Hepatotoxicity which is also known as liver damage is mainly caused by intake of medicine. It is common among patients who are co-administering Tuberculosis (TB) treatment and the antiretroviral therapy (ART) for the Human Immunodeficiency Viruses (HIV). If severe, hepatotoxicity sometimes necessitates cessation or interruption of treatment. Therefore, understanding, monitoring and managing hepatotoxicity in patients co-infected with TB and HIV is crucial for optimal treatment outcomes. Hepatotoxicity has been investigated in patients coinfected with TB and HIV, however, most studies have analyzed only the first occurrence of hepatotoxicity and discarded information relating to the resolution and recurrence of hepatotoxicity. Data from the ‘Starting Antiretroviral therapy at three Points in Tuberculosis' (SAPiT) trial is used in this project. This was a trial that was instrumental in finalizing treatment guidelines for patients co-infected with HIV and TB in South Africa. The clinical objectives of this project are to estimate incidence rates and determine risk factors associated with hepatotoxicity. The statistical objectives are to fit a Cox regression model, the resolution model of hepatotoxicity, and the extended Cox models for recurring events, including the Andersen Gill (AG) model, the Shared frailty model, the Prentice, Williams and Peterson (PWP) total time (TT) model, the PWP gap time (GT) model, as well as a Cox based recurrent model, that models only the second occurrence of hepatotoxicity. There were 593 patients assessed for hepatotoxicity in the study, 30% (179/593) developed the first occurrence of hepatotoxicity (grade >=1) and 2% (13/593) developed severe hepatotoxicity (grade >=3). Resolved cases (grade = 0) are 76% (136/179) and recurring cases (grade >=1) 24% (32/136). In the Cox multivariable analyses: time-varying treatment arm, older patients, alcohol consumption, low baseline total bilirubin and a positive baseline Hepatitis B surface antigen status, were associated with a higher risk of developing the first occurrence of hepatotoxicity. The extended Cox models (AG model, Shared frailty model, PWP TT model and PWP GT model) in combination identified that: time-varying treatment arm, older patients, alcohol consumption, baseline CD4 count that is greater than 50 cells per mm3 , low baseline total bilirubin, and a positive baseline Hepatitis B surface antigen status were associated with an increased risk of developing recurrent hepatotoxicity. In the resolution model multivariable analyses; non-consumers of alcohol and an abnormal liver function tests at baseline, were associated with an increased chance of resolving the first occurrence of hepatotoxicity. In the multivariable analyses of the recurrent model: younger patients and the time-varying treatment arm were associated with the development of the second occurrence hepatotoxicity. Since the Cox regression model utilized data up to the first occurrence of hepatotoxicity, in some instances, the time-varying treatment effect based on the Cox regression model was closer to unity and marginally significant. And the corresponding effect based on the recurrent event models (AG model, Shared frailty model, PWP TT model, PWP GT model and the recurrent model), that utilized data of the first and second occurrence of hepatotoxicity, generally produced a time-varying treatment effect slightly far from unity with a strong statistical significance. This trend was similar for other predictors of hepatotoxicity, like CD4 count and alcohol consumption. In conclusion, hepatotoxicity is common in this study, however, it is often transient or mild and did not necessitate treatment interruption. However, close monitoring of patients especially in the first 5 months of TB-treatment is recommended. The PWP TT model seemed to be the best model for modelling recurring hepatotoxicity, since the identified risk factors that were associated with hepatotoxicity, changed from the first occurrence of hepatotoxicity to the second occurrence of hepatotoxicity.

This thesis discusses the techniques involved in the fitting of nonlinear mixed effect (NLME) models. In particular, it looks at the application of these techniques to the analysis of concentration-time data for the aforementioned antimalarial compounds, and details the necessary extensions to the basic modeling process that were required in order to accommodate multiple responses and multiple observation phases (pregnant and postpartum).

