# Mathematical Biology

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

## Modelling the spread of malaria and antimalarial drug resistance

(Posted for 2018/2019)

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 have 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.

A project focusing on mathematical modelling of malaria and the emergence/spread of drug resistance is available. The aim of the project will be 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.

**Contacts: **Jennifer Flegg jennifer.flegg@unimelb.edu.au and Roslyn Hickson r.hickson@unimelb.edu.au

## Mathematical modelling the healing of skin wounds

(posted for 2018-2019)

The process by which a skin wound heals is complicated and requires the concerted action of a large number of cell types, chemicals and fibres. Mathematical modelling can synthesise the large number of interactions and can be used to gain insight into the healing process by numerical solution of the model and analytical investigation of the governing equations.

A project is available focusing on mathematical modelling of chronic, non-healing wounds and the stimulation of the healing process by treatment of the non-healing wounds. The project will aim to develop governing mathematical equations which capture the essential behaviour of the complex system and to provide clinical insight by numerical and analytical investigation of the model.

**Contact: **Jennifer Flegg jennifer.flegg@unimelb.edu.au

## 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.

**References:**

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 dbalding@unimelb.edu.au

## 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 jamesm@unimelb.edu.au

## 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 jamesm@unimelb.edu.au