Theses and Dissertations

Permanent URI for this collection

https://univendspace.univen.ac.za/handle/11602/2138

Browse

Now showing 1 - 20 of 70

Open Access
q- Enumeration of permutations avoiding adjacent patterns
(2009-09) Takalani, Ntendeni Annah; Tshifhumulo, T. A.
Open Access
Mathematical modelling of transmission and control of malaria
(2012-12-19) Mulaudzi, Matodzi Stanley; Garira, Winston
Malaria starts with plasmodium sporozoites infection of the host liver, where development into blood stage parasites occurs. A number of deterministic models are developed in this thesis. The release of modified mosquitoes aims to displace gradually the wild (natural) mosquito from the habitat. We discuss the suitability of this technique when applied to pre-domestically adapted plasmodium falciparum mosquitoes which are transmissor of malaria disease. The dynamics of interaction of sporozoites, liver cells, merozoites and red blood cells which cause the symptoms and pathology of the disease is comprehensively studied. We then show how variability of host-parasite immunity is incorporated in the model which are constructed to include liver and blood compartments by subdividing the host population into various mutually exclusive compartments. The increase in eggs, larval and pupal stages of mosquitoes increase the vector mosquito population and transmission of the disease, hence the suggestion that immature and adult mosquitoes be controlled extensively. The models which are in the form of nonlinear ordinary differential equations are rigorously analysed using ex tensively analytic and numerical techniques to determine important epidemiological thresholds, stability of the steady states and the persistence of infection in the respective populations. Conclusions are made based on the results obtained from the analysis of the models of malaria that have been developed
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.
In this study we present a condition for the existence and uniqueness of the solution y(x) for a system of nonhomogeneous linear first order Ordinary Differential Equations (ODE). The existence and uniqueness of the solution of y(x) was confirmed through the Picard Lindelof Theorem. We then study the stability of matrix A(x) using its spectrum, moreover, A(x) is symmetric. This is a pre-condition for the application of Lefschetz direct stability method. We then modify the given Lefschetz system (Meyer, 1964) to suit the problem at hand. The direct method requires the construction of a suitable Lyapunov function; not easy for a time-independent (non-dynamic) problem. For a time-dependent problem the energy thereof becomes a suitable candidate for a Lyapunov function. For a non-dynamic problem it is harder to construct a Lyapunov function as there are no rules for that purpose. In our study we modified the Lefschetz system for the direct stability method and applied it to confirm the Lefschetz stability criterion using the modified systems of linear first order ODEs with variable coefficients. The Lefschetz method afforded us the construction of a credible Lyapunov function which enabled us to confirm the stability of the null solution to our problem. From our modified Lefschetz direct stability system, we solved the Makhabane / Hlomuka equation (5) for B(x) (7) which we later confirmed as both symmetric and positive definite.
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.
Maternal death is the death of woman during pregnancy or within 42 days of termination of pregnancy from any cause related to or aggravated by the pregnancy or its management but not from accidental or external causes. Health complications during pregnancy and child birth are a major challenge worldwide. Statistics South African reports mortality data for South Africa classified according to various demographic characteristics and causes. The causes are classified using ICD10. Using the Statistics South Africa data, this study focused on the death of a women aged between 15 to 49 over the period of 2003 to 2008. The purpose of this study is to identify the level, trends, leading causes and factors associated with death due to maternal related causes among women aged 15-49 in South Africa and to explore the relationship between the socio-demographic and clinical factors on one hand with maternal deaths over the period 2003 to 2008. Logistic regression and log linear analysis were used to explore the relationships. The results show that the maternal mortality ratio of South Africa increased from 114 per 100 000 live births in 2003 to 195 per 100 000 live births in 2008. Free State province had the lowest maternal mortality ratio and the Western Cape province had the highest ratio. Northern Cape had the same levels of maternal mortality as Western Cape in 2003 - 2004, but increased at a faster rate afterwads. By 2008, the rate of maternal mortality in Northern Cape was about twice that of Western Cape. The top five causes of maternal death were eclampsia (015), puerperal sepsis (072), postpartum hemorrhage (085), maternal infectious and parasitic diseases classifiable elsewhere but complicating pregnancy, childbirth and the puerperium (098), other maternal diseases classifiable elsewhere but complicating pregnancy, childbirth and the puerperium (099). There is a significant association of maternal mortality with socio demographic variables (Marital Status, Age, Death Province, Place of Death) and other illnesses (HIV, TB, pneumonia and diarrhoea). There was no significant association between maternal deaths and educational level. When four or five causes of death were listed on the death notification form, maternal mortality is not directly associated with HIV. The link to HIV is only through the opportunistic diseases associated with HIV. When only two or three causes are listed, direct association exist.
