Department of Mathematics
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Design, analysis and simulation of a robust numerical method to solve Zika virus models
(University of the Western Cape, 2019)This thesis deals with the analysis and robust simulation of mathematical models describing Zika virus disease. Some background information about the occurrences of this disease and most recent literature indicating some ... -
Stochastic modeling of an HIV/AIDS epidemic with treatment
(University of the Western Cape, 2019)The HIV/AIDS epidemic continues to be among the most devastating diseases in human history despite the new scientific advances and serious public health interventions. The greatest burden of HIV/AIDS is still in sub-Saharan ... -
Valuation of options for hedging against exchange rate exposure
(University of the Western Cape, 2019)The risk associated with currency exposure is one of the main sources of risk in terms of internationally diversi ed portfolios. Controlling the risk is important for improving the performance of international investments. ... -
Quasi-uniform and syntopogenous structures on categories
(University of the Western Cape, 2019)In a category C with a proper (E; M)-factorization system for morphisms, we further investigate categorical topogenous structures and demonstrate their prominent role played in providing a uni ed approach to the theory ... -
Robust computational methods to simulate slow-fast dynamical systems governed by predator-prey models
(University of the Western Cape, 2019)Numerical approximations of multiscale problems of important applications in ecology are investigated. One of the class of models considered in this work are singularly perturbed (slow-fast) predator-prey systems which ... -
Mathematical modeling of the transmission dynamics of malaria in South Sudan
(University of the Western Cape, 2019)Malaria is a common infection in tropical areas, transmitted between humans through female anopheles mosquito bites as it seeks blood meal to carry out egg production. The infection forms a direct threat to the lives of ... -
Interior operators and their applications
(University of the Western Cape, 2019)Categorical closure operators were introduced by Dikranjan and Giuli in [DG87] and then developed by these authors and Tholen in [DGT89]. These operators have played an important role in the development of Categorical ... -
An analytical model for assessing the knowledge of statistical procedures amongst postgraduate students in a higher educational environment
(University of the Western Cape, 2019)Over the past decades, the use and application of statistical concepts for university students have been a big challenge learned from their previous courses. Aftermath of democracy, South African higher education focused ... -
Topogenous Structures on Categories
(University of the Western Cape, 2016)Although the interior operators correspond to a special class of neighbourhood operators, the closure operators are not nicely related to the latter. We introduce and study the notion of topogenous orders on a category ... -
On the primarity of some block intersection graphs
(University of the Western Cape, 2018)A tactical con guration consists of a nite set V of points, a nite set B of blocks and an incidence relation between them, so that all blocks are incident with the same number k points, and all points are incident with ... -
Mathematical models for optimal management of bank capital, reserves and liquidity
(University of the Western Cape, 2019)The aim of this study is to construct and propose continuous-time mathematical models for optimal management of bank capital, reserves and liquidity. This aim emanates from the global financial crisis of 2007 − 2009. In ... -
Codes, graphs and designs from maximal subgroups of alternating groups
(University of the Western Cape, 2018)The main theme of this thesis is the construction of linear codes from adjacency matrices or sub-matrices of adjacency matrices of regular graphs. We first examine the binary codes from the row span of biadjacency ... -
On the method of lines for singularly perturbed partial differential equations
(University of the Western Cape, 2017)Many chemical and physical problems are mathematically described by partial differential equations (PDEs). These PDEs are often highly nonlinear and therefore have no closed form solutions. Thus, it is necessary to ... -
On the numerical integration of singularly perturbed Volterra integro-differential equations
(University of the Western Cape, 2017)Efficient numerical approaches for parameter dependent problems have been an inter- esting subject to numerical analysts and engineers over the past decades. This is due to the prominent role that these problems play in ... -
Pricing European options : a model-free approach
(University of the Western Cape, 2016)This paper focuses on the newly revived interest to model free approach in finance. Instead of postulating some probability measure it emerges in a form of an outer-measure. We review the behavior of a market stock price ... -
Topogenous structures on categories
(University of the Western Cape, 2016)Although the interior operators correspond to a special class of neighbourhood operators, the closure operators are not nicely related to the latter. We introduce and study the notion of topogenous orders on a category ... -
Meta-Cayley Graphs on Dihedral Groups
(University of the Western Cape, 2017)The pursuit of graphs which are vertex-transitive and non-Cayley on groups has been ongoing for some time. There has long been evidence to suggest that such graphs are a very rarety in occurrence. Much success has been had ... -
A mathematical model for studying the impact of climate variability on malaria epidemics in South Africa
(University of the Western Cape, 2017)Malaria is most prevalent in tropical climates, where there are sufficient rainfall for mosquitoes to breed and conducive temperatures for both the mosquito and protozoa to live. A slight change in temperature can ... -
Fischer-clifford matrices and character tables of inertia groups of maximal subgroups of finite simple groups of extension type
(University of the Western Cape, 2011)The aim of this dissertation is to calculate character tables of group extensions. There are several well–developed methods for calculating the character tables of group extensions. In this dissertation we study the method ... -
Analysis of errors in derivatives of trigonometric functions: a case study in an extended curriculum programme
(University of the Western Cape, 2012)The purpose of this study was to explore errors that are displayed by students when learning derivatives of trigonometric functions in an extended curriculum programme. The first aim was to identify errors that are displayed ...
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