Doctoral Degrees (Applied Mathematics)
Recent Submissions

An analysis of symmetries and conservation laws of some classes of PDEs that arise in mathematical physics and biology.
(2016)In this thesis, the symmetry properties and the conservation laws for a number of wellknown PDEs which occur in certain areas of mathematical physics are studied. We focus on wave equations that arise in plasma physics, ... 
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 ... 
The CBand All Sky Survey commissioning and data analysis.
(2017)The CBand All Sky Survey (CBASS) is a ground based radio survey that scans the entire sky in Stokes I, Q and U at a central frequency of 5 GHz with a 1 GHz bandwidth and an angular resolution of 0.73 . The experiment ... 
Dynamics of radiating stars in the strong gravity regime.
(2017)We model the dynamics of a spherically symmetric radiating dynamical star, emitting outgoing null radiation, with three spacetime regions. The local internal atmosphere is a twocomponent system consisting of standard ... 
Conformal symmetry and applications to spherically symmetric spacetimes.
(2018)In this thesis we study static spherically symmetric spacetimes with a spherical conformal symmetry and a nonstatic conformal factor. We analyse the general solution of the conformal Killing vector equation subject to ... 
Investigation of gravitational collapse of generalized Vaidya spacetimes.
(2015)In this thesis, we study the gravitational collapse of generalized Vaidya spacetimes which describe a combination of lightlike and timelike matter elds, commonly known as Type I and Type II elds, respectively, in the ... 
Evolution of galaxy cluster scaling relations over half a Hubble time.
(2016)Abstract available in PDF file. 
Analysis of multiple control strategies for preexposure prophylaxis and postinfection interventions on HIV infection.
(2016)Abstract available in PDF file. 
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 ...