Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection

dc.contributor.advisorGarba, Salisu M.
dc.contributor.emailchibalemumba@yahoo.comen_ZA
dc.contributor.postgraduateMumba, Chibale K.
dc.date.accessioned2018-06-20T11:44:45Z
dc.date.available2018-06-20T11:44:45Z
dc.date.created2018-04-13
dc.date.issued2017
dc.descriptionDissertation (MSc)--University of Pretoria, 2017.en_ZA
dc.description.abstractDeterministic 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.en_ZA
dc.description.availabilityUnrestricteden_ZA
dc.description.degreeMScen_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.sponsorshipDST-NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering (M3B2)en_ZA
dc.identifier.citationMumba, 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>en_ZA
dc.identifier.otherA2018
dc.identifier.urihttp://hdl.handle.net/2263/65185
dc.language.isoenen_ZA
dc.publisherUniversity of Pretoria
dc.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.
dc.subjectBackward bifurcationen_ZA
dc.subjectControl strategiesen_ZA
dc.subjectReproduction numberen_ZA
dc.subjectTrichomonas vaginalisen_ZA
dc.subjectHIV/AIDSen_ZA
dc.subjectUCTDen_ZA
dc.titleMathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infectionen_ZA
dc.typeDissertationen_ZA

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