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When an emerging outbreak occurs, stable parameter estimation and reliable projections of future incidence cases using limited (early) data can play an important role in optimal allocation of resources and in the development of effective public health intervention programs. However, the inverse parameter identification problem is ill-posed and cannot be solved with classical tools of computational mathematics. In this dissertation, various regularization methods are employed to incorporate stability in parameter estimation algorithms. The recovered parameters are then used to generate future incident curves as well as the carrying capacity of the epidemic and the turning point of the outbreak. For the nonlinear generalized Richards model of disease progression, we develop a novel iteratively regularized Gauss-Newton-type algorithm to reconstruct major characteristics of an emerging infection. This problem-oriented numerical scheme takes full advantage of a priori information available for our specific application in order to stabilize the iterative process. Another important aspect of our research is a reliable estimation of time-dependent transmission rate in a compartmental SEIR disease model. To that end, the ODE-constrained minimization problem is reduced to a linear Volterra integral equation of the first kind, and a combination of regularizing filters is employed to approximate the unknown transmission parameter in a stable manner. To justify our theoretical findings, extensive numerical experiments have been conducted with both synthetic and real data for various infectious diseases.

South Africa currently faces multiple Cr(VI) contamination problems which are unsuccessfully remediated using available technologies. Cr(VI) is highly toxic, carcinogenic and mutagenic in nature and it is exclusively released through anthropogenic activities. A new treatment approach is proposed using locally isolated Cr(VI) reducing species of bacteria. This method is envisioned to be economical and ecologically friendly. Indigenous chromium(VI) reducing bacteria (CRBs) were isolated from a dried sludge consortium collected in the Brits Wastewater Treatment Plant, North-West Province (South Africa). Characterisation using 16S rRNA fingerprinting followed by taxonomic studies revealed a wide diversity of CRBs isolated under anaerobic conditions than under aerobic conditions. The consortium was determined to be predominantly gram-positive. The Cr(VI) reducing component of the culture was determined to be predominantly facultative, consisting predominantly of Bacillus sp., i.e. B. cereus, B. thuringiensis and B. mycoides. Batch experiments under both aerobic and anaerobic conditions showed a high Cr(VI) reducing performance under relatively high initial Cr(VI) concentrations. The reduction rate using this culture was 3 to 8 times higher than reduction rates reported in bacteria previously isolated and studied in North America and Europe. The culture performed best as a consortium with the different species operating cooperatively. The bacteria were acclimated to Cr(VI) toxicity through the long period of contact during the activated sludge treatment process at the source. A Monod like model was used to evaluate the rate of Cr(VI) reduction over a wide range of initial Cr(VI) concentrations. The model revealed that Cr(VI) reduction in the consortium culture followed quasi-first order kinetics with a Cr(VI) inhibitor term as a second exponential: C = C0 . exp [-p . exp (-q . C0 ) . t]. The parameter p and q for the semi-empirical first order model were statistically accurate with R2 values greater than 94% for all data ranges evaluated. Previous studies were not able to pick the variability of Monod coefficients, kmc and Kc, since at narrow ranges of initial Cr(VI) concentrations, the impact of the chromium toxicity variability was insignificant. This study demonstrates the potential of a biological approach using locally isolated Cr(VI) reducing bacteria to decontaminate Cr(VI) polluted sites in South Africa. / Dissertation (MSc)--University of Pretoria, 2009. / Chemical Engineering / unrestricted

The South African government implements numerous strategies with the aim of reducing poverty. The social grant system is one of these. Social grants are aimed at reducing poverty as well as income inequality. Considering the growing number of social grant beneficiaries, people often question whether these grants reduce poverty and, if they do, whether they are effective.This treatise investigates the impact of social grants in poverty reduction. In order to investigate this, the researcher used the Tshwane Metropolitan Municipality, Gauteng Province, as a study area. This study examines the different views of social grants beneficiaries, and the importance of prioritisation when using this unearned money. It alsoinvestigates the role played by the heads of household and shows how beneficiaries’ locations can influence the use of unearned income. Social grants dispense little money, but the researcher discovered that the responsibility of spending and allocating the money lies with the head of household. The descriptive statists show that social grants have created dependency and that families require exit strategies to stop depending entirely on these grants. Findings from the correlation matrix show both positive and negative correlations. Finally, the study has identified the need for an integrated strategy that will not only provide income, but that will also improve the lives of South Africans.

The aim of this thesis is to prove the existence of the Shilov boundary and the minimal boundary with respect to some function algebras and investigate their topological structures. / Science, Faculty of / Mathematics, Department of / Graduate

In the complexity of contemporary society, the welfare of individuals is dependent upon the co-operation of the helping professions and co-ordination of services provided by the many social institutions. This study considered the degree of cooperation between the two helping professions, social work and the ministry, in the suburban community of Richmond, British Columbia. The research method in this qualitative study included interviews with fifteen clergymen and ten social workers in order to apply the concepts of reciprocal awareness and utilization. This method facilitated evaluation of the knowledge one profession had of the other's role and function, and the extent to which this knowledge was used for the benefit of the population they served. Supplementing this main method was a brief historical consideration of the impact of industrialization on the development and contemporary role of the church and social welfare. The findings of the study showed the awareness one profession had of the other was based more on general knowledge than direct interprofessional contact. The utilization of each other's resources, as indicated by referral patterns, was minimal and typically the result of coincidence rather than planning. Reciprocity, the main concept evaluated, was virtually non-existent. This can primarily be accounted for by absence of communication, despite an acknowledgement by both professions, particularly social work, that there were several gains to be realized from more co-operation. / Arts, Faculty of / Social Work, School of / Graduate

