Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.537016
Title: Mathematical modelling and analysis of HIV transmission dynamics
Author: Hussaini, Nafiu
Awarding Body: Brunel University
Current Institution: Brunel University
Date of Award: 2010
Availability of Full Text:
Access from EThOS:
Access from Institution:
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.
Supervisor: Winter, M. Sponsor: Kano State Government of Nigeria
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.537016  DOI: Not available
Keywords: Susceptible-infected (SI) nonlinear models ; Susceptible-infected-removed (SIR) nonlinear models ; Public health education ; Backward bifurcation ; Travelling waves (travelling front) solutions
Share: