<p>The use of contexts in school mathematics is receiving much attention both nationally and internationally. This as well as the scarcity of research focusing on the topic stimulated me to research the contexts preferred by learners of mathematics. The large-scale project is called the Relevance of School Mathematics Education (ROSME) project. The current study essentially deals with that section of the larger project which investigates the issues and situations that learners in grades eight, nine and ten would prefer to deal with in mathematics. Broadly, this study focuses on the contexts preferred by grade 8, 9 and 10 learners as a domain in which to embed school mathematics.</p>

Genetic transformation techniques for pest insects have enabled the development of novel methods to mitigate the enormous harm done by insects to human health (through transmission of diseases) and to agriculture (through damage to crops or livestock). I use mathematical modelling to analyse strategies using autocidal genetic constructs (dominant lethal genes that are repressible during mass-rearing); in parallel several research groups are developing the strains and the laboratory and field experimental work. Engineered insects would be released in large numbers and compete for mates, and their progeny would inherit one copy of a dominant lethal gene and die. The lethal mechanism can be made stage- or sex-specific. The aim is to reduce the number of pest insects in a population, suppressing numbers to a less harmful level or local elimination. I examine the evolutionary, ecological, and economic cost and benefit aspects of these novel interventions. I consider application of this genetic technology against agricultural pest insects, combined with genetically modified crop plants engineered to produce insecticidal toxins, to which field-evolved resistance is emerging. Using a theoretical framework, I analyse the gene frequency evolution of resistant alleles and show that strategies using genetic constructs that are selectively lethal only to females could help to manage both pests and resistance. I investigate potential resistance to the lethal mechanism of the genetic construct itself. I use population genetics and population dynamics models to explore the impact of heritable biochemically-based resistance on the effectiveness of genetic strategies for reducing populations of important pests in agriculture or public health. Released insects are homozygous for susceptibility to the lethal construct; this has an inherent element of resistance dilution. Finally, I analyse genetic vector control methods to reduce the transmission of human disease. I combine vector population dynamics and epidemiological models with techniques for assessing cost-effectiveness of a genetic strategy for controlling a vector mosquito, and show that disease elimination is feasible on a practical timescale and economically beneficial.

No description available.

A brucelose bovina é uma zoonose que apresenta importância econômica por ocasionar perdas reprodutivas nas espécies animais acometidas. Em 2001, no Brasil, foi criado o Programa Nacional de Controle e Erradicação da Brucelose e da Tuberculose Animal. Uma das principais medidas instituídas pelo programa é a vacinação de fêmeas entre três e oito meses de idade pela cepa B19. Posteriormente, em 2007, ficaram definidas as normas para a utilização da cepa RB51 em fêmeas maiores que oito meses de idade, e em propriedades que apresentem foco da doença. Sabe-se que esta medida, se utilizada, abreviaria o período de tempo necessário para que a redução da prevalência da brucelose bovina fosse atingida. A fim de estimar a magnitude desta redução, bem como aferir o acumulado de animais a serem protegidos para que a diminuição na prevalência ocorra, foi realizado um modelo matemático associando a proteção de 80% das bezerras por B19, à proteção de 10, 40 e 80% das demais fêmeas por RB51. Para as simulações, foram consideradas as Unidades Federativas que apresentam prevalência da brucelose bovina acima de 2%. Comparando os cenários analisados, pôde-se concluir que a redução do período de tempo necessário para que se atingisse 2% de prevalência pouco diferiu quanto à cobertura vacinal de 40 ou 80% das fêmeas vacináveis. Isto faz com que a primeira alternativa possa, economicamente, ser tida como mais interessante, uma vez que abrangeria um acumulado menor de animais protegidos. Considerando o Estado de Goiás, que apresenta prevalência de 3,01% e um efetivo de 8.336.632 fêmeas bovinas, a proteção das fêmeas jovens por B19 juntamente à proteção de 40% das demais por RB51, faria com que a redução da prevalência alcançasse 2% em quatro anos, com um acumulado de 1.302.130 animais protegidos. Em relação ao Estado de Mato Grosso, que apresenta a maior prevalência, 10,25%, e 8.377.433 fêmeas com mais de 24 meses de idade, foi observado que a frequência da brucelose chegaria a 2% em quinze anos caso a proporção de fêmeas protegidas por RB51 fosse 40%, resultando em um acumulado de 1.656.098 animais. Em comparação à utilização da B19 como única medida preventiva, utilizando a RB51 em 40% das fêmeas vacináveis, se reduziria o período de tempo para se atingir 2% de prevalência de sete para quatro anos no Estado de Goiás, e de 22 para 15 anos no Mato Grosso. Além disso, a determinação dos acumulados a serem vacinados permite que se avalie economicamente a viabilidade ao uso da RB51 / Bovine brucellosis is a zoonosis that play important economic role for causing reproductive losses on animal species that are affected. In 2001, in Brazil, Brazilian National Program for the Control and Eradication of Bovine Brucellosis and Tuberculosis was created. One of the main action proposed by the program is vaccination of female between three to eight months of age by B19 strain. Later, in 2007, were defined the roles for RB51 strain use in females older than eight months, and in herds that are in outbreak situation. It is known that this measure, if used, would short the time needed for bovine brucellosis reduction. In order to estimate the magnitude of this reduction, as well as to measure the accumulated of protected animals for brucellosis prevalence decrease, a mathematical model was done associating protection by B19 in 80% of heifers, to protection by RB51 in 10, 40 and 80% of other females. For simulations, states that presented brucellosis prevalence superior than 2% were considered. Comparing these scenarios was possible to conclude that the time needed to reduce prevalence to 2% were similar between 40 and 80%. This turns the former alternative economically more interesting, once it will cover lower number of protected animals. Considering Goiás State, that presents prevalence of 3.01% and a amount of 8336,632 female bovine, protection of 80% of heifers by B19, along protection of 40% of other females by RB51, would make prevalence reach 2% in four years, with a total of 1302,130 protected animals. Relative to Mato Grosso State, that has the major prevalence, 10.25%, and 8377,433 female older than 24 months of age, were observed that brucellosis frequency would reduce to 2% in 15 years in case of 40% of female protected by RB51, resulting in an amount of 1656,098 animals. In comparison with the use of B19 as single preventive measure, time to reduce prevalence to 2% will reduce from seven to four years in Goiás, and from 22 to 15 years in Mato Grosso. Moreover, determination of accumulated of protected animals allows that RB51 use would be economically evaluated

The MAPK pathway plays a crucial role in regulating cellular response to external stimuli. Binding of growth factors and other mitogenic signals to cell surface receptors initiates a phosphorylation-dependent relay of protein activation, resulting in altered transcription, ultimately regulating cell proliferation and differentiation. Signalling through this pathway is regulated by the coordinated function of specific protein kinases and protein phosphatases. As perturbation of this signalling system is often associated with diseases such as cancer, modelling is a useful means to help understand the outcomes that may result following changes in component levels or activity. The determination of absolute quantification data, in copies per cell, for proteins of the MAPK pathway will allow the expansion of and improved accuracy within predictive models. The strategy used within this thesis is based on the established technique of stable isotope dilution, generating isotopically labelled peptides using the QconCAT methodology. Recombinant DNA techniques were used to generate artificial concatamers of large numbers of tryptic peptides as quantification standards. A QconCAT, LM1, of 49 KDa (29 tryptic peptides), corresponding to the scaffold proteins was designed and built to encode two peptides per protein. A second QconCAT, LM2, of 58 KDa (34 tryptic peptides), encoded peptides from the dual-specificity phosphatases (DUSPs) and substrates. Quantification was performed using ultra performance liquid chromatography coupled to mass spectrometry. A selected reaction monitoring (SRM) approach was employed where the most intense y-ions per peptide were selected either from experimental data or predictions in silico. Using the ratio of the signal for the light:heavy isotopologues, the amount of light isotopologue can be inferred, allowing copies per cell quantifications to be established. Native peptides were present below the lower limit of quantification, and therefore the upper bounds of copies per cell were obtained for the three cell lines; colon cancer cells HCT 116 (K-Ras mutant) and HT-29 (B-Raf mutant) and a control cell line of HEK-293. Finally, mathematical modelling was undertaken to explore the mass-action kinetics of a three component scaffold signalling molecule. It was found that the optimal scaffold concentration is between the lowest and second lowest concentration of signalling protein.

In this thesis we study a novel type of hydropower generation which uses a Venturi contraction to amplify the pressure drop across a turbine, allow- ing for cost-effective hydropower generation in situations where the head drop is small, such as in rivers and weirs. The efficiency is sensitive to how the secondary flow, which passes through the turbine, mixes with the accelerated primary flow, which is diverted around the turbine, within the confines of a closed geometry. In particular, it is important to understand the behaviour of the turbulent shear layers between the primary and sec- ondary flows, which grow downstream, mixing the flows together. The behaviour of the shear layers in the expanding part of the Venturi con- traction is strongly dependent on the shape of the channel. An important consequence of the channel shape, and hence the flow behaviour, is the degree of pressure amplification across the turbine, which determines the amount of generated power. We focus on mathematically modelling the mixing of the flows in turbu- lent shear layers, and we investigate two different ways to increase pres- sure amplification: optimising the shape of the channel, and using swirl to enhance mixing. The channel shape optimisation reveals an interest- ing balance between the effects of mixing and wall drag. Wide channel expansion tends to accentuate non-uniform flow, causing poor pressure amplification, whilst shallow expansion creates enhanced wall drag, which is also detrimental to pressure amplification. We show how the maximum power is generated with a channel shape that strikes a balance between these two effects. We find that swirl enhances mixing by increasing shear layer growth rates, but it produces large pressure losses in doing so, and for large amounts of swirl a slowly recirculating region can form along the channel centreline. Whilst swirl does not improve efficiency, there may be some inevitable swirl present in the flow, and we show how this affects the optimum channel shape. We also establish the criteria for the existence of such a recirculation region so that it may be avoided.

In this thesis we derive mathematical models for the glass sheet redraw process for the production of very thin glass sheets. In the redraw process, a prefabricated glass block is fed into a furnace, where it is heated and stretched by the application of draw rollers to reduce its thickness. Redrawn sheets may be used in various applications including smartphone and battery technology. Our aims are to investigate the factors determining the final thickness profile of a glass sheet produced by this process, as well as the growth of out-of-plane deformations in the sheet during redraw. Our method is to model the glass sheet using Navier–Stokes equations and free-surface conditions, and exploit small aspect ratios in the sheet to simplify and solve these equations using asymptotic expansions. We first consider a simple two-dimensional sheet to determine which physical effects should be taken into account in modelling the redraw process. Next, we derive a mathematical model for redraw of a thin threedimensional sheet. We consider the limits in which the heater zone is either short or long compared with the sheet half-width. The resulting reduced models predict the thickness profile of the redrawn sheet and the initial shape required to redraw a product of uniform thickness. We then derive mathematical models for buckling of thin viscous sheets during redraw. For buckling of a two-dimensional glass sheet due to gravity-induced compression, we predict the evolution of the centreline and investigate the early- and late-time behaviour of the system. For a three-dimensional glass sheet undergoing redraw, we use numerical solutions to investigate the behaviour of the sheet mid-surface.

Wet age related macular degeneration (wet AMD) is a highly debilitating retinal disease, the third leading cause of blindness in the world and one the most expensive ocular conditions to care for. Wet AMD is characterised by the proliferation of neovasculature through the retinal posterior and theorised to be, at least in part, induced and driven by excess vascular endothelial growth factor (VEGF). Many current treatments for wet AMD utilise anti-VEGF macromolecules that bind to VEGF. The retina, however, remains a largely inaccessible, and delicate, anatomical region. Due to difficulties in collecting clinical and experimental data, mathematical modelling is playing an increasingly prominent role in understanding the distribution (Pharmacokinetics, PK) and drug-to-target interactions (Pharmacodynamics, PD) for treatments of wet AMD. This thesis will focus on ordinary/partial differential equation (ODE/PDE) models for the PK/PD of anti-VEGF therapeutics, administered via intravitreal (IVT) injection into the mammalian eye. We start in Chapter 2 with a 2-compartment PK/PD ODE model of drug-VEGF interactions in the eye, analysing a clinical dataset to estimate key binding parameters between VEGF and the typical anti-VEGF molecule, ranibizumab. In Chapter 3, we extend the PK ODE framework of the 2-compartment model to include a mechanistic description of the retina, to estimate retinal permeability to macromolecules used for treating wet AMD. In Chapter 4, using the retinal PK model, we reintroduce VEGF to predict concentrations of free VEGF in the retina post-IVT injection. Chapters 5 and 6 model a hypothetical class of anti-VEGF molecules designed to bind not only VEGF but also existing vitreal superstructures, analysing how dose and binding kinetics impact ocular retention. Alongside these models we present analogous PDE models, addressing whether the assumption that concentrations are homogeneous across anatomical regions, as implicit in ODE models, is appropriate for macromolecular PK/PD in the mammalian eye.

