiveness of crime education together with strict security and legal system up to 70% were sufficient to eradicate criminal activities in a community.
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Akinpelu, F.O., Akinwande, R.: Mathematical model for Lassa fever and sensitivity analysis. J. Sci. Eng. Res. 5(6), 1–9 (2018)
Athithan, S., Ghosh, M., Li, X.Z.: Mathematical modeling and optimal control of corruption dynamics. Asian-Eur. J. Math. 11(6), 1850090 (2018)
Ayoade, A.A., Ibrahim, M.O.: Analyis of transmission dynamics and mitigation success of COVID-19 in Nigeria: an insight from a mathematical model. Aligarh Bull. Math. 41(1), 1–26 (2022)
Ayoade, A.A., Ibrahim, M.O.: Modeling the dynamics and control of rabies in dog population within and around Lagos, Nigeria. Eur. Phys. J. Plus 138, 397 (2023). https://doi.org/10.1140/epjp/s13360-023-03993-4
Ayoade, A.A., Thota, S.: Functional education as a nexus between agricultural and industrial revolution: an epidemiological modeling approach. Uniciencia 29, 1–16 (2023). https://doi.org/10.15359/ru.37-1.12
Ayoade, A.A., Agunbiade, S., Oyedepo, T.: Backward bifurcation in epidemic models of Toxoplasma gondii: a qualitative analysis. J. Nepal Math. Soc. 5(1), 1–9 (2022). https://doi.org/10.3126/jnms.v5i1.47369
Ayoade, A.A., Ikpechukwu, P.A., Thota, S., Peter, O.J.: Modeling the effect of quarantine and hospitalization on the spread of COVID-19 during the toughest period of the pandemic. J. Mahani Math. Res. 12(1), 339–361 (2023)
Ayoade, A., Nyerere, N., Ibrahim, M.: An epidemic model for control and possible elimination of Lassa fever. Tamkang J. Math. 54, 3 (2023). https://doi.org/10.5556/j.tkjm.55.2024.5031
Bertozzi, A.L., Johnson, S.D., Ward, M.J.: Mathematical modelling of crime and security: Special Issue of EJAM. Eur. J. Appl. Math. 27(3), 311–316 (2016)
Bhandari, A.: The role of the family in crime causation: a comparative study of ‘family of orientation’ and ‘family of procreation’ (a study of women prisoners in the central jails of Rajasthan). J. Int. Women’s Stud. 19(3), 109–118 (2018)
Calatayud, J., Jornet, M., Mateu, J.: A dynamical mathematical model for crime evolution based on a compartmental system with interaction. Int. J. Comput. Math. (2024). https://doi.org/10.1080/00207160.2024.2302840
Castillo-Chavez, C., Song, B.: Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1, 361–404 (2004)
Comissiong, D.M.G., Sooknanan, J.: A review of the use of optimal control in social models. Int. J. Dyn. Control 6(4), 1841–1846 (2018)
Diekmann, O., Heesterbeek, J.A.P.: Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation Wiley Series in Mathematical and Computational Biology. Wiley, Chichester (2000)
Diekmann, O., Heesterbeek, J.A.J., Metz, J.A.J.: On the definition and the computation of the basic reproduction ratio \(\cal{R} _{\circ }\) in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–373 (1990)
Edge, I. D., Bernard, T. J., Clarke, C., Antony, A. N., Thomas, D. A.: Crime, Encyclopedia Britannica,https://www.britannica.com/topic/crime-law (2022)
Eriksson, K.H., Hjalmarson, R.H., Lindquist, M.J., Sandberg, A.: The importance of family background and neighborhood effects as determinants of crime. J. Popul. Econ. 29, 219–262 (2016)
Glaze, L., Maruschak, L.: Parents in prison and their minor children, Bureau of Justice Statistics Special Report, NCJ 222984, (2008)
González-Parra, G., Chen-Charpentier, B., Kojouharov, H.V.: Mathematical modeling of crime as a social epidemic. J. Interdiscipl. Math. 21(3), 623–643 (2018)
Jeke, L., Chitenderu, T., Moyo, C.: Crime and economic development in South Africa: a panel data analysis. Int. J. Econ. Bus. Adm. (IJEBA) 9(2), 424–438 (2021)
Jonathan, O.E., Olusola, A.J., Bernadin, T.C.A., Inoussa, T.M.: Impacts of crime on socio-economic development. Mediterr. J. Soc. Sci. 12(5), 71 (2021)
Karamzadeh, O.A.S.: One-line proof of the AM-GM inequality. Math. Intell. 33, 3 (2011). https://doi.org/10.1007/s00283-010-9197-9
Kwofie, T., Dogbatsey, M., Moore, S.E.: Curtailing crime dynamics: a mathematical approach. Front. Appl. Math. Stat. 8, 1086745 (2023)
Lacey, A.A., Tsardakas, M.N.: A mathematical model of serious and minor criminal activity. Eur. J. Appl. Math. 27(3), 403–421 (2016)
Lakshmikantham, V., Leela, S.: Stability analysis of nonlin- ear systems. Marcel Dekker Inc, New York and Bassel (1989)
