Mathematical Model and Analysis of Corruption Dynamics with Optimal Control
In this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number R0 is computed using th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2022-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/8073877 |
| _version_ | 1798025231921577984 |
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| author | Abayneh Kebede Fantaye Zerihun Kinfe Birhanu |
| author_facet | Abayneh Kebede Fantaye Zerihun Kinfe Birhanu |
| author_sort | Abayneh Kebede Fantaye |
| collection | DOAJ |
| description | In this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number R0 is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever R0<1. Also, the endemic equilibrium point is locally and globally asymptotically stable whenever R0>1. Then, the model was extended to optimal control, and some numerical simulations with and without optimal control are also performed to verify the theoretical analysis using MATLAB. Numerical simulation of optimal control model shows that the prevention and punishment strategy is the most effective strategy to reduce the dynamic transmission of corruption. |
| first_indexed | 2024-04-11T18:15:26Z |
| format | Article |
| id | doaj.art-956fc6532c0248ab81897b9d5bc66237 |
| institution | Directory Open Access Journal |
| issn | 1687-0042 |
| language | English |
| last_indexed | 2024-04-11T18:15:26Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj.art-956fc6532c0248ab81897b9d5bc662372022-12-22T04:09:56ZengHindawi LimitedJournal of Applied Mathematics1687-00422022-01-01202210.1155/2022/8073877Mathematical Model and Analysis of Corruption Dynamics with Optimal ControlAbayneh Kebede Fantaye0Zerihun Kinfe Birhanu1Debre Tabor UniversityHawassa UniversityIn this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number R0 is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever R0<1. Also, the endemic equilibrium point is locally and globally asymptotically stable whenever R0>1. Then, the model was extended to optimal control, and some numerical simulations with and without optimal control are also performed to verify the theoretical analysis using MATLAB. Numerical simulation of optimal control model shows that the prevention and punishment strategy is the most effective strategy to reduce the dynamic transmission of corruption.http://dx.doi.org/10.1155/2022/8073877 |
| spellingShingle | Abayneh Kebede Fantaye Zerihun Kinfe Birhanu Mathematical Model and Analysis of Corruption Dynamics with Optimal Control Journal of Applied Mathematics |
| title | Mathematical Model and Analysis of Corruption Dynamics with Optimal Control |
| title_full | Mathematical Model and Analysis of Corruption Dynamics with Optimal Control |
| title_fullStr | Mathematical Model and Analysis of Corruption Dynamics with Optimal Control |
| title_full_unstemmed | Mathematical Model and Analysis of Corruption Dynamics with Optimal Control |
| title_short | Mathematical Model and Analysis of Corruption Dynamics with Optimal Control |
| title_sort | mathematical model and analysis of corruption dynamics with optimal control |
| url | http://dx.doi.org/10.1155/2022/8073877 |
| work_keys_str_mv | AT abaynehkebedefantaye mathematicalmodelandanalysisofcorruptiondynamicswithoptimalcontrol AT zerihunkinfebirhanu mathematicalmodelandanalysisofcorruptiondynamicswithoptimalcontrol |