Dynamics and optimal control strategies of Corruption model

Abstract

In this work, we propose a nonlinear Mathematics effect model of media on the phenomenon of corruption. We suggest a model that is more general than the ones we are familiar with in this domain as we work in a structure of nine compartments. Moreover, we have proved the existence and the uniqueness of the solution through the fixed point theorem. The question of stability is well examined. We argue that the corruption free equilibrium is stable when R_0 is less than one. The endemic equilibrium, which indicates the presence of corruption in the community, exists only when R_0>1. Based on the principle of Pontryagin's maximum, an assessment of the requirements for optimal control of corruption spread. We perform extensive numerical simulations to support the analytical results.

Keywords

• Corruption
• epidemic model
• epidemiology
• modeling corruption

Kaynakça

1. N.  Ozdemir ve E. Uçar, \Investigating of an immune system-cancer mathematical model with Mittag-Leer kernel", AIMS Mathematics, vol. 5, no. 2, pp. 1519{1531, (2020).
2. Uçar Sumeyra (2021). Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives. Discrete and Continuous Dynamical Systems Series S, 14(7).
3. Uçar Esmehan, Uçar Sumeyra, Evirgen Firat,  Ozdemir Necati (2021). A Fractional SAIDR Model in the Frame of Atangana-Baleanu Derivative. Fractal and Fractional, 5(2).
4. Uçar Esmehan, Uçar Sumeyra, Evirgen Firat,  Ozdemir Necati (2021). Investigation of E-Cigarette Smoking Model with Mittag-Leer Kernel. Foundations of Computing and Decision Sciences, 46(1), 97-109.
5. Evirgen Firat, Uçar Sumeyra, Ozdemir Necati (2020). System Analysis of HIV Infection Model with CD4T under Non-Singular Kernel Derivative. Applied Mathematics and Nonlinear Sciences, 5(1), 139-146.
6. Uçar, S. (2020). Existence Results for a Computer Virus Spreading Model with Atangana-Baleanu Derivative . Celal Bayar University Journal of Science , 17 (1) , 67-72. E. Uçar, N. Ozdemir, A fractional model of cancer-immune system with Caputo and Caputo Fabrizio derivatives", The European Physical Journal Plus, vol. 136, (2021).
7. Uçar Sumeyra (2020). Analysis of a basic SEIRA model with Atangana-Baleanu derivative. AIMS Mathematics, 5(2), 1411-1424.
8. Alla Hamou, A., Azroul, E.,& Lamrani Alaoui, A. (2021). Fractional model and numerical algorithms for predicting covid-19 with isolation and quarantine strategies. International Journal of Applied and Computational Mathematics, 7(4), 1-30.