LaSalle, J. P.: The stability of dynamical systems. Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, Pa, (1976)
Martinez-Vaquero, L.A., Dolci, V., Trianni, V.: Evolutionary dynamics of organised crime and terrorist networks. Sci. Rep. 9(1), 9727 (2019)
Mataru, B., Abonyo, O.J., Malonza, D.: Mathematical model for crimes in develo** countries with some control strategies. J. Appl. Math. 2023, 1–14 (2023). https://doi.org/10.1155/2023/8699882
McMillon, D., Simon, C.P., Morenoff, J.: Modeling the underlying dynamics of the spread of crime. PLoS ONE 9(4), e88923 (2014)
Mebratie, M.A., Dawed, M.Y.: Mathematical model analysis of crime dynamics incorporating media coverage and police force. J. Math. Comput. Sci. 11(1), 125–148 (2020)
Nur, W.: Darmawati mathematical model of armed criminal group with pre-emitive and repressive intervention. J. Math. Theory Appl. 2(2), 27–32 (2020)
Ogunmiloro, O.M., Obayomi, A.A., Agboola, G.O.: The menace of ghost workers, job racketeers, and creators of online job offer scam sites on unemployment in Nigeria: a mathematical model analysis and control. SN Oper. Res. Forum 5(2), 1–38 (2024)
Okuonghae, D., Omame, A.: Analysis of a mathematical model for COVID-19 population dynamics in Lagos. Nigeria, Chaos, Solitons & Fractals: Nonlinear Sci. Nonequilib.Complex Phenomena 139, 1–18 (2020)
Olsson, T.M.: Productivity loss, victim costs and the intangible costs of crime: follow-up to a longitudinal study of criminal justice system involvement and costs of women with cooccurring substance abuse and mental disorders in Sweden. Ment. Health Subst. Use 7(2), 102–109 (2014)
Opoku, N.K.D.O., Bader, G., Fiatsonu, E.: Controlling crime with its associated cost during festive periods using mathematical techniques. Chaos, Solitons & Fractals 145, 110801 (2021)
Park, J., Kim, P.: Mathematical analysis of crime dynamics in and out ofprisons. Math Meth Appl Sci. 44, 650–667 (2021)
Pulido, C., Prieto, J., Gómez, F.: How the social interactions in communities affect the fear of crime. Syst. Res. Behav. Sci. 36(6), 789–798 (2019)
Rivera-Castro, M., Padmanabhan, P., Caiseda, C., Seshaiyer, P., Boria-Guanill, C.: Mathematical modelling, analysis and simulation of the spread of gangs in interacting youth and adult populations. Lett. Biomath. 6, 1–19 (2019)
Short, M.B., D’orsogna, M.R., Pasour, V.B., et al.: A statistical model of criminal behavior. Math. Models Methods Appl. Sci. 18(supp01), 1249–1267 (2008)
Soemarsono, A.R., Fitria, I., Nugraheni, K., Hanifa, N.: Analysis of mathematical model on impact of unemployment growth to crime rates. J. Phys. Conf. Series 1726(1), 012003 (2021)
Srivastav, A.K., Athithan, S., Ghosh, M.: Modeling and analysis of crime prediction and prevention. Soc. Netw. Anal. Min. 10(1), 1–21 (2020)
Sundar, S., Tripathi, A., Naresh, R.: Does unemployment induce crime in society? A mathematical study. Am. J. Appl. Math. Stat. 6, 44–53 (2018)
Torcicollo, I., Vitiello, M.: Turing instability and spatial pattern formation in a model of urban crime. Mathematics 12(7), 1097 (2024). https://doi.org/10.3390/math12071097
Ugwuishiwu, C.H., Sarki, D.S., Mbah, G.C.E.: Nonlinear analysis of the dynamics of criminality and victimisation: a mathematical model with case generation and forwarding. J. Appl. Math. 2019, 1–17 (2019)
Van den Driessche, P., Watmough, J.: Further notes on the basic reproduction number, In Mathematical Epidemiology, pp. 159-178, Springer Berlin Heidelberg, (2008)
Van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1), 29–48 (2002)
van Dijk, J., Nieuwbeerta, P., Joudo Larsen, J.: Global crime patterns: an analysis of survey data from 166 countries around the world, 2006–2019. J. Quant. Criminol. 22, 1–36 (2021)
Yaacoub, S.: Poverty, inequality and the social causes of crime: a study between United States and Europe. Int. J. Sci. Res. 2015, 2319–7064 (2017)
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A.A.A and O.M.O wrote the main manuscript text and S.T. prepared figures 2-5. All authors reviewed the manuscript.
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Ayoade, A.A., Ogunmiloro, O.M. & Thota, S. Mathematical modeling and analysis of the influence of family background on the spread of crime. Qual Quant (2024). https://doi.org/10.1007/s11135-024-01920-y
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DOI: https://doi.org/10.1007/s11135-024-01920-y