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Modeling population dynamics of rhino-poacher interaction across South Africa and the Kruger National Park using ordinary differential equations
In this thesis, a system of ordinary differential equations (ODES) is presented to model the population dynamics between poachers and rhino as a predator-prey system in both South Africa (SA) and the Kruger National Park (KNP). The data used in this thesis consists mainly of government and police re...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2021
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| _version_ | 1867613226113433600 |
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| access_status_str | Open Access |
| author | Makic, Vladimir |
| author2 | Shock, Jonathan |
| author_browse | Makic, Vladimir Shock, Jonathan |
| author_facet | Shock, Jonathan Makic, Vladimir |
| author_sort | Makic, Vladimir |
| collection | Thesis |
| description | In this thesis, a system of ordinary differential equations (ODES) is presented to model the population dynamics between poachers and rhino as a predator-prey system in both South Africa (SA) and the Kruger National Park (KNP). The data used in this thesis consists mainly of government and police reports, as well publications from several NGOs and the limitations caused by this lack of applicable data are explored. The system dynamics are based on Lotka-Volterra differential equations, which are extended to include both a carrying capacity and the Allee effect. This thesis parameterises a model of the dynamics of the interaction between rhino and poachers for some time t and makes predictions based on the interpolation of the available data. The unknown rates and parameters relating to the behaviour of populations R and P are optimised by initially using a combination of educated guesses made from the available data or trial and error until set values are obtained. The remaining unknowns are numerically optimised based on the fixed value parameters. This is considered a constrained system, and the results obtained can only be viewed as constrained predictions based on parameter values obtained by a combination of trial and error and numerical optimisation; namely root mean square (RMS) error considering the available data and model solution at time t. Those parameter values obtained through RMS are regarded as error-minimising parameters within the scope of this research, and make up the final models which are referred to as the models which have been fitted to data. This thesis is an introductory, exploratory work into future attempts at modeling population dynamics with very little or no available data. The models are solved for in a constrained system, limiting the resulting predictions to constrained estimates based on the assigned values to unknown parameters. These solutions predict rhino stabilisation for both models, with active poachers dying out in the KNP but general co-existence observed across SA, within the constrained system. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/32798 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:46.693Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/32798 Modeling population dynamics of rhino-poacher interaction across South Africa and the Kruger National Park using ordinary differential equations Makic, Vladimir Shock, Jonathan Rhino poaching mathematical modeling Lotka Volterra differential equations In this thesis, a system of ordinary differential equations (ODES) is presented to model the population dynamics between poachers and rhino as a predator-prey system in both South Africa (SA) and the Kruger National Park (KNP). The data used in this thesis consists mainly of government and police reports, as well publications from several NGOs and the limitations caused by this lack of applicable data are explored. The system dynamics are based on Lotka-Volterra differential equations, which are extended to include both a carrying capacity and the Allee effect. This thesis parameterises a model of the dynamics of the interaction between rhino and poachers for some time t and makes predictions based on the interpolation of the available data. The unknown rates and parameters relating to the behaviour of populations R and P are optimised by initially using a combination of educated guesses made from the available data or trial and error until set values are obtained. The remaining unknowns are numerically optimised based on the fixed value parameters. This is considered a constrained system, and the results obtained can only be viewed as constrained predictions based on parameter values obtained by a combination of trial and error and numerical optimisation; namely root mean square (RMS) error considering the available data and model solution at time t. Those parameter values obtained through RMS are regarded as error-minimising parameters within the scope of this research, and make up the final models which are referred to as the models which have been fitted to data. This thesis is an introductory, exploratory work into future attempts at modeling population dynamics with very little or no available data. The models are solved for in a constrained system, limiting the resulting predictions to constrained estimates based on the assigned values to unknown parameters. These solutions predict rhino stabilisation for both models, with active poachers dying out in the KNP but general co-existence observed across SA, within the constrained system. 2021-02-05T08:46:31Z 2021-02-05T08:46:31Z 2020 2021-02-04T22:56:59Z Master Thesis Masters MSc http://hdl.handle.net/11427/32798 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Rhino poaching mathematical modeling Lotka Volterra differential equations Makic, Vladimir Modeling population dynamics of rhino-poacher interaction across South Africa and the Kruger National Park using ordinary differential equations |
| thesis_degree_str | Master's |
| title | Modeling population dynamics of rhino-poacher interaction across South Africa and the Kruger National Park using ordinary differential equations |
| title_full | Modeling population dynamics of rhino-poacher interaction across South Africa and the Kruger National Park using ordinary differential equations |
| title_fullStr | Modeling population dynamics of rhino-poacher interaction across South Africa and the Kruger National Park using ordinary differential equations |
| title_full_unstemmed | Modeling population dynamics of rhino-poacher interaction across South Africa and the Kruger National Park using ordinary differential equations |
| title_short | Modeling population dynamics of rhino-poacher interaction across South Africa and the Kruger National Park using ordinary differential equations |
| title_sort | modeling population dynamics of rhino poacher interaction across south africa and the kruger national park using ordinary differential equations |
| topic | Rhino poaching mathematical modeling Lotka Volterra differential equations |
| url | http://hdl.handle.net/11427/32798 |
| work_keys_str_mv | AT makicvladimir modelingpopulationdynamicsofrhinopoacherinteractionacrosssouthafricaandthekrugernationalparkusingordinarydifferentialequations |