9. Hamou, A. A., Azroul, E., Hammouch, Z., & Alaoui, A. L. (2020). A fractional multi-order model to predict the COVID-19 outbreak in Morocco. Appl. Comput. Math, 20(1), 177-203.
10. Allahamou, A., Azroul, E., Hammouch, Z., & Alaoui, A. L. (2022). Modeling and numerical investigation of a conformable co-infection model for describing Hantavirus of the European moles. Mathematical Methods in the Applied Sciences, 45(5), 2736-2759.
11. S. Abdulrahman, Stability analysis of the transmission dynamics and control of corruption, Pacic Journal of Science and Technology, vol. 15, no. 1, pp. 99{113, 2014.
12. Alemneh, Haileyesus Tessema. Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics . Journal of Applied Mathematics 2020 (1 ao^ut 2020): 1-13. https://doi.org/10.1155/2020/5109841.
13. Akinsola, Victor, et Adeyemi Binuyo. Stability Analysis of the Corruption Free Equilibrium of the Mathematical Model of Corruption in Nigeria . Mathematical Journal of Interdisciplinary Sciences 8 (30 mars 2020): 61-68. https://doi.org/10.15415/mjis.2020.82008.
14. Bacaer, Nicolas. A Short History of Mathematical Population Dynamics. London: Springer London, 2011. https://doi.org/10.1007/978-0-85729-115-8.
15. Baum, Anja, Clay Hackney, Paulo Medas, et Mouhamadou Sy. Governance and State-Owned Enterprises: How Costly Is Corruption? IMF Working Papers 2019, no 253 (22 novembre 2019). https://doi.org/10.5089/9781513519296.001.
16. Chitnis N, Hyman JM, Cushing JM. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol. 2008 Jul;70(5):1272-96. doi: 10.1007/s11538-008-9299-0. .
17. Cuervo-Cazurra, Alvaro. Corruption in International Business . Journal of World Business 51, no 1 (janvier 2016): 35-49. https://doi.org/10.1016/j.jwb.2015.08.015.
18. Dietz, K. The Estimation of the Basic Reproduction Number for Infectious Diseases . Statistical Methods in Medical Research 2, no 1 (mars 1993): 23-41. https://doi.org/10.1177/096228029300200103.
19. Athithan, S., Ghosh, M., Li, X. Z.: Mathematical modeling and optimal control of corruption dynamics. Asian-Eur J Math 11(6) (2018)
20. Dietz, K., Schenzle, D. Proportionate mixing models for age-dependent infection transmission. J. Math. Biology 22,117{120 (1985). https://doi.org/10.1007/BF00276550.
21. DeJesus, E. X., & Kaufman, C. (1987). Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Physical Review A, 35(12), 5288.
22. Dublin, Louis I., & Alfred J. Lotka. On the True Rate of Natural Increase . Journal of the American Statistical Association 20, no 151 (septembre 1925): 305. https://doi.org/10.2307/2965517.
23. Education Manual, The conceptual basis of the ght against corruption, 2014.
24. F.B. Agusto, M.A. Khan, Optimal control strategies for dengue transmission in pakistan, Mathematical Biosciences, Vol 305, 2018, 102-121, ISSN 0025-5564, https://doi.org/10.1016/j.mbs.2018.09.007.
25. Fleming, W. H., & Rishel, R. W. (2012). Deterministic and stochastic optimal control (Vol. 1). Springer Science & Business Media.
26. Gail, Mitchell H., & Philip S. Rosenberg. Perspectives on Using Back calculation to Estimate HIV Prevalence and project AIDS incidence . in AIDS Epidemiology, 1-38. Boston, 1992. https://doi.org/10.1007/978-1-4757-1229-2-1.
27. Heesterbeek, J. A. P., & K. Dietz. The Concept of R o in Epidemic Theory . Statistica Neerlandica 50, no 1 (mars 1996): 89-110. https://doi.org/10.1111/j.1467-9574.1996.tb01482.x.
28. H. Soa and F. Rodrigues , \Optimal Control and Numerical Optimization Applied to Epidemiological Models," Applications of Mathematics, 2012.
29. I. Yusuf, S. Abdulrahman, B. Musa and G. Adamu, "Controlling the Spread of Corruption through Social Media: A Mathematical Modelling Approach", Nigeria 2016.
30. Kermack William Ogilvy and McKendrick A. G. 1927A contribution to the mathematical theory of epidemics Proc. R. Soc. Lond. A115700{721 http://doi.org/10.1098/rspa.1927.0118.
31. Ktjczynski, R R. The balance of births and deaths, s. d., 8. 1928.
32. Lemecha, L., & Feyissa, S. (2018). Mathematical modeling and analysis of corruption dynamics. Ethiopian Journal of Science and Sustainable Development, 5(2), 13-25.
33. MACDONALD G. The analysis of equilibrium in malaria. Trop Dis Bull. 1952 Sep;49(9):813-29. PMID: 12995455.
34. Mokaya, Nathan Oigo, Haileyesus Tessema Alemmeh, Cyrus Gitonga Ngari, & Grace Gakii Muthuri. Mathematical Modelling and Analysis of Corruption of Morals amongst Adolescents with Control Measures in Kenya . Discrete Dynamics in Nature and Society 2021 (21 avril 2021): 1-16. https://doi.org/10.1155/2021/6662185.
35. P. van den Driessche, James Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, Vol 180, Issues 1{2, 2002, 29-48, ISSN 0025-5564, https://doi.org/10.1016/S0025-5564(02)00108-6.
36. Sharomi, Oluwaseun, & Tufail Malik. Optimal Control in Epidemiology . Annals of Operations Research 251, no 1-2 (avril 2017): 55-71. https://doi.org/10.1007/s10479-015-1834-4.
37. Smith, D. & Keytz, N. Mathematical demography: selected papers. Biomathematics, vol. 6. Berlin: Springer.1977.
38. Sharpe, F R. 13. A Problem in Age-Distribution , s. d., 2., 435{438.
39. Trirogo, K.N. (2000). L. S. Pontryagin Selected Works: The Mathematical Theory of Optimal Processes (L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, & L.W. Neustadt, Eds.) (1st ed.). Routledge. https://doi.org/10.1201/9780203749319.
40. T. Vito, International monetary fund "corruption around the world: Causes, consequences, scope and cures" Fiscal Affairs Department, 1998.
41. Ullah, Saif, Muhammad Altaf Khan, & J.F. Gomez-Aguilar. "Mathematical Formulation of Hepatitis B Virus with Optimal Control Analysis" . Optimal Control Applications and Methods 40, no 3 (mai 2019): 529-44. https://doi.org/10.1002/oca.2493.
42. YORKE, JAMES A., & al. Dynamics and Control of the Transmission of Gonorrhea." Sexually Transmitted Diseases, vol. 5, no. 2, 1978, pp. 51{56. JSTOR, http://www.jstor.org/stable/44966942. Accessed 20 Jul. 2022.
43. Carmen Chicone, Ordinary Dierential Equations with Applications. (2006). In Texts in Applied Mathematics. Springer New York. https://doi.org/10.1007/0-387-35794-7