Australian mathematicians rise to the challenge of COVID-19

(This is a guest post by Dr Joel Miller, introducing a miniseries of articles/essays by Australian mathematicians involved in the pandemic response)

Mathematics plays an integral role in our daily lives.  A smart phone that guides you to your destination relies on mathematical routines to calculate your position, other algorithms find the optimal route, and yet others ensure that the communications from your phone are secure.  The central role that mathematics plays throughout scientific disciplines comes largely because our mathematical models of the natural world, built on observation, give us remarkable predictive power and allow us to design systems that perform optimally.

At the outset of the COVID-19 pandemic, we did not have time to do careful experiments comparing different policies before implementing them.  What we had was information about how efficiently the disease spreads, some hints that it could spread through asymptomatic or presymptomatic infected individuals, and estimates of the distribution of severity in different age groups.  That knowledge grew as different countries began to experience outbreaks.

Armed with this knowledge policy makers were forced to make decisions about their response.  They needed a way to turn this limited information about the mechanisms underlying disease spread into projections of what the future would hold.  Mathematical modelling was the tool that let us rigorously determine what consequences could follow from different policy decisions and different plausible disease properties.  The modelling effort relied on a wide range of techniques and modellers from different backgrounds and career levels, ranging from student to senior academic, as well as researchers working within health departments.

Lives have been upended by the COVID-19 pandemic, and by our response to it.  In this series some of the mathematical modellers who played a role in advising Australia’s (thus far) stunningly successful response give their perspective on the role that they played, showing how mathematicians at many levels played a key role in the decisions that led to COVID-19’s effective elimination in Australia.

National Science Week with MATRIX – Maths Documentaries

MATRIX is excited to host free online screenings of the following documentaries that celebrate the wonders of the mathematical sciences during National Science Week. We’d be extremely grateful if you could help us promote these events.  We would love for you, your teams and those in your networks to join us too. 

  • Maths Circles Around The World – 16 August 2021, 16.30 AEST 
  • Secrets of The Surface – The Mathematical Vision of Maryam Mirzakhani – 16 August 2021, 19.30 AEST 
  • Colors of Math – 17 August 2021, 19.30 AEST 
  • The Discrete Charm of Geometry – 18 August 2021, 19.30 AEST 

See the MATRIX webpage, the pdf flyer or the National Science Week website for more.

Applied Mathematician


Closing date: 6th Aug 2021

Category:Engineering / Technical
Position Type:Permanent
Job Reference:BOE/1550763

An exciting new role has opened up within Boeing Research & Technology Australia’s Brisbane Research Centre, located within the University of Queensland, St Lucia.

The successful candidate will work within a team of passionate mathematicians and engineers to develop state of the art GPU based multi-physics solvers. Essential skills include a familiarity with a range of computational methods for solving partial differential equations as well as experience in the implementation of such methods in a compiled language, particularly C, C++ or FORTRAN.  Experience in developing computational fluid dynamics codes, structural finite element codes or multi-physics codes is considered an advantage. Experience with high performance computing frameworks such as CUDA, OpenACC, OpenMP & MPI will also be considered beneficial.  

Required Qualifications:

  • Research higher degree in Mathematics (PhD or masters)
  • Bachelor degree in Math, Physics or Engineering

Applicants must be Australian Citizens to meet defence security requirements.

More information and application at this page.

Mathematical Modeller

Burnet Institute, Melbourne

Closing date: Tue, 17 Aug 2021 11:59pm Australian Eastern Time

The Opportunity 

Are you an early career researcher eager to undertake real-world mathematical modelling projects in infectious diseases and global health? This could be the role for you!

A unique opportunity exists for a Mathematical Modeller to join Burnet’s Modelling & Biostatistics team. Join an innovative team that is developing and applying epidemiological and costing models around the world across a range of disease areas including COVID-19, HIV, TB, malaria, viral hepatitis, maternal and child health.  