Includes bibliographical references. / Environmental data is very costly and difficult to collect and are often vague (subjective) or imprecise in nature (e.g. hazard level of pollutants are classified as "harmful for human beings"). These realities in practise (fuzziness and small datasets) leads to uncertainty, which is addressed by my research objective: "To model spatial environmental data with .fuzzy uncertainty, and to explore the use of small sample data in spatial modelling predictions, within Geographic Information System (GIS)." The methodologies underlying the theoretical foundations for spatial modelling are examined, such as geostatistics, fuzzy mathematics Grey System Theory, and (V,·) Credibility Measure Theory. Fifteen papers including three journal papers were written in contribution to the developments of spatial fuzzy and grey uncertainty modelling, in which I have a contributed portion of 50 to 65%. The methods and theories have been merged together in these papers, and they are applied to two datasets, PM10 air pollution data and soil dioxin data. The papers can be classified into two broad categories: fuzzy spatial GIS modelling and grey spatial GIS modelling. In fuzzy spatial GIS modelling, the fuzzy uncertainty (Zadeh, 1965) in environmental data is addressed. The thesis developed a fuzzy membership grades kriging approach by converting fuzzy subsets spatial modelling into membership grade spatial modelling. As this method develops, the fuzzy membership grades kriging is put into the foundation of the credibility measure theory, and approached a full data-assimilated membership function in terms of maximum fuzzy entropy principle. The variable modelling method in dealing with fuzzy data is a unique contribution to the fuzzy spatial GIS modelling literature. In grey spatial GIS modelling, spatial predictions using small sample data is addressed. The thesis developed a Grey GIS modelling approach, and two-dimensional order-less spatially observations are converted into two one-dimensional ordered data sequences. The thesis papers also explored foundational problems within the grey differential equation models (Deng, 1985). It is discovered the coupling feature of grey differential equations together with the help of e-similarity measure, generalise the classical GM( 1,1) model into more classes of extended GM( 1,1) models, in order to fully assimilate with sample data information. The development of grey spatial GIS modelling is a creative contribution to handling small sample data.

Protected areas are tracts of land set aside primarily for the conservation of biodiversity and natural habitats. They are intended to mitigate biodiversity loss caused by land-use change worldwide. Climate change has been shown to disrupt species' natural distributions and patterns, and poses a significant threat to global biodiversity. The goals of this thesis are to address these important issues, and understand how protected areas and climate change affect the range dynamics of common, resident bird species in South Africa. Common species were used because they have been shown to drive important ecosystem patterns, and a decline in abundance and diversity of common species can indicate drastic declines in ecosystem integrity. This thesis comprises four data chapters; in the first three I model the occupancy dynamics of 200 common, resident bird species in South Africa to gain an understanding of how the proportion of protected areas within a landscape affects common species. For the last data chapter, I examined the effects of protected areas and a changing climate on the range dynamics of Cape Rock-jumper (Chaetops frenatus), a species endemic to the southwestern part of South Africa and whose population is declining rapidly in response to climate change. I modelled its occupancy dynamics in relation to climate, vegetation, and protected area. Overall, my key findings show bird abundances vary widely as a function of protected areas, but on average, bird abundances are higher in regions with a higher proportion of protected areas, compared to regions with a lower proportion. I found that the conservation ability of protected areas was influenced by the type of land-use found in the surrounding landscape. For example, the extent of agricultural land in proximity to a protected area significantly increased the mean abundance of birds in that protected area, whilst the average abundance of most species was not affected by the extent of urban area near protected area. On average, species preferentially colonized and persisted within landscapes with a higher proportion of protected area, compared to landscapes with a lower proportion of protected area. However, protected areas were not able to slow the extinction rate for all species, and the average extinction rate for some groups of species actually increased as the extend of protected areas within a landscape increased. Furthermore, Cape Rock-jumper also preferentially occupied regions with higher proportions of protected area. Despite this, Cape Rock-jumper’s range is predicted to shrink considerably in response to a hotter and mildly drier climate forecast for the region. As a result, Cape Rock-jumper will likely be of conservation concern as the climate over its range continues to change. I conclude that, in general, protected areas are effective at conserving common bird species over a heterogeneous landscape in South Africa, and should be prioritised as key conservation strategies in the future. I further conclude that climate change will be a concern to an endemic species, and to biodiversity in general. This will likely place extra stress on the importance of protected areas to mitigate responses of species to climate change.

