Department of Mathematical and Computational Sciences

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Now showing 1 - 20 of 69

Open Access
q- Enumeration of permutations avoiding adjacent patterns
(2009-09) Takalani, Ntendeni Annah; Tshifhumulo, T. A.
See the attached abstract below
Open Access
Mathematical modelling of transmission and control of malaria
(2012-12-19) Mulaudzi, Matodzi Stanley; Garira, Winston
Open Access
Analysis of a boundary value problem for a system on non-homogeneous ordinary differential equations (ODE), with variable coefficients
(2015-01-16) Makhabane, Paul Suunyboy; Hlomuka, V. J.; Garira, W.
Open Access
Factors associated with maternal mortality in South Africa (2003-2008)
(2015-03-02) Mukondeleli, Livhuwani Ellen; Amey, A. K. A.; Kyei, K. A.
Open Access
A stochastic programming framework for financial intermediaries liquidity in South Africa
(2015-05) Chagwiza, Wilbert; Garira, W.; Moyo, S.
See the attached abstract below
Open Access
Existence and Uniqueness of a solution to a flow problem about a Rotating Obstacle at low Reynolds number
(2015-05) Nyathi, Freeman; Moyo, S.
See the attached abstract below
Open Access
Stochastic modelling of HIV/AIDS epidemiology with TB co-infection drug reaction in South Africa
(2015-07-16) Shoko, Claris; Garira, W; Amey, A. K. A; Bessong, P. O
Open Access
Modelling flood heights of the Limpopo River at Beitbridge Border Post using extreme value distributions
(2016) Kajambeu, Robert; Sigauke, Caston; Bere, Alphonce
Haulage trucks and cross border traders cross through Beitbridge border post from landlocked countries such as Zimbabwe and Zambia for the sake of trading. Because of global warming, South Africa has lately been experiencing extreme weather patterns in the form of very high temperatures and heavy rainfall. Evidently, in 2013 tra c could not cross the Limpopo River because water was owing above the bridge. For planning, its important to predict the likelihood of such events occurring in future. Extreme value models o er one way in which this can be achieved. This study identi es suitable distributions to model the annual maximum heights of Limpopo river at Beitbridge border post. Maximum likelihood method and the Bayesian approach are used for parameter estimation. The r -largest order statistics was also used in this dissertation. For goodness of t, the probability and quantile- quantile plots are used. Finally return levels are calculated from these distributions. The dissertation has revealed that the 100 year return level is 6.759 metres using the maximum likelihood and Bayesian approaches to estimate parameters. Empirical results show that the Fr echet class of distributions ts well the ood heights data at Beitbridge border post. The dissertation contributes positively by informing stakeholders about the socio- economic impacts that are brought by extreme flood heights for Limpopo river at Beitbridge border post
Open Access
A class of efficient iterative solvers for the steady state incompressible fluid flow : a unified approach
(2016-02-01) Muzhinji, Kizito;
Open Access
A mathematical modelling frame-work for immuno-epidemiology of Guinea worm infection
(2016-02-12) Netshikweta, Rendani; Garira, W.; Moyo, S.
Open Access
Mathematical modelling of Cholera Immunology
(2016-05) Maphiri, Azwindini Delinah; Garira, W.; Musie, E.
See the attached abstract below
Open Access
Mathematical modelling of fungal contamination of citrus produce along the pre-harvest supply chain
(2016-05) Muleya, Nqobile; Garira, W.; Mchau, G. R. A.
See the attached abstract below
Open Access
Profit risk models for South African banking sector
(2016-05) Antwi, Albert; Kyei, K. A.; Manda, D. C.; Gyamfi, E. N.
See the attached abstract below
Open Access
Determination of factors contributing towards women's unemployment in the Capricorn and Sekhukhune districts in the Limpopo Province
(2017-09-18) Maboko, Tumisho; Kyei, K. A.