A brucelose bovina é uma zoonose que apresenta importância econômica por ocasionar perdas reprodutivas nas espécies animais acometidas. Em 2001, no Brasil, foi criado o Programa Nacional de Controle e Erradicação da Brucelose e da Tuberculose Animal. Uma das principais medidas instituídas pelo programa é a vacinação de fêmeas entre três e oito meses de idade pela cepa B19. Posteriormente, em 2007, ficaram definidas as normas para a utilização da cepa RB51 em fêmeas maiores que oito meses de idade, e em propriedades que apresentem foco da doença. Sabe-se que esta medida, se utilizada, abreviaria o período de tempo necessário para que a redução da prevalência da brucelose bovina fosse atingida. A fim de estimar a magnitude desta redução, bem como aferir o acumulado de animais a serem protegidos para que a diminuição na prevalência ocorra, foi realizado um modelo matemático associando a proteção de 80% das bezerras por B19, à proteção de 10, 40 e 80% das demais fêmeas por RB51. Para as simulações, foram consideradas as Unidades Federativas que apresentam prevalência da brucelose bovina acima de 2%. Comparando os cenários analisados, pôde-se concluir que a redução do período de tempo necessário para que se atingisse 2% de prevalência pouco diferiu quanto à cobertura vacinal de 40 ou 80% das fêmeas vacináveis. Isto faz com que a primeira alternativa possa, economicamente, ser tida como mais interessante, uma vez que abrangeria um acumulado menor de animais protegidos. Considerando o Estado de Goiás, que apresenta prevalência de 3,01% e um efetivo de 8.336.632 fêmeas bovinas, a proteção das fêmeas jovens por B19 juntamente à proteção de 40% das demais por RB51, faria com que a redução da prevalência alcançasse 2% em quatro anos, com um acumulado de 1.302.130 animais protegidos. Em relação ao Estado de Mato Grosso, que apresenta a maior prevalência, 10,25%, e 8.377.433 fêmeas com mais de 24 meses de idade, foi observado que a frequência da brucelose chegaria a 2% em quinze anos caso a proporção de fêmeas protegidas por RB51 fosse 40%, resultando em um acumulado de 1.656.098 animais. Em comparação à utilização da B19 como única medida preventiva, utilizando a RB51 em 40% das fêmeas vacináveis, se reduziria o período de tempo para se atingir 2% de prevalência de sete para quatro anos no Estado de Goiás, e de 22 para 15 anos no Mato Grosso. Além disso, a determinação dos acumulados a serem vacinados permite que se avalie economicamente a viabilidade ao uso da RB51 / Bovine brucellosis is a zoonosis that play important economic role for causing reproductive losses on animal species that are affected. In 2001, in Brazil, Brazilian National Program for the Control and Eradication of Bovine Brucellosis and Tuberculosis was created. One of the main action proposed by the program is vaccination of female between three to eight months of age by B19 strain. Later, in 2007, were defined the roles for RB51 strain use in females older than eight months, and in herds that are in outbreak situation. It is known that this measure, if used, would short the time needed for bovine brucellosis reduction. In order to estimate the magnitude of this reduction, as well as to measure the accumulated of protected animals for brucellosis prevalence decrease, a mathematical model was done associating protection by B19 in 80% of heifers, to protection by RB51 in 10, 40 and 80% of other females. For simulations, states that presented brucellosis prevalence superior than 2% were considered. Comparing these scenarios was possible to conclude that the time needed to reduce prevalence to 2% were similar between 40 and 80%. This turns the former alternative economically more interesting, once it will cover lower number of protected animals. Considering Goiás State, that presents prevalence of 3.01% and a amount of 8336,632 female bovine, protection of 80% of heifers by B19, along protection of 40% of other females by RB51, would make prevalence reach 2% in four years, with a total of 1302,130 protected animals. Relative to Mato Grosso State, that has the major prevalence, 10.25%, and 8377,433 female older than 24 months of age, were observed that brucellosis frequency would reduce to 2% in 15 years in case of 40% of female protected by RB51, resulting in an amount of 1656,098 animals. In comparison with the use of B19 as single preventive measure, time to reduce prevalence to 2% will reduce from seven to four years in Goiás, and from 22 to 15 years in Mato Grosso. Moreover, determination of accumulated of protected animals allows that RB51 use would be economically evaluated

This thesis is concerned with the mathematical modelling for human immunodeficiency virus (HIV) and hepatitis C virus (HCV) epidemics in Australia. There are two parts to this thesis. Part I is aimed at modelling the transmission of HIV and HCV via needle sharing among injecting drug users (IDUs). The dynamical model of an epidemic through needle sharing among IDUs is derived. This model reveals the correlation between needle sharing and the epidemic prevalence among IDUs. The simulations of HIV and HCV prevalence and incidence among IDUs in Australia are made with this model. The comparison of simulated results with literature estimates shows that the modelled results are consistent with the literature estimates. The effects of needle sharing and cleaning on HIV and HCV prevalence and incidence among IDUs in Australia are evaluated. Part II is devoted to modelling the spread of HIV in the general community in Australia. A mathematical model is formulated to assess the epidemiological consequences of injecting drug use and sexual transmission in Australia. The effects of highly active antiretroviral therapies (HAART) on the HIV epidemic are included. The modelled results are in broad agreement with the literature estimates and observed data. The long-term effects of HAART are also discussed.