Markowitz's modem portfolio theory has played a vital role in investment portfolio management, which is constantly pushing the development on volatility models. Particularly, the stochastic volatility model which reveals the dynamics of conditional volatility. Financial time series and volatility models has become one of the hot spots in operations research. In this thesis, one of the areas we explore is the theoretical formulation of the optimal portfolio selection problem under Ito calculus framework. Particularly, a stochastic variation calculus problem, i.e., seeking the optimal stochastic volatility diffusion family for facilitating the best portfolio selection identified under the continuous-time stochastic optimal control theoretical settings. One of the properties this study examines is the left-shifting role of the GARCH(1, 1) (General Autoregressive Conditional Heteroskedastic) model's efficient frontier. This study considers many instances where the left shifting superior behaviour of the GARCH(1, 1) is observed. One such instance is when GARCH(1, 1) is compared within the volatility modelling extensions of the GARCH environ in a single index framework. This study will demonstrate the persistence of the superiority of the G ARCH ( 1, 1) frontier within a multiple and single index context of modem portfolio theory. Many portfolio optimization models are investigated, particularly the Markowitz model and the Sharpe Multiple and Single index models. Includes bibliographical references (p. 313-323).

Includes bibliographical references (p. 177-190).

Includes bibliographical references. / Two software tools decision making in wildlife management were developed as part of the Transboundary Mammal Project, a joint initiative between the Ministry of Environment and Tourism, Namibia (MET) and the Namibia Nature Foundation (NNF). This project aimed to improve the management of selected rare and high value species in Namibia by building a knowledge base for better informed decision making. The knowledge base was required to encapsulate current knowledge and experience of conservation experts and specialists. To provide an electronic representation of this knowledge base a hypermedia Information System for Rare Species Management (known as IRAS) was designed and implemented. The research therefore explores the disciplinary interstices of information technology, conservation and ethics, against the cultural background of a post-colonial society in which the deficits of the past constrain the impact and the efficacy of technological interventions.

The COVID-19 pandemic has had devastating consequences across the globe, and has led many governments into completely new decision making territory. Developing models which are capable of producing realistic projections of disease spread under extreme uncertainty has been paramount for supporting decision making by many levels of government. In South Africa, this role has been fulfilled by the South African COVID-19 Modelling Consortium's generalised Susceptible-ExposedInfectious-Removed compartmental model, known as the National COVID-19 Epi Model. This thesis adapted and contributed to the Model; its primary contribution has been to incorporate the feature that resources available to the health system are limited. Building capacity constraints into the Model allowed it to be used in the resource-scarce context of a pandemic. This thesis further designed and implemented a goal programming framework to shift ICU beds between districts intra-provincially in a way that aimed to minimise deaths caused by the non-availability of ICU beds. The results showed a 15% to 99% decrease in lives lost when ICU beds were shifted, depending on the scenario considered. Although there are limitations to the scope and assumptions of this thesis, it demonstrates that it is possible to combine mathematical modelling with optimisation in a way that may save lives through optimal resource allocation.

Includes bibliographical references (leaves 72-75). / A key feature of the local bond market is that trade is concentrated in a few liquid government bonds. We review and implement the filtered term structure model proposed by Gombani, Jaschke and Runggaldier that defines an arbitrage free pricing system that is consistent with liquid bond prices. The model is derived in two stages called the underlying and perturbed models. The underlying model defines the theoretical arbitrage free term structure. It is assumed to be a multi-factor, affine HNM type model where the stochastic factors satisfy a linear diffusion equation. Gombani et al. argue that the differences between the theoretical and market prices should be interpreted as unobserved errors. The perturbed model the prices of the observed bonds as their theoretical values distorted by noise. Assuming that the information at any point in time is the market prices of a finite number of liquidly traded bonds, the perturbed model is used to derive a continually updated pricing system that is arbitrage free with respect to the observed prices. The method is based on the Kalman filter. We implement a particular three-factor version of the model and calibrate it to the South African market. We discuss the relevant data and numerical and statistical techniques including principal component analysis and yield curve construction. We apply the formulas for pricing European options on zero-coupon and coupon bearing bonds for Gaussian HJM models to the perturbed model and present two examples to demonstrate the application of the model to bond and option pricing.

Includes bibliographical references (leaves 75-77).