Listed on this page are current research projects being offered for the Vacation Scholarship Program.
For more information on this research group see: Mathematical Biology The list of project is under construction.
Mathematical modelling in biology
Various projects are available in mathematical biology, including mathematical modelling of wound healing, tumour growth and infectious disease dynamics. Methods used will be dynamical modelling, Bayesian inference and/or differential equations.
Contact: Jennifer Flegg jennifer.flegg@unimelb.edu.au
Identifying diversity in cell division
Biological systems are highly heterogeneous, with even genetically identical cells exhibiting variability in features such as their division rate. One challenge is determining whether these differences reflect real biological variation or are simply due to stochasticity in division or measurement uncertainty. This project will extend tools from the field of identifiability analysis to study these probability distributions that describe the timings of cellular events.
Contact: Alex Browning alex.browning@unimelb.edu.au
How many genes should be used for Gene Ontology analysis?
Gene Ontology analysis is widely used in bioinformatics to interpret lists of genes by identifying biological processes that are over-represented. For example, after comparing two biological conditions, researchers may take a list of differentially expressed genes and ask whether the list is enriched for terms such as immune response, cell cycle or metabolism.
A key practical question is how many genes should be included in the analysis. In many studies, this choice is made arbitrarily, such as using the top 50. However, the number of selected genes can strongly affect the resulting Gene Ontology terms and therefore the biological interpretation.
This project will explore how Gene Ontology results change as the number of selected genes varies. The student will use public gene-expression data, generate ranked gene lists, run enrichment analyses across a range of gene-list sizes, and compare the stability, specificity and interpretability of the resulting GO terms. The aim is to develop practical guidance for choosing gene-list sizes in exploratory bioinformatics analyses.
Contact: Jiadong Mao jiadong.mao@unimelb.edu.au
Here is the 2025-2026 list of research Projects.
Distinguishing heterogeneity from model misspecification
Deterministic mathematical models are widely applied to describe phenomena throughout the natural sciences and beyond. Allowing model parameters to vary according to probability distributions enables deterministic models to capture the sometimes significant variability between individuals. Given a specific mathematical model, it is, in many cases, possible to infer these individual-level distributions from population-level data. Many models are, however, likely to be misspecified (i.e., not an accurate representation of reality) to some extent. This project will explore whether it is ever possible to distinguish variability between individuals from model misspecification. Depending on student interests, this project can involve either or both of analytical work (based on calculus, analysis, and Taylor series expansions) or computational work.
Contact: Alexander Browning alex.browning@unimelb.edu.au and Adriana Zanca adriana.zanca@unimelb.edu.au
Multiscale modelling in biology
Many biological processes evolve over multiple scales, from molecular interactions within a cell to the dynamics of entire populations. Modelling such systems, and calibrating these models to data, is an open challenge. Various projects are available in this area that will use stochastic dynamical modelling, Bayesian inference and machine learning methods.
Contact: Tom Kimpson tom.kimpson@unimelb.edu.au and Jennifer Flegg jennifer.flegg@unimelb.edu.au
Multicellular Systems Biology
My research is on the interface between applied mathematics numerical methods scientific computing and biology. We use theoretical tools to try to get a better understanding of organ and tissue development and disease.
Due to recent increases in the amount and quality of cell level imaging data, and matching advances in computational power, multicellular modelling has become ever more popular. Multicellular modelling considers cells as discrete entities and represents their interactions using mathematical formalisms, both stochastic and mechanics based. This allows tissues to be simulated, with tissue level behaviour and properties being emergent rather than imposed.
Various projects are available focusing on modelling and on numerical methods. See my website for examples of my work.
Contact: James Osborne jmosborne@unimelb.edu.au
Go with the flow: mathematically modelling hormonal fluctuations throughout the menstrual cycle
No one menstrual cycle looks exactly like another. How a person experiences their period is influenced by how their hormones fluctuate throughout the menstrual cycle. Understanding a person’s unique menstrual cycle is crucial to monitoring health outcomes and assessing the efficacy of hormonal contraception at an individual level.
Previous mathematical studies of the menstrual cycle have often neglected the individual experience. This project aims to explore how we can model the hormonal fluctuations throughout a menstrual cycle, and how these fluctuations are impacted by individual menstrual cycle characteristics.
Contact: Adriana Zanca adriana.zanca@unimelb.edu.au, James Osborne jmosborne@unimelb.edu.au, and Isobel Abell isobel.abell@unimelb.edu.au