Open Access
A stochastic programming framework for financial intermediaries liquidity in South Africa
(2015-05) Chagwiza, Wilbert; Garira, W.; Moyo, S.
We provide a thorough overview of the current liquidity problem, dis cussing what are considered to be state-of-the-art approaches in both in dustry and in academia, and clearly establish our motivation to depart from current liquidity management standards. We noted that during 2007 to 2009 financial crisis different countries throughout the whole world faced serious challenges that ranged from chronic liquidity problems, deep-rooted risk management deficiencies and poor corporate governance practices. The liq uidity crisis, especially in the USA, was caused by low real interest rates stimulating an asset price bubble fuelled by new financial products that were not stress-tested and that failed in the downturn. Large depository institu tions face the question of how to optimally utilise funds and manage liquid ity problems. The existing liquidity models are not standardised, and do not take into consideration the complexity and the nature of the bank. As evi denced by the late 2000 financial crisis, it is evident that nowadays there is not a metric that seems to be completely adequate to prevent liquidity crises. Our contribution is fourfold. First we investigate appropriate scenario gener ation methods and perform a rigorous investigation on how to generate mul tistage scenario trees. Further, we investigate the inclusion of all qualifying liquid asset instruments into the portfolio optimisation. We propose a novel multistage stochastic programming methodology for liquid asset control. Thus we define how to construct and solve stochastic programming models for liquidity needs-driven sub-portfolios. Our approach is based on scenario trees and makes no assumption on the distributions of random variables. Fi nally, we investigate the inclusion of liquidity needs-driven strategies which are core liquidity, cash cushion, operational cash and discretionary liquidity into the overall liquidity portfolio. Stochastic programming is a multi-faceted problem, and even the most fo cused treatment necessarily incorporates techniques from a wide range of disciplines. Through the development of fully coherent models and a suffi ciently robust solution methodology, we provide a thorough overview of the problem at hand, discussing approaches in both industry and in academia. We introduce practical and theoretical advances that are to our best knowl edge unexplored in the current literature, and document the usefulness of these avenues through a systematic series of increasingly complex applica tions and experiments. The data used is from the South African Reserve Bank (SARB) and International Monetary Fund (IMF) from January 1988 to May 2014. Most corporations such as commercial banks generally hold a unitary liquidity portfolio and not necessarily segmented to focus on bank specific cash and liquidity needs. Banks do have different cash needs at different times. Financial intermediaries to manage liquidity efficiently and effectively, segmenting the optimal liquid asset portfolio is the best manage ment strategy. We construct different stochastic programming models based on decision making under risk and provision of powerful paradigm for de cision making under uncertainty. The stochastic programming models with recourse are clear, easy to implement, very efficient and provide the optimal solution according to future possible set of scenarios. In defining and con structing stochastic programming models with recourse, sensitivity analysis should be carried out to increase the decision maker's understanding of the problem and to show the effect of different assumptions. Constructing an SP model with more stages provides better approximations compared to a single-period model. We found that the use of the proposed models through segmenting the unitary liquidity portfolio improves the management of liq uidity compared to current techniques which are based on simulation, ex perience and trial-and-error. Thus high quality liquidity buffers insure the bank against any adverse liquidity risk. We found that liquidity buffer is best modelled as a stochastic process than deterministic. High net cash flow enhance effective and efficient liquidity management. Finally, excess re serves improve country monetary policy and broaden the scope of central bank lending programmes to address conditions in credit markets but on the other hand, may lead banks to loosen standards by weakening lending crite ria in an attempt to increase returns. In designing the sub-portfolios, liquidity determinants such as liquid asset returns, loan returns, payment flow, interest rates and gross income are un certain, and to avoid liquidity problems caused by these variables, we need to include randomness