Doctoral Degrees (Applied Mathematics)
Recent Submissions

Bivariate pseudospectral collocation algorithms for nonlinear partial differential equations.
(2016)Abstract available in PDF file. 
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 ... 
Windwave interactions, density stratification and double diffusive convection in rotating flows.
(2015)Abstract available in PDF file. 
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 ... 
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, ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
Generalized travelling wave solutions for a microscopic chemotaxis model.
(2014)In biology cell migration is one of the most critical processes, for it is decisive in the mechanisms leading to the beginning of life. The collective migration of cells via wave motion plays a key role in understanding ... 
Differential equations for relativistic radiating stars.
(2013)We consider radiating spherical stars in general relativity when they are conformally flat, geodesic with shear, and accelerating, expanding and shearing. We study the junction conditions relating the pressure to the ... 
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 ... 
Group theoretic approach to heat conducting gravitating systems.
(20150107)We study shearfree heat conducting spherically symmetric gravitating fluids defined in four and higher dimensional spacetimes. We analyse models that are both uncharged and charged via the pressure isotropy condition ... 
Exact models of compact stars with equations of state.
(20150105)We study exact solutions to the EinsteinMaxwell system of equations and relate them to compact objects. It is well known that there are substantial analytic difficulties in the modelling of selfgravitating, static fluid ... 
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 ... 
Age structured models of mathematical epidemiology.
(20141121)We consider a mathematical model which describes the dynamics for the spread of a directly transmitted disease in an isolated population with age structure, in an invariant habitat, where all ... 
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 ... 
Initial conditions of the universe : signatures in the cosmic microwave background and baryon acoustic oscillations.
(2012)In this thesis, we investigate the signatures of isocurvature initial conditions in the cosmic microwave background (CMB) through the temperature and polarization anisotropies, and in the largescale structure distribution ... 
Applications of embedding theory in higher dimensional general relativity.
(20140422)The study of embeddings is applicable and signicant to higher dimensional theories of our universe, highenergy physics and classical general relativity. In this thesis we investigate local and global isometric ...