School of Mathematics and Statistics Vacation Scholarships

Mathematical & Computational Biology

Mathematical modelling of immune cell behaviour
(posted for 2017-2018)

Supervisors: Dr Jennifer Flegg, Professor Phil Hodgkin (WEHI)

T cells are important for launching specific immune responses against invading microbes, as well as eliminating some cancer cells. Errors in the control of T cells can lead to harmful ‘autoimmune’ responses that attack the body’s own tissues, the underlying cause of diseases including type 1 diabetes and rheumatoid arthritis.

The aim of this project is to combine laboratory data with mathematical models to clarify how different external signals impact on T cell proliferation and to understand how complex signalling impacts the size of the response by key infection-fighting immune cells called T cells. Such models can provide particular insights into how immune responses might be manipulated to improve health (1). Data is available from Professor Hodgkin’s laboratory at the Walter and Eliza Hall Institute. The mathematics of the project would involve modelling with ordinary differential equations and parameter estimation with statistical inference.

(1) Marchingo, Julia M and Kan, Andrey and Sutherland, Robyn M and Duffy, Ken R and Wellard, Cameron J and Belz, Gabrielle T and Lew, Andrew M and Dowling, Mark R and Heinzel, Susanne and Hodgkin, Philip D (2014) Antigen affinity, costimulation, and cytokine inputs sum linearly to amplify T cell expansion. Science, 346(6213):1123-1127.

Contact Jennifer Flegg

The population history of indigenous Australians: what can the available genetic data tell us?
(posted for 2017-2018)

Supervisors: Professor David Balding, Dr Jennifer Flegg and Dr Ashley Farlow
Centre for Systems Genomics, University of Melbourne
School of Mathematics and Statistics, University of Melbourne

In recent months 3 major papers have appeared making strong claims about the population history of indigenous Australians from genetic data: two appeared in Nature. One of them used autosomal DNA, the others relying on only the mitochondrial DNA. The claims from these papers appear to conflict with each other, and many appear to be too precise to be adequately supported from genetic data alone. Much of the data from these papers is available to other researchers, and other data genetic resources are available for indigenous Australians and New Guineans. Broadly speaking, the thinking behind this project is that more careful statistical inferences may be able to resolve some of the differences among these authors, and to distinguish claims that are strongly supported from those that are more speculative. There is a range of publicly available software for demographic inference from genetic data. We will investigate these and choose the most useful to examine the support for alternative population histories. In particular we will consider the use of simulation-based approximate Bayesian computation, for which generic software is already available but many parameter settings will require careful assessment.

The project will require some familiarity with statistical methods for genetic data, and the student should have enough computing expertise to be confident downloading and exploring scientific software developed by other groups.


Malaspinas et al (2016) A genomic history of Aboriginal Australia, Nature 538, 207-14, 13 October 2016, doi:10.1038/nature18299

Nagle et al (2017) Mitochondrial DNA diversity of present-day Aboriginal Australians and implications for human evolution in Oceania, Journal of Human Genetics 62, 343-353 (March 2017) | doi:10.1038/jhg.2016.147

Tobler et al (2017) Aboriginal mitogenomes reveal 50,000 years of regionalism in Australia, Nature doi:10.1038/nature21416

Contact Professor David Balding

Modelling the spread of malaria and antimalarial drug resistance
(posted for 2017-2018)

Malaria elimination will only be possible by appropriate treatment. However, the drugs used against malaria are only effective in locations where resistance to the drugs has yet to spread. Mathematical modelling of the spread of malaria and resistance to the drugs used to treat the disease will allow insight into the biological mechanisms involved.

The aim of this project is to use an existing model and software (1) to simulate the spread of malaria through a population and the subsequent emergence of drug resistance, with the aim to identify public health interventions that are most effective.

(1) IDM Malaria Model (

Contact Jennifer Flegg

Modelling within-host pathogen dynamics
(posted for 2017-2018)

Projects focusing on varied aspects of the host-pathogen interaction are available, on diseases such as influenza and malaria. Mathematical techniques required are varied but include: deterministic and stochastic modelling, dynamical systems analyses including numerical bifurcation studies and biostatistical studies, including Bayesian hierarchical modelling of dynamic non-linear systems. Biological topics for investigation include: the role of innate and adaptive immunity in controlling infection, the role of drugs in controlling infection and the development of drug resistance, and evolutionary aspects of infection including genetic drift and selection.

Contact James McCaw

Mathematical epidemiology and infectious diseases modelling
(posted for 2017-2018)

Description: Projects are available on the development, analysis and application of models of infectious disease transmission in human populations. Both theoretically focussed projects and applied public health projects are available. Diseases of interest include influenza, malaria, emerging and re-emerging diseases such as Ebola and vaccine preventable diseases such as pertussis.

Contact James McCaw

For more information on this research group see:
Mathematical & Computational Biology
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