Mathematical modelling can provide vital information on the effectiveness and practical implementation of microbicides and vaccines against HIV. This project will produce mathematical models of the earliest stages of HIV infection suitable for investigation of the implementation of vaccines and microbicides. It will provide a framework to investigate why these interventions have performed poorly to date, and how these may be better implemented.
Discovery Early Career Researcher Award - Grant ID: DE140100741
Funder
Australian Research Council
Funding Amount
$389,564.00
Summary
Analysis of defect driven pattern formation in mathematical models. . Defects, or heterogeneities, are common in nature and technology and therefore in mathematical models. This project will underpin the effects a defect can have on the dynamics of a model, characterise the new patterns created by a heterogeneity and see how the dynamics can be controlled by manipulating the heterogeneity. Moreover, these new insights will be applied to a model for skin cancer, resulting in a more appropriate mo ....Analysis of defect driven pattern formation in mathematical models. . Defects, or heterogeneities, are common in nature and technology and therefore in mathematical models. This project will underpin the effects a defect can have on the dynamics of a model, characterise the new patterns created by a heterogeneity and see how the dynamics can be controlled by manipulating the heterogeneity. Moreover, these new insights will be applied to a model for skin cancer, resulting in a more appropriate model and a mathematically justifiable analysis of a very important scientific problem.Read moreRead less
Classification of Microarray Gene-Expression Data. The broad aim is to provide statistical methodology for the classification of microarray gene-expression data. Microarrays are part of a new biotechnology that allows the monitoring of expression levels for thousands of genes simultaneously. The explosion in microarrays has produced massive quantities of data that require new statistical techniques for analysis in order to exploit their enormous scientific potential. One of the main uses of ....Classification of Microarray Gene-Expression Data. The broad aim is to provide statistical methodology for the classification of microarray gene-expression data. Microarrays are part of a new biotechnology that allows the monitoring of expression levels for thousands of genes simultaneously. The explosion in microarrays has produced massive quantities of data that require new statistical techniques for analysis in order to exploit their enormous scientific potential. One of the main uses of the methodology to be developed is to expedite the discovery of new subclasses of diseases. Another is to provide prediction rules for the diagnosis and treatment of diseases.Read moreRead less
Nonlinear Time Series Analysis in Cardiac Physiology. We will develop innovative mathematically-based diagnostics with potentially significant savings in mortality and quality of life for affected individuals and health care costs to the community.
Cardiac diseases kill more Australians than any other disease group. According to the National Heart Foundation the prevalence to heart conditions increased by 18% over the last decade.
Medical practitioners are in need of reliable diagnostic too ....Nonlinear Time Series Analysis in Cardiac Physiology. We will develop innovative mathematically-based diagnostics with potentially significant savings in mortality and quality of life for affected individuals and health care costs to the community.
Cardiac diseases kill more Australians than any other disease group. According to the National Heart Foundation the prevalence to heart conditions increased by 18% over the last decade.
Medical practitioners are in need of reliable diagnostic tools to decide whether a person in front of them is at high risk from developing sudden cardiac death, and whether they should be fitted with an implant that could save their life.Read moreRead less
Mathematical modelling unravels the impact of social dynamics on evolution. This project aims to mathematically model human evolution as a dynamical process. The anticipated goal is to quantitatively analyse theories of human origins. The project expects to develop innovative mathematical models, improve our understanding of the evolutionary process, and advance a unique area of interdisciplinary collaboration: applied mathematics and anthropology. Expected outcomes include refined methods fo ....Mathematical modelling unravels the impact of social dynamics on evolution. This project aims to mathematically model human evolution as a dynamical process. The anticipated goal is to quantitatively analyse theories of human origins. The project expects to develop innovative mathematical models, improve our understanding of the evolutionary process, and advance a unique area of interdisciplinary collaboration: applied mathematics and anthropology. Expected outcomes include refined methods for mathematical modelling of human evolution and improved techniques for analysing such models. It should provide benefits, such as increasing research in mathematical biology, an important growth area of science in Australia, and advancing mathematical approaches to engaging questions arising from anthropology.Read moreRead less
Dynamical systems theory and mathematical modelling of viral infections. This project aims to use mathematical modelling to elucidate the emergence of complex, population-level behaviour from local interactions. In particular, the project will study the self-organising dynamics of the immune response. The project expects to develop new mathematical models of self-organisation, advance links between computational agent-based modelling and dynamical systems modelling, and build new tools for mat ....Dynamical systems theory and mathematical modelling of viral infections. This project aims to use mathematical modelling to elucidate the emergence of complex, population-level behaviour from local interactions. In particular, the project will study the self-organising dynamics of the immune response. The project expects to develop new mathematical models of self-organisation, advance links between computational agent-based modelling and dynamical systems modelling, and build new tools for mathematically analysing complex biological systems. Expected outcomes include strengthened collaborations within Australia and with South Korea. Expected benefits include joint research funding with Korean institutions, increased international visibility, and expanded scope for high school and community outreach.Read moreRead less
Mathematical measurement and modelling of neuronal degeneration. Currently about 150,000 Australian's suffer from cognitive impairment due to Alzheimer's disease or dementia and this number is expected to double over the next few decades. By combining newly developed mathematical methods in complex systems with sophisticated neural imaging we will develop new techniques to advance the diagnosis and treatment of cognitive decline in normal ageing and neurodegenerative disease.
This project will ....Mathematical measurement and modelling of neuronal degeneration. Currently about 150,000 Australian's suffer from cognitive impairment due to Alzheimer's disease or dementia and this number is expected to double over the next few decades. By combining newly developed mathematical methods in complex systems with sophisticated neural imaging we will develop new techniques to advance the diagnosis and treatment of cognitive decline in normal ageing and neurodegenerative disease.
This project will also maintain the collaborative link between researchers in Biomathematics at Mount Sinai School of Medicine, New York and researchers in Applied Mathematics at UNSW that enables training of Australian scientists in the vital area of mathematical bio-complexity.Read moreRead less
A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
A geometric theory for travelling waves in advection-reaction-diffusion models. Cell migration patterns often develop distinct sharp interfaces between identifiably different cell populations within a tissue. This research will develop new geometric methods for the mathematical analysis of cell migration models, and will design diagnostic tools to identify key parameters that cause and control these patterns and interfaces.
New mathematics to improve understanding of anomalously diffusing reactions. Standard mathematical models for particles that diffuse and react are based on assumptions that improving technologies have revealed do not always hold. This project aims to create a mathematical framework that generalises existing approaches, taking into account observations of complicated transport behaviour at many scales, and including the impact of this anomalous transport on reactions. The development of the fram ....New mathematics to improve understanding of anomalously diffusing reactions. Standard mathematical models for particles that diffuse and react are based on assumptions that improving technologies have revealed do not always hold. This project aims to create a mathematical framework that generalises existing approaches, taking into account observations of complicated transport behaviour at many scales, and including the impact of this anomalous transport on reactions. The development of the framework will involve innovative approaches utilising mathematical techniques, including dynamical systems, fractional calculus, and stochastic processes. This project aims to deliver new mathematical models that can be adopted in applications across different discipline areas, and especially in biological systems. Read moreRead less