Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics
In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. Th...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/5109841 |
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| _version_ | 1832554359542513664 |
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| author | Haileyesus Tessema Alemneh |
| author_facet | Haileyesus Tessema Alemneh |
| author_sort | Haileyesus Tessema Alemneh |
| collection | DOAJ |
| description | In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. The conditions for local and global asymptotic stability of corruption-free and endemic equilibria are established. From the analysis using center manifold theory, the model exhibits forward bifurcation. Then, the model was extended by reformulating it as an optimal control problem, with the use of two time-dependent controls to assess the impact of corruption on human population, namely, campaigning about corruption through media and advertisement and exposing corrupted individuals to jail and giving punishment. By using Pontryagin’s maximum principle, necessary conditions for the optimal control of the transmission of corruption were derived. From the numerical simulation, it was found that the integrated control strategy must be taken to fight against corruption. |
| format | Article |
| id | doaj-art-6d6a727d2c5f4529b4bc4d5c7fe6538e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6d6a727d2c5f4529b4bc4d5c7fe6538e2025-02-03T05:51:47ZengWileyJournal of Applied Mathematics1110-757X1687-00422020-01-01202010.1155/2020/51098415109841Mathematical Modeling, Analysis, and Optimal Control of Corruption DynamicsHaileyesus Tessema Alemneh0Department of Mathematics, College of Natural and Computational Sciences, University of Gondar, Gondar, EthiopiaIn this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. The conditions for local and global asymptotic stability of corruption-free and endemic equilibria are established. From the analysis using center manifold theory, the model exhibits forward bifurcation. Then, the model was extended by reformulating it as an optimal control problem, with the use of two time-dependent controls to assess the impact of corruption on human population, namely, campaigning about corruption through media and advertisement and exposing corrupted individuals to jail and giving punishment. By using Pontryagin’s maximum principle, necessary conditions for the optimal control of the transmission of corruption were derived. From the numerical simulation, it was found that the integrated control strategy must be taken to fight against corruption.http://dx.doi.org/10.1155/2020/5109841 |
| spellingShingle | Haileyesus Tessema Alemneh Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics Journal of Applied Mathematics |
| title | Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics |
| title_full | Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics |
| title_fullStr | Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics |
| title_full_unstemmed | Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics |
| title_short | Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics |
| title_sort | mathematical modeling analysis and optimal control of corruption dynamics |
| url | http://dx.doi.org/10.1155/2020/5109841 |
| work_keys_str_mv | AT haileyesustessemaalemneh mathematicalmodelinganalysisandoptimalcontrolofcorruptiondynamics |