Brunel University Research Archive (BURA) >
College of Engineering, Design and Physical Sciences >
Dept of Mathematics >
Dept of Mathematics Theses >

Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/5672

Title: Mathematical modelling and analysis of HIV transmission dynamics
Authors: Hussaini, Nafiu
Advisors: Winter, M
Keywords: Susceptible-infected (SI) nonlinear models
Susceptible-infected-removed (SIR) nonlinear models
Public health education
Backward bifurcation
Travelling waves (travelling front) solutions
Publication Date: 2010
Publisher: Brunel University, School of Information Systems, Computing and Mathematics
Abstract: This thesis firstly presents a nonlinear extended deterministic Susceptible-Infected (SI) model for assessing the impact of public health education campaign on curtailing the spread of the HIV pandemic in a population. Rigorous qualitative analysis of the model reveals that, in contrast to the model without education, the full model with education exhibits the phenomenon of backward bifurcation (BB), where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the effective reproduction number (Reff ), is less than unity. Furthermore, an explicit threshold value is derived above which such an education campaign could lead to detrimental outcome (increase disease burden), and below which it would have positive population-level impact (reduce disease burden in the community). It is shown that the BB phenomenon is caused by imperfect efficacy of the public health education program. The model is used to assess the potential impact of some targeted public health education campaigns using data from numerous countries. The second problem considered is a Susceptible-Infected-Removed (SIR) model with two types of nonlinear treatment rates: (i) piecewise linear treatment rate with saturation effect, (ii) piecewise constant treatment rate with a jump (Heaviside function). For Case (i), we construct travelling front solutions whose profiles are heteroclinic orbits which connect either the disease-free state to an infected state or two endemic states with each other. For Case (ii), it is shown that the profile has the following properties: the number of susceptible individuals is monotone increasing and the number of infectives approaches zero, while their product converges to a constant. Numerical simulations are shown which confirm these analytical results. Abnormal behavior like travelling waves with non-monotone profile or oscillations are observed.
Description: This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.
Sponsorship: Kano State Government of Nigeria
URI: http://bura.brunel.ac.uk/handle/2438/5672
Appears in Collections:Mathematical Science
Dept of Mathematics Theses

Files in This Item:

File Description SizeFormat
FulltextThesis.pdf1.42 MBAdobe PDFView/Open

Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.