On the design and implementation of a hybrid numerical method for singularly perturbed two-point boundary value problems

>Magister Scientiae - MScWith the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these solvers are tailor-made for specific classes of problems. Therefore, more of such must be developed to accompany the growing need for mathematical models that help in the understanding of the contemporary world. This thesis treats two point boundary value singularly perturbed problems. The solution to this type of problem undergoes steep changes in narrow regions (called boundary or internal layer regions) thus rendering the classical numerical procedures inappropriate. To this end, robust numerical methods such as finite difference methods, in particular fitted mesh and fitted operator methods have extensively been used. While the former consists of transforming the continuous problem into a discrete one on a non-uniform mesh, the latter involves a special discretisation of the problem on a uniform mesh and are known to be more accurate. Both classes of methods are suitably designed to accommodate the rapid change(s) in the solution. Quite often, finite difference methods on piece-wise uniform meshes (of Shishkin-type) are adopted. However, methods based on such non-uniform meshes, though layer-resolving, are not easily extendable to higher dimensions. This work aims at investigating the possibility of capitalising on the advantages of both fitted mesh and fitted operator methods. Theoretical results are confirmed by extensive numerical simulations

Adjustable loop ACL suspension devices demonstrate less reliability in terms of reproducibility and irreversible displacement.

PURPOSE The aim of this study was to perform a comprehensive biomechanical examination of frequently applied femoral cortical suspension devices, comparing the properties of both fixed and adjustable fixation mechanisms. It was hypothesized that adjustable loop devices demonstrate less consistent fixation properties with increased variability compared to fixed loop devices. METHODS Nine frequently applied fixation button types were tested, six adjustable and three rigid loop devices. Six samples of each device type were purchased. Each device was installed in a servo-hydraulic mechanical testing machine, running a 2000 cycle loading protocol at force increments between 50 and 500 N. Irreversible displacement in mm was measured for all of the tested samples of each implant. Ultimately, maximum load to failure was applied and measured in Nm. An irreversible displacement of 3 mm was considered failure of the implant. RESULTS Three of the six adjustable devices (GraftMax™, TightRope® ToggleLoc™) demonstrated a median displacement above the threshold of clinical failure before completion of the cycles. All adjustable loop devices showed a wide intragroup variation in terms of irreversible displacement, compared to fixed-loop devices. Fixed-loop devices provided consistent reproducible results with narrow ranges and significantly lower irreversible displacement (p < 0.05), the maximum being 1.4 mm. All devices withstood an ultimate force of more than 500 N. CONCLUSION Adjustable loop devices still show biomechanical inferiority and demonstrate heterogeneity of fixation properties with wide- and less-reproducible displacement ranges resultant to the mechanism of adjustment, denoting less reliability. However, three adjustable devices (RIGIDLOOP™ Adjustable, Ultrabutton ◊, ProCinch™) demonstrate fixation capacities within the margins of clinical acceptance. RIGIDLOOP™ Adjustable provides the most comparable fixation properties to fixed loop devices

Using a Programme Science approach to substantially reduce the risk of HIV transmission and acquisition in sex transactions among female sex workers in Zimbabwe

Introduction: We used a Programme Science platform, to generate evidence to support the implementation of programmes for sex workers in Africa. Female sex workers are estimated to make up 1.6% (1.3%–1.8%) of the population of women aged 15−49 years in Zimbabwe. We highlight how programme science can be used to help distinguish between when, where and with whom programmes need to be implemented and discuss two case studies that exemplify implementing better (Case study 1 (1 June 2019−30 June 2021) Optimizing implementation of a risk differentiated microplanning intervention) and implementing differently (Case study 2 (1 October 2016−30 September 2022) Reorientating implementation of DREAMS for young women selling sex). Methods: Zimbabwe's nationally scaled programme for sex workers was established in 2009 in partnership with sex workers to provide comprehensive services for sex workers and generate evidence for programme design, implementation and scale up. Since inception, comprehensive data have been collected from all sex workers seeking services. As the scope of service provision has expanded so has the scope of data collection and analysis. At enrolment, sex workers are assigned an alphanumeric unique identifier which links consultations within and across programme sites. We conduct descriptive analyses of the Key Population (KP) programme data to guide programme implementation and redesign, embedding programmatic qualitative enquiry as required. Results: Two case studies describing different approaches to programme optimization are presented. In the first, an optimization exercise was used to strengthen programme implementation ensuring that the KP programme got back on track after SARS‐COV‐2. In the second, an in‐depth review of research and programme data led to a re‐orientation of the DREAMS programme to ensure that young women at the highest risk of HIV acquisition were enrolled and had access to DREAMS social support interventions in turn strengthening their uptake of HIV prevention. Conclusions: Optimizing and sustaining HIV care and treatment programmes requires effective delivery with sufficient scale and intensity for population impact. Our programme science approach guided the scale up of the KP programme in Zimbabwe, providing evidence to support strategy, implementation and ongoing management, and importantly helping us distinguish between when we needed to just implement, implement better or implement differently