This is an exciting chance for you to:

  • Contribute to the development and application of epidemic and economic models to address major public health issues
  • Work with a globally based team of expert modellers, epidemiologists, economists, health and policy specialists, and computer scientists to improve models
  • Undertake modelling and analytical support that will be provided to governments, policy makers, and other partners including the World Bank, Global Fund, and international health agencies, to improve health budget investment towards better decision-making and impact around the world
  • Apply innovations and analytical skills to ensure high quality deliverables in a fast-paced environment
  • Contribute to and produce policy briefs, presentations, scientific papers and technical reports 

Refer to the attached position description for full details.

This is a full-time position, initially for a 2-year period with the possibility of extension. Work from the comfort of your own home or join us in the office, location is flexible!

Full details and application form at this link.

Mathematical models to support Victoria’s COVID-19 response: a blunt instrument to a complex problem

(This is a guest post by Dr Michael Lydeamore as part of our miniseries of articles/essays by Australian mathematicians involved in the pandemic response. A pdf version of this article is available here.)

Throughout Victoria’s COVID-19 response, a suite of mathematical and statistical models have been used to understand the spread and subsequent control of the pandemic. High-profile mathematical outputs, such as case forecasts, give a good picture of the general epidemic activity in a given region. However, when case numbers are small, forecasts can be very sensitive. Moreso, when there is only a handful of cases, more detailed factors such as geographic distribution of cases, or at-risk industries, are possibly more informative.

As part of my role in Victoria’s COVID-19 response, my team applied a number of statistical techniques to case data. These techniques have varying levels of sophistication, but one of the most used was Diggle’s space-time K-function [2]. This model is relatively unrefined, but the advantage of that is that very little information is required to compute it: just the date of infection of cases, and their geographical location. Both of these are collected almost immediately once the case is notified, meaning that this function can be calculated regularly and quickly, two factors that are critical in informing epidemic response.

The D_0 function can be interpreted as the proportional increase in case events at a given space-time arising from interactions at that space-time. In an infectious diseases context, this is a proxy measure of disease contagiousness. The lower this increase, the stronger the indication of successful intervention measures.

To calculate the D0 function, we start with the K-function (For some reason, spatial science has some of the most non-transparent function naming). The K-function is defined as the cumulative number of expected case events, K, as a function of the (straight-line) distance from an arbitrarily selected case [7]. That is,

Kd (s) = N -1i  ∑j≠i I [dij<s],      (1)

where N is the total number of cases, dij is the distance between case i and case j, and I is an indicator function. Eq (1) is sometimes termed the ‘spatial’ K-function, but by swapping out the dij term, it is possible to calculate a K-function across any attribute. For COVID-19, we used time, denoted Kt(t), as well as space. The time between two cases was the number of days between their onset dates (which we assumed were a proxy for infection dates) as opposed to the notification dates, for which there was sometimes a long delay. Figure 1 gives an illustration of calculating the K-function in (a) space and (b) time. For the arbitrarily chosen case—case B here—the K-function in space at 1 unit, KdB(1)=2/6, and at 2 units, KdB(2)=5/6. Comparatively, in time, KtB(1) = 1/6, and KtB(3) = 5/6. To estimate the K-function in it’s entirety, we would repeat this process for each of the other cases A–F.

So far, we have considered space and time completely separately. As the last example has shown, often the clustering of cases in space and time can be different. If space and time were completely independent, then the space-time K-function, denoted K(s,t), would be the product of the space and time K-functions. That is,

K(s,t) = Kd (s) × Kt(t).

