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Mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society
Thesis (MMil)--Stellenbosch University, 2024.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867614138929250304 |
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| access_status_str | Open Access |
| author | Tibane, Naledi Shelter |
| author2 | Makinde, Oluwole Daniel |
| author_browse | Makinde, Oluwole Daniel Tibane, Naledi Shelter |
| author_facet | Makinde, Oluwole Daniel Tibane, Naledi Shelter |
| author_sort | Tibane, Naledi Shelter |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MMil)--Stellenbosch University, 2024. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/131936 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:47:17.083Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/131936 Mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society Tibane, Naledi Shelter Makinde, Oluwole Daniel Stellenbosch University. Faculty of Military Science. School for Science and Technology. Corruption Dynamics Mathematical models Differential equations Fertility, Human -- Statistics Mathematical optimization Control theory UCTD Pontryagin's Maximum Principle in Practice Thesis (MMil)--Stellenbosch University, 2024. ENGLISH ABSTRACT: Corruption is defined as a criminal activity (such as bribery, nepotism, manipulation fraud, financial crime, abuse, counterfeiting, favouritism, etc) implemented by public (government) or private (corporate) officials through the abuse of authority or influence for private gain and benefit, whether financial or otherwise. Corruption is like a disease that has existed for centuries and is slowly penetrating society, affecting economic development in different countries, which is why many authors, especially in the field of epidemiology, study corruption dynamics as a disease using mathematical models to better understand corruption dynamics. Although corruption has existed for centuries, it continues to be a huge problem, even after the implementation of anti-corruption measures. Therefore, mathematical modelling will give and help policymakers with how to best apply anti-corruption strategies at a minimal cost, while reducing corruption spread and ultimately increasing productivity and service delivery. We proposed a mathematical model for corruption dynamics with its impact on productivity and service delivery within a society (focusing more on underdeveloped or developing African countries). The compartmental deterministic model is analysed under both constant and time-dependent control strategies that include preventive measures, such as moral education and adequate security, and punitive measures, such as suspension, confiscation of properties, imprisonment, etc. Both positivity and the invariant region of the model are determined. We calculated the basic reproductive number (𝑅0) via the next-generation-matrix method, conducted stability analysis of equilibrium points. We proved for both local and global stability that is, if 𝑅0<1, then corruption will be eliminated using the Jacobian matrix, Routh-Hurwitz and appropriate Lyapunov function. We showed the global stability of the corruption endemic equilibrium that, if 𝑅0>1, corruption will continue to spread. Sensitivity analysis of each parameter and bifurcation analysis were conducted (and the model exhibits a forward bifurcation). Additionally, the implementation both of optimal control based on Pontryagin’s maximum principle with two variable control strategies (preventative and punitive measures) and cost-effectiveness analysis, which uses an incremental cost-effectiveness ratio (ICER) was introduced. Numerical simulations are conducted. Graphical results and the cost-effective analysis show that the least cost-effective strategy to help reduce or eliminate corruption and help improve productivity together with service delivery in communities is control strategy B, which is punitive measures such as imprisonment. AFRIKAANSE OPSOMMING: Geen Afrikaanse opsomming nie. Masters 2025-04-29T12:42:28Z 2025-04-29T12:42:28Z 2024-12 Thesis https://scholar.sun.ac.za/handle/10019.1/131936 en Stellenbosch University ix, 87 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Corruption Dynamics Mathematical models Differential equations Fertility, Human -- Statistics Mathematical optimization Control theory UCTD Pontryagin's Maximum Principle in Practice Tibane, Naledi Shelter Mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society |
| title | Mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society |
| title_full | Mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society |
| title_fullStr | Mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society |
| title_full_unstemmed | Mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society |
| title_short | Mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society |
| title_sort | mathematical modelling of corruption dynamics and its impact on productivity and service delivery in a society |
| topic | Corruption Dynamics Mathematical models Differential equations Fertility, Human -- Statistics Mathematical optimization Control theory UCTD Pontryagin's Maximum Principle in Practice |
| url | https://scholar.sun.ac.za/handle/10019.1/131936 |
| work_keys_str_mv | AT tibanenaledishelter mathematicalmodellingofcorruptiondynamicsanditsimpactonproductivityandservicedeliveryinasociety |