DYNAMIC OPTIMIZATION APPLIED TO A CRIMINOLOGICAL MODEL FOR REDUCING THE SPREAD OF SOCIETAL CORRUPTION

Kazi Nusrat  Islam; Tahera  Parvin; Md. Haider Ali  Biswas

doi:10.53808/KUS.2022.ICSTEM4IR.0148-se

Authors

Kazi Nusrat Islam Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
Tahera Parvin Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
Md. Haider Ali Biswas Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh

DOI:

https://doi.org/10.53808/KUS.2022.ICSTEM4IR.0148-se

Keywords:

Corruption, mathematical model, boundedness, optimal control, numerical analysis

Abstract

Corruption is rapidly affecting any country’s economic, democratic, financial, social, and political stability. It has been a consistent social phenomenon that happens in all civilizations. Only in the last 20 years has this phenomenon been given serious attention. It has different forms and different impacts on the economy as well as society as a whole. Economic growth is slowed by corruption, which also has a detrimental effect on business operations, employment, and investment. Additionally, it has a detrimental effect on tax revenues as well as the effectiveness of various financial aid programs. So, it is necessary to reduce this global problem. For this reason, we propose a nonlinear deterministic model for the transmission dynamics of societal corruption in terms of optimal control problem, using two time-dependent controls namely the efforts aimed at preventing corruption through the use of social networks, media, and social organizations; including a strong and effective anti-corruption policy, and also the attempt to encourage the punishment of corrupt people to analyze the model. The goal of this study is to reduce the problem of corruption. The results show that our proposed model can help to alleviate this social issue. Our findings also reveal that by using both control strategies instead of just one we get a more effective result. Overall, this research suggests that the impact of corruption can be reduced by implementing anti-corruption media and advertising campaigns, as well as exposing corrupted people to jail and punishing them.

Downloads

Download data is not yet available.

References

Abdulrahman, S. (2014). Stability analysis of the transmission dynamics and control of corruption. Pacific Journal of Science and Technology, 15, 99–113.

Athithan, S., Ghosh, M. & Li, X. Z. (2018). Mathematical modeling and optimal control of corruption dynamics. Asian-European Journal of Mathematics,11, 1-13.

Binuyo, A. (2019). Eigenvalue elasticity and sensitivity analyses of the transmission dynamic model of corruption. Journal of Nigerian Society of Physical Sciences, 1, 30–34.

Biswas, M. H. A. (2013). Necessary Conditions for Optimal Control Problems with State Constraints: Theory and Applications, PhD Thesis, Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Portugal.

Caiden, G. (2011). Dealing with administrative corruption. in Handbook of administrative ethics, CRC Press.

Crokidakis, N. & Sá Martins, J. S. (2018). Can honesty survive in a corrupt parliament?. International Journal of Modern Physics, 29, 1850094.

Danford, O., Kimathi, M. & Mirau, S. (2020) Mathematical modeling and analysis of corruption dynamics with control measures in Tanzania. Mathematics and Informatics, 19, 57–79.

Eguda, F., Oguntolu, F. & Ashezua, T. (2017). Understanding the dynamics of corruption using mathematical modeling approach. International Journal of Innovative Science, Engineering & Technology, 4, 190–197.

Gweryina, R. I., Kura, M. Y. & Okwu, E. (2019). An epidemiological model of corruption with immunity clause in Nigeria. World Journal of Modelling and Simulation, 15, 262–275.

Hathroubi, S. and Trabelsi, H. (2014). Epidemic corruption: a bioeconomic homology. European Scientific Journal, 10, 228–235.

Hattaf, K. (2020). A new generalized definition of fractional derivative with non-singular kernel. Computation, 8, 49.

Kebede, G. (2013). Political corruption: political and economic state capture in Ethiopia. European Scientific Journal, 9, 250-279.

Khan, Md. & Talukder, Md. I. (2021). Spatial Distribution of Crime in Bangladesh: An Analysis. Journal of Penal Law and Criminology, 9, 479-523.

Legesse, L. & Shiferaw, F. (2018). Modelling corruption dynamics and its analysis. Ethiopian Journal of Sciences and Sustainable Development, 5, 13–27.

Lenhart, S. & Workman, J.T. (2007). Optimal Control Applied to Biological Models. Chapman and Hall, New York, USA.

Nathan, O. & Jackob, K. (2019). Stability analysis in a mathematical model of corruption in Kenya. Asian Research Journal of Mathematics, 15, 1–15.

Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V. & Mischenko, E. F. (1962). The Mathematical Theory of Optimal Processes. John Wiley, New York.

Rudin, W. (1987). Real and Complex Analysis. McGraw Hill, New York.

Side, S., Sanusi, W. & Badwi, N. (2019). A SEIRS model analysis and simulation for dengue fever transmission. International Journal of Scientific & Technology Research, 8, 1048–1053.

Wang, X. Y., Hattaf, K., Huo, H. F. & Xiang, H. (2016). Stability analysis of a delayed social epidemics model with general contact rate and its optimal control. Journal of Industrial and Management Optimization, 12, 1267–1285.

World Bank (1997), Helping Countries Combat Corruption: The Role of the World Bank, World Bank.

Zhao, J. Q., Bonyah, E. and Yan, B. (2021). A mathematical model for the coinfection of buruli ulcer and cholera. Results in Physics, 29, 2211-3797.