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Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus)
Dissertation (MSc (Applied Mathematics))--University of Pretoria, 2018.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2025
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| _version_ | 1867613570718498816 |
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| access_status_str | Open Access |
| author2 | Chapwanya, Michael |
| author_browse | Chapwanya, Michael |
| author_facet | Chapwanya, Michael |
| collection | Thesis |
| dc_rights_str_mv | © 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc (Applied Mathematics))--University of Pretoria, 2018. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/107108 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:15.015Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/107108 Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus) Chapwanya, Michael phindiledumani94@gmail.com Dumani, Phindile UCTD Sustainable Development Goals (SDGs) Rabies Culling Incubation period Basic Reproduction number Dissertation (MSc (Applied Mathematics))--University of Pretoria, 2018. Simplified models representing rabies epidemic are presented to better understand the epidemiological dynamics of the disease. We extensively study the transmission and progression dynamics of rabies in African wild dogs, Lycaon pictus, by adapting a stan-dard sei model to include both the asymptomatic and symptomatic stages to simulate the time-delay. Furthermore, we investigate the contribution of other rabies hosts in the environment (e.g, stray dogs) have on the transmission dynamics. The study is based on the assumption that there are no vaccination programmes introduced, hence, we consider culling as a possible control strategy to reduce the rabid population or the uncontrollable spread of the disease to a level below the threshold. The threshold quantity, the basic reproduction number, which in this case is the expected number of new infectious dogs in a perfectly susceptible population produced by a single infected dog is used to give a quantitative discussion on the control of rabies. We present the mathematical analysis of the proposed continuous and discrete models. Numerical simulations are provided to support theoretical results. Mathematics and Applied Mathematics MSc (Applied Mathematics) Unrestricted Faculty of Natural and Agricultural Sciences SDG-03: Good health and well-being 2025-12-08T06:57:56Z 2025-12-08T06:57:56Z 2019-04 2018-11 Dissertation * A2019 http://hdl.handle.net/2263/107108 en © 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Sustainable Development Goals (SDGs) Rabies Culling Incubation period Basic Reproduction number Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus) |
| title | Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus) |
| title_full | Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus) |
| title_fullStr | Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus) |
| title_full_unstemmed | Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus) |
| title_short | Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus) |
| title_sort | mathematical analysis and simulations of models for rabies epidemic among african wild dogs lycaon pictus |
| topic | UCTD Sustainable Development Goals (SDGs) Rabies Culling Incubation period Basic Reproduction number |
| url | http://hdl.handle.net/2263/107108 |