Student topics

In this research project, you will develop a mathematical model, known as an agent-based model, to capture the development of a brain cancer in a patient. The model will then be matched to clinical samples from patients and used to make predictions around treatment efficacy.

Study level

Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Information about the state of the environment can be critical for promoting environmentally friendly and socially beneficial behaviors when people are facing social dilemma choices. However, it is not clear if individuals will be willing to spread this information for the benefit of everyone else. This project aims to understand how socially beneficial actions propagate when information is asymmetric.

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Stochastic simulation-based models are very attractive to study population-biology, disease transmission, development and disease. These models naturally incorporate randomness in a way that is consistent with experimental measurements that describe natural phenomena.Standard statistical techniques are not directly compatible with data produced by simulation-based stochastic models since the model likelihood function is unavailable. Progress can be made, however, by introducing an auxiliary likelihood function can be formulated, and this auxiliary likelihood function can be used for identifiability analysis, parameter estimation and …

Study level

PhD, Master of Philosophy

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Reaction-diffusion waves describe the progression in space of wildfires, species invasions, epidemic spread, and biological tissue growth. When diffusion is linear, these waves are known to advance at a rate that strongly depends on the curvature of the wave fronts. How nonlinear diffusion affects the curvature dependence of the progression rate of these wavefronts remains unknown.

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Biomedical Technologies

Bone is a dynamic tissue that optimises its shape to the mechanical loads that it carries. Bone mass is accrued where loads are high, and reduced where loads are low. This adaptation of bone tissue to mechanical loads is well-known and observed in many instances. However, what serves as a reference mechanical state in this shape optimisation remains largely unknown.

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Biomedical Technologies

Cancer is an extremely heterogeneous disease, particularly at the cellular level. Cells within a single cancerous tumour undergo vastly different rates of proliferation based on their location and specific genetic mutations. Capturing this stochasticity in cell behaviour and its effect on tumour growth is challenging with a deterministic system, e.g. ordinary differential equations, however, is possible with an agent-based model (ABM). In an ABM, cells are modelled as individual agents that have a probability of proliferation and movement in each …

Study level

Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

High fidelity mathematical models of biological phenomena are often complex and can require long computational runtimes which can make computational inference for parameter estimation intractable.  In this project we will overcome this challenge by working with computationally simple low fidelity models and build a simple statistical model of the discrepancy between the high and low fidelity models.  This approach provides the best of both worlds: we obtain high accuracy predictions using a computationally cheap model surrogate.

Study level

PhD, Master of Philosophy

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Branching processes are stochastic mathematical models used to study a range of biological processes, including tissue growth and disease transmission.This project will implement a simple stochastic branching process to generate simulations of biological growth, and then consider differential equation-based description of the stochastic model.Using computation we will compare the two models, and use phase plane and perturbation analysis to analyze the resulting traveling wave solutions.

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Ecosystems respond to gradual change in unexpected ways. Feedback processes between different parts of an environment can perpetuate ecosystem collapse, leading to potentially irreversible biodiversity loss. However, it is unclear if greater knowledge of feedbacks will ultimately change environmental decisions.The project aims to identify when feedbacks matter for environmental decisions, by generating new methods that predict the economic benefit of knowing more about feedbacks. Combining ecological modelling and value-of-information theory, the outcomes of these novel methods will provide significant and …

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science
Centre for the Environment

This project seeks to explore the complex dynamics that might arise from multiple interacting feedbacks in marine ecosystems, by designing ordinary and/or partial differential equation models of these feedbacks and analysing the steady states and/or temporal dynamics of the proposed model(s).It has been hypothesised that many social and ecological systems exhibit alternative stable states due to feedback processes that keep the ecosystem in one state or the other. The result can be tipping points, which are difficult to predict but …

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science
Centre for the Environment

Mathematical models of particle transport are fundamental to many applied disciplines including physics, biology, ecology and medicine. Particle transport is typically modelled using either a stochastic model, where probability rules govern the motion of individual particles, or a continuum model, where partial differential equations govern the concentration of particles in space and time. This project aims to use analytical and numerical techniques from applied and computational mathematics to address one or both of the following questions:what is the average time …

Study level

Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Various spatial patterns naturally emerge in ecology.  These include stripes, spots, hexagons, and donuts, to name just a few. However, it can be puzzling to figure out how these patterns form.Systems of partial differential equation models can be used to simulate these patterns, and thereby provide ecologists with testable hypotheses for how these patterns formed.

Study level

Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science
Centre for the Environment