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Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection
Dissertation (MSc)--University of Pretoria, 2017.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2018
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| _version_ | 1867613703694712832 |
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| access_status_str | Open Access |
| author2 | Garba, Salisu M. |
| author_browse | Garba, Salisu M. |
| author_facet | Garba, Salisu M. |
| collection | Thesis |
| dc_rights_str_mv | © 2018 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)--University of Pretoria, 2017. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/65185 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:40:22.099Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| 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:2263/65185 Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection Garba, Salisu M. chibalemumba@yahoo.com Mumba, Chibale K. Backward bifurcation Control strategies Reproduction number Trichomonas vaginalis HIV/AIDS UCTD Dissertation (MSc)--University of Pretoria, 2017. Deterministic models for the transmission dynamics of HIV/AIDS and trichomonas vaginalis (TV) in a human population are formulated and analysed. The models which assumed standard incidence formulations are shown to have globally asymptotically stable (GAS) disease-free equilibria whenever their associated reproduction number is less than unity. Furthermore, both models possess a unique endemic equilibrium that is GAS whenever the associated reproduction number is greater than unity. An extended model for the co-infection of TV and HIV in a human population is also designed and rigorously analysed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. This phenomenon can be removed by assuming that the co-infection of individuals with HIV and TV is negligible. Furthermore, in the absence of co-infection, the DFE of the model is shown to be GAS whenever the associated reproduction number is less than unity. This study identifies a sufficient condition for the emergence of backward bifurcation in the model, namely TV-HIV co-infection. The endemic equilibrium point is shown to be GAS (for a special case) when the associated reproduction number is greater than unity. Numerical simulations of the model, using initial and demographic data, show that increased incidence of TV in a population increases HIV incidence in the population. It is further shown that control strategies, such as treatment, condom-use and counselling of individuals with TV symptoms, can lead to the effective control or elimination of HIV in the population if their effectiveness level is high enough. DST-NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering (M3B2) Mathematics and Applied Mathematics MSc Unrestricted 2018-06-20T11:44:45Z 2018-06-20T11:44:45Z 2018-04-13 2017 Dissertation Mumba, CK 2017, Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/65185> A2018 http://hdl.handle.net/2263/65185 en © 2018 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 | Backward bifurcation Control strategies Reproduction number Trichomonas vaginalis HIV/AIDS UCTD Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection |
| title | Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection |
| title_full | Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection |
| title_fullStr | Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection |
| title_full_unstemmed | Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection |
| title_short | Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection |
| title_sort | mathematical modelling and analysis of hiv aids and trichomonas vaginalis co infection |
| topic | Backward bifurcation Control strategies Reproduction number Trichomonas vaginalis HIV/AIDS UCTD |
| url | http://hdl.handle.net/2263/65185 |