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. / Dissertation (MSc)--University of Pretoria, 2017. / DST-NRF SARChI Chair in
Mathematical Models and Methods in Biosciences and Bioengineering (M3B2) / Mathematics and Applied Mathematics / MSc / Unrestricted
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/65185 |
| Date | January 2017 |
| Creators | Mumba, Chibale K. |
| Contributors | Garba, Salisu M., chibalemumba@yahoo.com |
| Publisher | University of Pretoria |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Rights | © 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. |
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