on them. To effectively and efficiently manage liq uidity, a bank may be required to follow certain key liquidity principles. The first is that the bank needs to understand and categorise its cash needs into at least four liquidity sub-portfolios as explained in the research. In this study, we strongly recommend that the banks' management should design the following sub-portfolios; liquidity buffer, cash cushion, operational cash and discretionary liquidity. The bank should clearly maintain the holdings of high quality liquid assets that can provide reliable reserves under all con ditions. In addition, strict and relatively comprehensive disclosure practices in relation to liquidity risk management objectives should be submitted to central banks. Finally, there should be improvement on funding markets and public confidence by broadening the scope of bank guarantees to ensure future financial stability. We need to emphasise the point that bank liquid ity is restricted by capital adequacy, required reserves, liability and deposit insurance defined by the central bank. Research can therefore be done on models that can be used to efficiently and accurately forecast future cash outflow taking into consideration the behavioural cash flows and estimating the discretionary and excess reserves. Further research can also be done on comparing the benefits of the calculated strategies in the stochastic programming context to more traditional methods.
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.
The flow is described by the Navicr-Stokes equations in the domain n C R3. The open-bounded domain is assumed to have a cone property. The rotation of a 3- dimensional symmetrical impermeable cylindrical rigid body in the fluid is studied. The model is constructed in a manner that the equations describe a system in a frame attached to the obstacle.The system of the governing equations is constructed on the basis of conservation of angular momentum of the rigid body and the conservation of linear momentum of the fluid. When the conservation of angular momentum is taken into account, a dynamic boundary condition is considered. The uniqueness of this unknown velocity vector field is confirmed by using the so called energy method. In this study we chose the incompressible viscous Navier-Stokes flow and thus the fluid density does not change through out the flow.
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
The study explores the stochastic approach to multi-state modeling of HIV dynamic evolution and identification of the model that best describes HIV progression on individuals under ART. The effects of TB co-infection, as well as the patients' development of adverse reaction to drugs to the transition rates are also examined. The study uses a cohort analysis of the surveillance data for HIV-infected patients under antiretroviral (ART) from the Wellness Clinic in Bela Bela, South Africa. The survey was conducted between 2005 and 2009 and a follow up was done after every 6 months. The method par titions the HIV infection period into five CD4-cell count intervals followed by the end points, that is, death and withdrawal from study. The analysis is based on transition probabilities, transition rates (hazards), mean sojourn times, and time to absorption. The effects of the covariates, namely sex, age, TB co-infection, drug reaction, body mass index (BMI), baseline viral load (VLBL) and the CD4+ cell count baseline on enrollment, on transition in tensities for each model are also analysed. The likelihood ratio test is used to compare the fitted models, and the test shows that the time inhomogeneous model describes the data better than the time homogeneous models. The results show that the rates of immune recovery are generally higher than the rates of immune deterioration. The patients who developed TB during treat ment have higher rates of immune deterioration than recovery. Having TB as the initial marker of AIDS has higher contributory effects to the deaths from all the stages except from the AIDS defining stage. Reaction to drugs was the leading cause of transition from a CD4+ cell count 2: 750 to a CD4+ cell count between 500 and 750.
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 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
Mathematical modelling of Cholera Immunology
(2016-05) Maphiri, Azwindini Delinah; Garira, W.; Musie, E.
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
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
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
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
Unsteady hydromagnetic chemically reacting mixed convection MHD flow over a permeable stretching sheet embedded in a porous medium with thermal radiation and heat source/sink
(2018-05-18) Machaba, Mashudu Innocent; Shateyi, Stanford; Netshiozwi, N. J.
