Browsing Doctoral Degrees (Applied Mathematics) by Title
Now showing items 2945 of 45

Mathematical modeling of cancer treatments and the role of the immune system response to tumor invasion.
(2015)Despite the success of traditional cancer treatments, a definite cure to several cancers does not exist. Further, the traditional cancer treatments are highly toxic and have a relatively low efficacy. Current research ... 
A modelling approach for determining the freshwater requirements of estuarine macrophytes.
(1998)Increased abstraction of water in the catchment results in a reduced or altered pattern of river flow and this holds serious consequences for the downstream estuarine ecosystem. In South Africa this is a serious concern ... 
Modelling waterborne diseases.
(20150320)Waterborne diseases are among the major health problems threatening the life of individuals globally. This thesis investigates the dynamics of waterborne disease under different conditions and consequently determines ... 
Models in isotropic coordinates with equation of state.
(20150904)In this thesis we consider spacetimes which are static and spherically symmetric related to the Einstein and EinsteinMaxwell system of equations in isotropic coordinates. We study both neutral and charged matter ... 
New models for quark stars with charge and anisotropy.
(2014)We find new classes of exact solutions for the EinsteinMaxwell field equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field ... 
Noncircularity of beams in the CMB polarization power spectrum estimation.
(20150105)Precise measurements of the Cosmic Microwave Background (CMB) anisotropies have been one of the foremost concerns in modern cosmology as it provides valuable information on the cosmology of the Universe. However, an ... 
On new and improved seminumerical techniques for solving nonlinear fluid flow problems.
(2012)Most real world phenomena is modeled by ordinary and/or partial differential equations. Most of these equations are highly nonlinear and exact solutions are not always possible. Exact solutions always give a good account ... 
On singularly perturbed problems and exchange of stabilities.
(2015)Singular perturbation theory has been used for about a century to describe models displaying different timescales, that arise in applied sciences; particularly, models displaying two timescales, namely slow time and fast ... 
Optimisation of the population Monte Carlo algorithm : application to cosmology.
(20150904)In this thesis we study the Population Monte Carlo (PMC) algorithm and utilise simulations to improve the efficiency of the algorithm by optimising the algorithm parameters. We then ap ply these optimisation results to ... 
Partial exchangeability and related topics.
(1991)Partial exchangeability is the fundamental building block in the subjective approach to the probability of multitype sequences which replaces the independence concept of the objective theory. The aim of this thesis is ... 
Relativistic radiating stars with generalised atmospheres.
(2010)In this dissertation we construct radiating models for dense compact stars in relativistic astrophysics. We first utilise the standard Santos (1985) junction condition to model Euclidean stars. By making use of the ... 
Scalar perturbations of Schwarzschild black holes in modified gravity.
(2017)This thesis is concerned with the physics related to scalar perturbations in the Schwarzschild geometry that arise in modifed gravity theories. It has already been shown that the gravitational waves emitted from a ... 
Thermal evolution of radiation spheres undergoing dissipative gravitational collapse.
(20150904)In this study we investigate the physics of a relativistic radiating star undergoing dissipative collapse in the form of a radial heat flux. Our treatment clearly demonstrates how the presence of shear affects the collapse ... 
Transport on network structures.
(20140512)This thesis is dedicated to the study of flows on a network. In the first part of the work, we describe notation and give the necessary results from graph theory and operator theory that will be used in the rest of ... 
Using epidemiological mathematical models to understand the transmission dynamics of bovine tuberculosis in buffalo and cattle populations.
(2015)In South Africa, buffalo are the maintenance hosts of Mycobacterium bovis (M. bovis), a pathogen that causes bovine tuberculosis in wildlife and domesticated animals. To understand the transmission dynamics of M. bovis, ... 
Wadley's problem with overdispersion.
(2009)Wadley’s problem frequently emerges in dosagemortality data and is one in which the number of surviving organisms is observed but the number initially treated is unknown. Data in this setting are also often overdispersed, ... 
Windwave interactions, density stratification and double diffusive convection in rotating flows.
(2015)Abstract available in PDF file.