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Stability Analysis and Simulation of a Dynamical Systems Trendy in Computer-Generated Criminality Detection and Its Optimal Control Measures

Osuala, Victoria Uchechukwu, Nkuturum, Christiana

Abstract

This study adopted a 5-compactmental nonlinear differential equations to represent the dynamical systems trendy in computer-generated criminality detection and its control measures using the concept of epidemiological mathematical modeling to formulate and analyse the model. The formulated classic was analysed to obtain the positivity of the solutions, existence of equilibrium: bio-cybernetic ecosystem and bionomic, dynamical behavior of equilibrium points with conditions for stability and instability of the system. The Computer- generated criminality reproduction number was obtain using next-generation matrix, and the conditions for local and global stability of the model. The exact solutions of the model and simulations also supports the dynamical behavior of cybernetic system. Sensitivity analysis was carried out and the sensitivity index of each parameter was obtained to determine their impact on the model. The study also revealed that contact rate and removal rate existed and significantly influenced the system's behaviour; unemployment, contact rate between jobless indiiduals increased computer-generated criminality and lack of vocational training opportunities were the causes of cybernetic criminality and that vocational education and high rate of employment were the optimal control measures and panaceas to leverage cybercrime. The numerical simulations of the model confirmed the validity of analytical solutions in using MATLAB R2013b which showed that the number of computer-generated criminals decreased as more unemployed individuals secured jobs. Therefore, it was recommended that computer- generated criminality could be controlled if unemployment issues were prioritized and vocational training for youth was made available in society.

Keywords

Stability Analysis; Simulation; Dynamical system; Computer-generated; Criminality detection

References

[1] Abdubai, A., Humble, V., Chowhen, S., & Aldubai, Y. (2017). Intruder detection: Using fuzzy min-max neural network. [2]Adamy J. (2022). Nonlinear Systems and Controls. Springer Berlin Heidelberg. [3] Ahmed, A., Deb, S., Habib, A., Mollan, M., & Ahmed, A. (2018). Simplistic approach to detect cybercrime and detect cybercrime criminals. International Conference on Computer Communication, Chemical, Material, and Electronic Engineering (IC4MEZ), 1-4. IEEE. [4] Ahmed, A. A., & Mohammed, F. (2018). SAIRI: A similarity approach for attack intention recognition using fuzzy minimax neural network, 25, 467-473. [5] Akhgar, B., Staniforth, A., & Bosco, F. (2014). Cybercrime and cyber terrorism investigators handbook. Syngress. [6] Aziz RM, Hussain A, Sharma P. (2023). Cognizable crime rate prediction and analysis under Indian penal code using deep learning with novel optimization approach. Multimedia Tools and Applications. 83(8): 22663-22700. doi: 10.1007/s11042- 02316371-0 [7]Azuaba, E., Oluwafemi, T.J. & Akinwande, NI, et al. (2022). Solution of substance abuse and domestic violence mathematical model using homotopy perturbation method. International Journal of Mathematical Analysis and Modelling. 5(2): 99-107. [8]. Bala, B. K., Arshad, F. M., & Noh, K. M. (2017). System Dynamics: Modelling and Simulation. Singapore:Springer Science and Business Media. [9] Butrimas, V. (2016). Threat intelligence report cyberattack against Ukrainian ICS. Retrieved from http://www.sentryo.net/wpcontent/upload/2017/10/FBook: Ukrain cyberattack [10] Carr, J. (2011). Inside cyber warfare: Mapping the cyber underworld. O'Reilly Media Inc. [11] Carrington, P. (2011). Corine and social network analysis. In J. Scott & P. J. Carrington (Eds.), Sage Handbook of Social Network Analysis (pp. 236-255). London, UK: Sage. [12]Chouhan, V.S., Badsara, A.K. & Shukla, R. (2024). Zika Virus Model with the Caputo– Fabrizio Fractional Derivative. Symmetry. 16(12): 1606. doi: 10.3390/sym16121606 [13] Costa, L., Oliveira, O., Travies, U., Rodrigues, F., Villas Boas, A., Anliqueira, V., Viana, M., & Correa Rocha, L. (2011). Analyzing and modeling real-world phenomena with concept networks: A survey of applications. Advances in Physics, 63(2), 329-412. [14]. Dunn, P. K., & Marshman, M. F. (2020). Teaching mathematical modelling: A framework to support teachers’choice of resources. Teaching Mathematics and its Applications: An International Journal of the IMA, 39(2), 127–144. [15]Falaye AA, Oluyemi ES, Ale S, et al. Quantitative model for dynamic propagation and countermeasure of malicious cyberattack on the mobile wireless network. In: Proceedings of the 2017 Intelligent Systems Conference (IntelliSys); 2017. [16]. Greer, B. (2023). The mathematical modeling perspective on world problems. The Journal of Mathematical Behavior, 12(3), 239–250 [17] Harrow, F., Bouyeddoun, B., Sun, Y., & Kadri, B. (2013). Detecting cyber-attacks using a CRPS-based monitoring approach. IEEE Symposium on Computational Intelligence , 618-622. [18]He CH, El-Dib YO. (2021). A heuristic review on the homotopy perturbation method for non-conservative oscillators. Journal of Low Frequency Noise, Vibration and Active Control. 41(2): 572-603. doi: 10.1177/14613484211059264 [19]Hirsch MW, Smale S, Devaney RL. (2012). Discrete dynamical systems. In: Differential equations, dynamical systems, and an introduction to chaos. Academic Press. [20] Higgins, K. J. (2016). Lessons from the Ukrainian electric grid hack. Retrieved from http://www.darkreading.com/d/d.id/1324743 E- ISSN 2489-009X , [21] Joshi, D. M. (2021). Cyber pornography: An interdisciplinary study of technology-led crime against women and children. International Journal of Creative Research Thoughts (IJCRT, 9(12), B297-B301. [22] Khan, M., Pradhan, S., & Fatima, H. (2017). Applying data mining techniques in cybercrime. In 2nd International Conference on Anti-Cyber Crime , 21-216. IEEE. [23] Khan M, Farasat Saddiq S, Khan S, et al. (2014). Application of homotopy perturbation method to an SIR epidemic model. Journal of Applied Environmental and Biological Sciences. 4: 49-54. [24] Lacey AA, Tsardakas MN. (2016). A mathematical model of serious and minor criminal activity. European Journal of Applied Mathematics. 27(3): 403-421. doi: 10.1017/s0956792516000139 [25] Lekha, K., & Prakasan, S. (2017). Data mining techniques in detecting and predicting cyber crime. International Conference on Emerging Electrical and Data Analytics Systems , 1639-1643. IEEE. [26] Lim, M., Abdullah, A., Jhanjhi, N., Khan, M., & Supramanian, M. J. (2019). Link prediction in time-evolving criminal networks with deep reinforcement learning. Link Production Model for Evolving Criminal Network. [27] Mancuso, M. (2014). Not all madams have a central role: Analysis of a Nigerian sex trafficking network. Trends in Organized Crime, 17(2), 66-88. [28] Mataru, B., Abonyo, O. J. & Malonza, D. (2023). Mathematical Model for Crimes in Developing Countries with Some Control Strategies. Journal of Applied Mathematics, https://doi.org/10.1155/2023/8699882Digital Object Identifier [29] Meera, W., Isaac, M., & Balan, C. (2013). Forensics acquisition and analysis of VMware virtual machine artifacts. International Multi-Conference on Automation, Computing, Communication, Control and Compressed Sensing (IMac45), 255-259. IEEE. [30] Mohler GO, Short MB, Brantingham PJ, et al.(2011). Self-Exciting Point Process Modeling of Crime. Journal of the American Statistical Association. 106(493): 100- 108. doi: 10.1198/jasa.2011.ap09546 [31] Mutawa, N. A., Bryce, J. V. N., Franqueira, N., & Mannington, A. (2015). Behavioral evidence analysis applied to digital forensics: An empirical analysis of child pornography cases using P2P networks. Proceedings of the 10th International Conference on Availability, Reliability, and Security. [32] Newman, M. E. (2011). Complex systems: A survey. American Journal of Physics, 79(8), 800-810. [33]. Nkuturum, C. & George, I. (2022): Mathematical Modelling of Skilling Fishery Management for Sustainable Development of an Economy. IJMAM 5(3),121-136 [34]. Nkuturum, C. & Onwubuya, M.N. (2022). Mathematical Modeling of Rape under the Influence of Human Disturbance and Noise. IJMAM 5(2),121-136. [35] Nuño JC, Herrero MA. & Primicerio M. (2008). A triangle model of criminality. Physica A: Statistical Mechanics and its Applications. 2008; 387(12): 2926-2936. doi: 10.1016/j.physa.2008.01.076 [36] Ñuño, JC, Herrero MA, Primicerio M. (2011). A mathematical model of a criminal-prone society. Discrete and continuous dynamical systems. 2011; 4(1): 193-207. doi: 10.3934/dcdss.2011.4.193 [37]. Onwumere, J. & Eleodinmuo, P.O. (2015) Enhancing innovativeness among small and medium scale leather enterprises to boost performance in Abia State, Nigeria: International Journal of Community and Cooperative Studies; 3(1), pp. 1-14. E- ISSN 2489-009X , [38]Raimundo SM, Yang HM, Rubio FA, et al. (2023). Modeling criminal careers of different levels of offence. Applied Mathematics and Computation. 453: 128073. doi: 10.1016/j.amc.2023.128073 [39] Short MB, Mohler GO, Brantingham PJ, et al. (2014). Gang rivalry dynamics via coupled point process networks. Discrete & Continuous Dynamical Systems - B. 19(5): 1459- 1477. doi: 10.3934/dcdsb.2014.19.1459 [40] Sibi, H., Chakkaravartty, D., Sangeetha, M., Venkata Rathnam, K., & Srinthi, V. Y. (2018). Futuristic cyber attacks. 22(3), 195-204. [41] Sindhu, K., & Meshram, B. (2017). Digital forensics and cybercrime data mining. 3(3),196-212. [42] Sooknanan J, Bhatt B, Comissiong DMG. (2013). Catching a gang ? a mathematical model of the spread of gangs in a population treated as an infectious disease. International Journal of Pure and Apllied Mathematics. 83(1). doi: 10.12732/ijpam.v83i1.4 [43] Stoji?i?, S., Stojanovi?, V., Radovanovi?, R., Joksimovi?, D., & Jovanovi?, M. (2025). Mathematical Modeling of Criminal Activities: An Approach Based on Homotopy Perturbations. Advances in D