Suppose q₁,q₂,…,qn are the generalised coordinates of a mechanical system moving with constraints expressed by r non-integrable equations (r〈n) (1) [equation omitted] where the dots denote differentiation with respect to the time t, and fα are nonlinear in the q’s. The equations (1) are said to represent nonlinear nonholonomic constraints and the system moving with such constraints is called nonlinear nonholonomic. From a purely analytical point of view, the author has obtained the equations of motion for a nonlinear nonholonomic mechanical system in many a different form. The importance of these forms lies in their simplicity and novelty. Some of these forms are deduced from the principle of d'Alembert-Lagrange using the definition of virtual (possible) displacements due to Četaev [ll] . The others are obtained as a result of certain transformations. Moreover, these different forms of equations of motion are written either in terms of the generalised coordinates or in terms of nonlinear nonholonomic coordinates introduced by V.S. Novoselov [23]. These forms involve the energy of acceleration of the system or the kinetic energy or some new functions depending upon the kinetic energy of the system. Two of these new functions, denoted by R (Sec. 2.3) and K (Sec. 2.4), can be identified, to a certain approximation, with the energy of acceleration of the system and the Gaussian constraint, respectively. An alternative proof (Sec.2.5) is given to the fact that, if virtual displacements are defined in the sense of N.G. Četaev [ll], the two fundamental principles of analytical dynamics - the principle of d'Alembert-Lagrange and the principle of least constraint of Gauss -are consistent. If the1 constraints are rheonomic but linear, a generalisation of the classical theorem of Poisson is obtained in terms of quasi-coordinates and the generalised Poisson's brackets introduced by V.V. Dobronravov [17]. The advantage of the various novel forms for the equations of motion is illustrated by solving a few problems. / Science, Faculty of / Mathematics, Department of / Graduate

Techniques from the theory of matrix problems have proven to be helpful for studying problems within representation theory. In particular, matrix problems are well suited to use in problems related to classifying indecomposable representations of quivers and of posets. However, throughout the literature, there are many different types of matrix problems and little clarification of the relationships between them. In this thesis, we choose six types of matrix problems, place them all within a common framework and find correspondences between them. Moreover, we show that their use in the classification of finite-dimensional representations of quivers and posets are, in general, well-founded. Additionally, we investigate a direct relationship between the problem of classifying quiver representations and the problem of classifying poset representations.

In the last decade, global instability has led to higher demands placed on military members and their families, especially in the area of deployment. Longer and more frequent deployments have had significant psychological consequences on soldiers who have been deployed. Deployment has also been shown to negatively impact child adjustment; however, the research in this area is limited, particularly within a Canadian military context. The purpose for the two current studies was to examine specific areas of child adjustment affected by military status, particularly deployment, and to explore potential pathways through which this impact occurs. Study 1 included an examination of the effect of military status on maternal depressive symptoms, parental stress, and marital satisfaction, as well as on the quality of the child's attachment to the parent at home. Further analyses were conducted to determine if maternal well-being mediated the effect of military status on attachment, and if there was a moderating role of social support on these associations. In Study 2, the unique role of military status in predicting reported behaviour problems over and above what was accounted for by child attachment and parental stress was explored. Findings from these studies revealed an association between deployment and higher levels of insecure attachment; and although deployment modestly predicted maternal depressive symptoms, there was no mediating effect found for maternal well-being. Furthermore, while insecure attachment and higher levels of parental stress were associated with elevated behaviour problems, deployment uniquely predicted conduct problems, internalizing problems, and total behaviour problems. Findings from the current studies add a valuable contribution to the limited available literature on how deployment affects young children in military families. Moreover these findings provide a basis in which to direct further research, and to also guide the development and implementation of interventions to support at-risk children in military families.

Although researchers have often focused on the victims of aggression, the detrimental effects of engaging in aggression and/or displaying symptoms of externalizing disorders have been clearly identified in children and adolescents. Longstanding consequences of externalizing problems include internalizing difficulties such as depression. There is an increasing interest in identifying the direction of effect and understand whether externalizing problems precede internalizing problems, vice-versa, or whether they share a bi-directional relation. However, the study of the temporal sequence between aggression, externalizing disorders, and internalizing disorders in children and adolescents has yielded inconsistent findings. The sequential relation between externalizing and internalizing difficulties in children and adolescents was examined in this dissertation consisting of three studies. In Study 1, the moderating role of worry in the relation between aggression and depression was examined. The sample consisted of girls nominated as either relationally or physically aggressive by their peers. Results indicated that worry exacerbated the risk of reporting elevated depressive symptoms concurrently and one year later for physically aggressive girls. In Study 2, three competing hypotheses on the longitudinal relation between aggression and depression were compared. Findings from this study supported the hypothesis that symptoms of depression are preceded by aggressive behaviour. Additionally, it was found that engaging in physical aggression predicted depressive symptoms for girls but not for boys. The results of the first two studies suggest that for girls, engaging in non-normative forms of aggression is associated with greater mental health problems. In Study 3, the temporal relation between symptoms of externalizing disorders, namely oppositional defiant disorder and conduct disorder, and symptoms of depression was examined. Results provided support that the progressive relation between symptoms of externalizing and internalizing disorders was bi-directional. In summary, although it seems that engaging in externalizing behaviour, such as aggression, predicts symptoms of depression, findings from the third study suggest that the sequential relation between symptoms of externalizing problems, which may or may not include aggressive behaviour, and symptoms of depression seem to share a reciprocal relation.