See the attached abstract below
Open Access
Modeling and Forecasting Ghana's Inflation Rate Under Threshold Models
(2017-09-18) Antwi, Emmanuel; Kyei, K. A.; Gyampi, E. N
Over the years researchers have been modeling inflation rate in Ghana using linear models such as Autoregressive Integrated Moving Average (ARIMA), Autoregressive Moving Average (ARMA) and Moving Average (MA). Empirical research however, has shown that financial data, such as inflation rate, does not follow linear patterns. This study seeks to model and forecast inflation in Ghana using nonlinear models and to establish the existence of nonlinear patterns in the monthly rates of inflation between the period January 1981 to August 2016 as obtained from Ghana Statistical Service. Nonlinearity tests were conducted using Keenan and Tsay tests, and based on the results, we rejected the null hypothesis of linearity of monthly rates of inflation. The Augmented Dickey-Fuller (ADF) was performed to test for the presence of stationarity. The test rejected the null Hypothesis of unit root at 5% significant level, and hence we can conclude that the rate of inflation was stationary over the period under consideration. The data were transformed by taking the logarithms to follow nornal distribution, which is a desirable characteristic feature in most time series. Monthly rates of inflation were modeled using threshold models and their fitness and forecasting performance were compared with Autoregressive (AR ) models. Two Threshold models: Self-Exciting Threshold Autoregressive (SETAR) and Logistic Smooth Threshold Autoregressive (LSTAR) models, and two linear models: AR(1) and AR(2), were employed and fitted to the data. The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were used to assess each of the fitted models such that the model with the minimum value of AIC and BIC, was judged the best model. Additionally, the fitted models were compared according to their forecasting performance using a criterion called mean absolute percentage error (MAPE). The model with the minimum MAPE emerged as the best forecast model and then the model was used to forecast monthly inflation rates for the year 2017. The rationale for choosing this type of model is contingent on the behaviour of the time-series data. Also with the history of inflation modeling and forecasting, nonlinear models have proven to perform better than linear models. The study found that the SETAR and LSTAR models fit the data best. The simple AR models however, out-performed the nonlinear models in terms of forecasting. Lastly, looking at the upward trend of the out-sample forecasts, it can be predicted that Ghana would experience double digit inflation in 2017. This would have several impacts on many aspects of the economy and could erode the economic gains i made in the year 2016. Our study has important policy implications for the Central Bank of Ghana which can use the data to put in place coherent monetary and fiscal policies that would put the anticipated increase in inflation under control.
Open Access
Hybrid multi-scale mathematical modelling of malaria infection transmission
(2017-09-18) Vele, Khathutshelo; Garira, W.; Moyo, S.
See the attached abstract below
Open Access
Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction
(De Gruyter, 2017-11-27) Shateyi, Stanford; Marewo, Gerald T.
We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.
Open Access
Alternative methods for solving nonlinear two-point boundary value problems
(2018-03-18) Ghomanjani, Fateme; Shateyi, Stanford
In this sequel, the numerical solution of nonlinear two-point boundary value problems (NTBVPs) for ordinary di erential equations (ODEs) is found by Bezier curve method (BCM) and orthonormal Bernstein polynomials (OBPs). OBPs will be constructed by Gram-Schmidt technique. Stated methods are more easier and applicable for linear and nonlinear problems. Some numerical examples are solved and they are stated the accurate findings.
Open Access
Modelling average maximum daily temperature using r largest order statistics: An application to South African data
(OASIS, 2018-05-02) Nemukula, M. M.; Sigauke, Caston
Natural hazards (events that may cause actual disasters) are established in the literature as major causes of various massive and destructive problems worldwide. The occurrences of earthquakes, floods and heat waves affect millions of people through several impacts. These include cases of hospitalisation, loss of lives and economic challenges. The focus of this study was on the risk reduction of the disasters that occur because of extremely high temperatures and heat waves. Modelling average maximum daily temperature (AMDT) guards against the disaster risk and may also help countries towards preparing for extreme heat. This study discusses the use of the r largest order statistics approach of extreme value theory towards modelling AMDT over the period of 11 years, that is, 2000–2010. A generalised extreme value distribution for r largest order statistics is fitted to the annual maxima. This is performed in an effort to study the behaviour of the r largest order statistics. The method of maximum likelihood is used in estimating the target parameters and the frequency of occurrences of the hottest days is assessed. The study presents a case study of South Africa in which the data for the non-winter season (September–April of each year) are used. The meteorological data used are the AMDT that are collected by the South African Weather Service and provided by Eskom. The estimation of the shape parameter reveals evidence of a Weibull class as an appropriate distribution for modelling AMDT in South Africa. The extreme quantiles for specified return periods are estimated using the quantile function and the best model is chosen through the use of the deviance statistic with the support of the graphical diagnostic tools. The Entropy Difference Test (EDT) is used as a specification test for diagnosing the fit of the models to the data.