The unsteady hydromagnetic chemically reacting mixed convection MHD ow over a permeable stretching sheet embedded in a porous medium with thermal radiation and heat source/sink is investigated numerically. The original partial di erential equations are converted into ordinary di erential equations by using similarity transformation. The governing non-linear partial di erential equations of Momentum, Energy, and Concentration are considered in this study. The e ects of various physical parameters on the velocity, temperature, and species concentration have been discussed. The parameters include the Prandtl number (Pr), Magnetic parameter (M), the Schmidt number (Sc), Unsteady parameter (A), buoyancy forces ratio parameter (N), Chemical reaction (K), Radiation parameter (Nr), Eckert number (Ec), local heat source/sink parameter (Q) and buoyancy parameter due to temperature ( ). The coe cient of Skin friction and Heat transfer are investigated. The coupled non-linear partial di erential equations governing the ow eld have been solved numerically using the Spectral Relaxation Method (SRM). The results that are obtained in this study are then presented in tabular forms and on graphs and the observations are discussed.
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
Open Access
Numerical analysis of unsteady MHD mixed conversion flow past an infinite vertical plate in the presence of Dufour and Soret effects with viscous dissipation
(2018-05-18) Mukwevho, Nancy; Shateyi, S.; Netshiozwi, N. J.
Magnetohydrodynamics ows have gained signi cant attention due to their importance in engineering applications. In this study, we numerically analysed the Dufour and Soret e ects on an unsteady MHD mixed convection ow past an in nite vertical plate with viscous dissipation. The governing non-linear partial di erential equations (PDEs) are transformed into a system of ordinary di erential equations (ODEs) by the suitable similarity transformations. The resulting equations consist of the momentum, energy and mass di usion equations. These resulting equations are solved using the Spectral Local Linearization Method (SLLM). Results obtained by the SLLM are in good agreement with the bvp4c technique. The e ects of di erent physical parameters entering into the problem are displayed graphically. The values of the Skin-friction (f0(0)), Nusselt number (􀀀 0(0)) and Sherwood number (􀀀 0(0)) are shown in tabular form for di erent values of the parameters. From the results, it is noted that the Soret number (Sr) and the Dufour number (Du) have negligible e ects on temperature pro le, whereas the decrease in the Soret number (Sr) leads to a decrease in both velocity and concentration of the uid, and the increase in Dufour number (Du) reduces the velocity and also has negligilbe e ect on the concentration pro le.
Open Access
Multiscale Modelling of HIV/AIDS Transmission Dynamics
(2018-09-21) Mafunda, Martin Canaan; Garira, W.; Moyo, S.
Infectious diseases remain a major public health concern. Well-known for causing sickness and death, enormous pain and suffering, increased time spent on patient care and huge economic losses due to lost production. Infectious diseases continue to be a scourge without equal. In this work, we address the following research question: Can we use a multiscale model of HIV/AIDS transmission dynamics to assess the comparative effectiveness of health interventions that are implemented at different scale domains? To achieve the set objectives of the study, we use multiscale modelling approach, a new and emerging computational high-throughput technique for mathematically studying problems that have many characteristics across several scales. To be more specific, we perform three tasks in addressing the research question. First, we develop a within-host submodel and use it to show it’s associated limitations which only a multiscale model can resolve. Second, we develop a between-host submodel and use it to motivate the need for multiscale modelling of the HIV/AIDS disease system. Finally, we link the two submodels to produce a nested HIV/AIDS multiscale model that affords us the opportunity to compare effectiveness of five preventive and treatment HIV/AIDS health interventions. Analysis of the multiscale model shows that it is possible to jointly study two key aspects (immunology and epidemiology) of infectious diseases. The multiscale model provides the means for making meaningful comparative effectiveness on available preventive and treatment health interventions. Consequently, we employ the multiscale model to show that impact of HIV/AIDS packages increases as more interventions are integrated into the packages. Specifically, the study shows that combined HAART and male circumcision is more effective than an intervention involving HAART alone. Overall, our study successfully illustrates the utility of multiscale modelling methodology as a tool for assessing the comparative effectiveness of HIV/AIDS preventive and treatment interventions. For purposes of informing public health policy, we use the study results to infer that condom use, male circumcision and pre-exposure prophylaxis are more effective in controlling the transmission dynamics of HIV/AIDS at the start of the epidemic as compared to when the disease is endemic in the community while the converse is also true for HAART.