Open Access
Market Efficiency of African Stock Markets
(2018-05-18) Numapau, Gyamfi Emmanuel; Kyei, Kwabena; Gill, Ryan
There has been a growing interest in investment opportunities in Africa. The net foreign direct investment (FDI) to Sub-Saharan Africa has increased from $13 billion in 2004 to about $54 billion in 2015. Investing on the stock markets is one of such investment opportunities. Stock markets in Africa have realised growth in market capitalization, membership, value and volume traded due to an increase in investments. This level of growth in African stock markets has raised questions about their efficiency. This thesis examined the weak-form informational efficiency of African stock markets. The aim therefore of this thesis is to test the efficiency of African stock markets in the weak-form of the Efficient Market Hypothesis (EMH) for eight countries, namely, Botswana, Egypt, Kenya, Mauritius, Morocco, Nigeria, South Africa and Tunisia. Since, the researcher will be testing the weak-form of the EMH, the data to be used is on past price information on the markets of the eight countries. Data for the eight countries were obtained from DataStream for the period between August 28, 2000 to August 28, 2015. The data is for a period of 180 months which resulted in 3915 data points. Although there have been studies on the weak-form market efficiency of African stock markets, the efficiency conclusions on the markets have been mixed. This problem might be due to the methods used in the analyses. First, most of the methods used were linear in nature although the data generating process of stock market data is nonlinear and hence nonlinear methods maybe more appropriate in its analysis. Also these linear methods tested the efficiency of African markets in absolute form, however, an efficiency conclusion relying solely on absolute efficiency might be misleading because, stock markets become efficient with time due to improvements in the quality of information processing from reforms on the markets. The researcher solved this problem of using absolute frequency by comparing the results when the presence of long-memory in frequency and time domains of the markets were examined. The researcher used a semi-parametric estimator, the Local Whittle estimator to test for long-memory in frequency domain and the Detrended Fluctuation Analysis (DFA) to test for long-memory in time domain. The DFA method is suitable for both stationary and nonstationary time series which makes it to have more power over methods like the rescaled range analysis (R/S) in the estimation of Hurst exponent. Second, the researcher examined whether the markets were predictable under the Adaptive Market Hypothesis (AMH). The researcher employed the Generalised Spectral (GS) test to examine the Martingale difference hypothesis (MDH) of the markets. The Generalised spectral (GS) test is a non-parametric ii test designed to detect the presence of linear and nonlinear dependencies in a stationary time series. The GS test considers dependence at all lags. Third, because of the nonlinear nature in the data-generating process on the markets, the stationarity of the market returns under a nonlinear Exponential Smooth Threshold Autoregressive (ESTAR) model was examined. A nonlinear ADF unit root test against ESTAR and a modified Wald-type test against ESTAR in the analysis were employed. Fourth, the self-exciting threshold Autoregressive (SETAR) method was employed to model the returns when non-linear patterns were observed as a result of nonlinear data generating process on the markets. The literature on market efficiency of African stock markets has shown that variations exist in the study characteristics. There are variations in the method of analysis, type of test, type of data employed, time period chosen and the scope of analysis for the studies. The researcher therefore quantitatively reviewed previous studies by means of meta-analysis to identify which study characteristics affects efficiency conclusions of African markets using the mixed effects model. The findings showed the presence of long-memory in the returns of the stock markets when the whole sample was used. This made the markets weak-form inefficient, however, when the researcher tested for the persistence of long-memory through time, there were periods the markets were efficient in the weak-form. The memory effect was low in the South African market but high in the Mauritian market. Furthermore, it was observed that, the returns for Egypt, which were highly predictable when the whole data was analysed became not highly predictable when the rolling window approach of the GS test was used. Egypt had one of the lowest percentages of the windows that had a p-value less than 0.05 after South Africa. The results obtained from using the non-linear unit root tests on the logarithmic price series of the markets under study showed that, the markets were non-stationary and hence weak-form efficient under an ESTAR framework but for Botswana. Thus the markets were weak-form efficient when analysed using a non-linear method. This observation means that Africa’s foreign direct investment would have been increased over the years if the appropriate methods are used. This is because, over the years, studies on the weak-form efficiency African stock markets have ended with mixed conclusions with most of the markets being concluded to be weak-form inefficient as a result of the use of linear methods in the analysis. This finding, to us, has had an effect on investors commitments to Africa because the right methodology was not employed. iii The findings from modelling the returns under the non-linear SETAR model showed that, the SETAR model performs better than the standard AR(1) and AR(2) model for all the markets under study after the non-linear patterns were identified in the returns series. The SETAR (2,2,2) model is a threshold model, therefore, investors are able to move freely in search of higher opportunities between the low and high regimes. Investors main aim is to make profits, hence, the threshold model of SETAR gives them the freedom to move to a regime where the rate of returns is increasing unlike the standard AR(1) and AR(2) linear models where there are no switching of regimes. Finally, none of the study characteristics in the market efficiency studies was found to be significant in efficiency conclusions of African stock markets but the indicator for publication bias was significant. This means that there has been a change in attitude in recent years towards studies on informational market efficiency whose results do not support the Efficient Market Hypothesis (EMH), unlike the earlier years when the EMH was formulated and acclaimed to be one of the best propositions in economics. It was therefore concluded that when time-varying methods are used in analysing weak-form efficiency, the dynamics of the markets become known to investors for proper decision-making. Also, nonlinear methods should be used in order to reflect the nonlinear nature of data capturing on the stock markets