However, that is rarely the case, particularly in infectious diseases, where disease spreads from one individual to another. In the example visualised in Figure 1, K(1,1) = 1/36 as cases A and B are within 1 unit and 1 day of each other (Note that we have N 2 here as we are considering the two dimensions). However, Kd (1) × Kt(1) = 2/6 × 1/6 = 2/36. (Note that we have labelled the cases here for the purposes of the example, but when actually calculating these functions the cases are considered unlabelled.) Because of this dependence between space and time, we are interested in estimating how many times greater K(s,t) is compared to the product of Kd (s) and Kt(t). Thus, we arrive at the definition of D0 function,

D0(s,t) = K(s,t)/(Kd(s) × Kt(t)).      (2)

The actual value of the D0 function is not particularly important. Rather, it is how this function changes over time or geographically that is the most important. The absence of space-time interaction (i.e. a relatively flat D0 function) is a sign of control success.


Figure 1: Graphical illustration of the K-function in (a) space and (b) time.

From March until the end of 2020, we estimated the D0 function as part of the routine reporting framework. It was regularly one of the fastest measures to show control success, but perhaps one of the most valuable moments was the reporting in mid-June. The period from May through to the start of June was one of relative calm, with 218 cases diagnosed over the 31 days, an average of roughly 7 notifications per 24 hours. A similar story was true at the start of June, with 114 community acquired or unknown source cases over the first 20 days: an average of under 6, relatively the same as what we had so far. In our routine report, using data up to June 20, 2020, something seemed amiss with the D0 function, reproduced in Figure 2. What was once a nicely clustered mass near 0 days and 0 kilometres seemed to have spread out, particularly over distance. There was, unusually, relatively little clustering to be seen.

After digesting this figure, we got together with the epidemiology team who had been compiling notes on all the cases and their contacts across Victoria. When we pooled all the evidence together—statistical models, case notes, forecasts of incoming numbers, genomic information, geographic risk profiles, and so much more—we arrived at a hypothesis we hoped would not be true: infection had been scatter-gunned across the greater Melbourne area. The more we looked, the more it seemed like it could be true. In the 10 days that followed, a further 369 community acquired or unknown cases would be notified, more than 6 times as many cases per day than that of the previous 3 weeks. Victoria’s second wave had arrived.

Figure 2: Estimate of the D0 function based on COVID-19 data up to June 20, 2020 in Victoria. The contagiousness estimated by this function is very low, despite signs of increasing case numbers.

The D0 function is not a new concept to infectious diseases. Although not typically applied in human diseases (as thankfully we don’t have many pandemics), it has been used in Rift Valley fever [6], highly pathogenic avian influenza [4,5] as well as a handful of others [1,3,8]. The technique is well-known, and in an environment where time is of the essence, it’s quick compute time was proven valuable. COVID-19 was, and is, an infection that we knew little about, and the ability to apply a tried and tested model when it was needed most meant that our ability to respond was as strong as it could be.

There is no crystal ball when it comes to pandemic predictions. No matter how complex the model we develop and apply, no one can ever accurately predict the future. Much of my and my team’s role was to synthesise the information from these relatively unsophisticated models and communicate them to the people who needed to know. In the example discussed here, it was the discussion of information with our epidemiologists that led to the conclusion, not a piece of data or a model. No-one knows when exactly the peak of infections will be, but between the epidemiology and the modelled data, we can come together and give an idea of whether we’re likely to see increases or if the control measures being applied are working.

Victoria has since reached a state of elimination for COVID-19, along with the rest of Australia. A feat shared only by a few globally. Here, we have seen one example of a response coming together to solve an issue, but it is far from the only example. If there’s one thing to take away from Victoria’s COVID-19 response, it’s that the pieces of the puzzle are always stronger together.

Acknowledgements: The author would like to thank Mark A. Stevenson and Kira Leeb for their comments on this article, as well as the Victorian Department of Health Analytics Team (COVID-19 Intelligence) for their work throughout the pandemic.

[1] E. Delmelle, I. Casas, J. H. Rojas, and A. Varela. Spatio-Temporal Patterns of Dengue Fever in Cali, Colombia. International Journal of Applied Geospatial Research (IJAGR), 4(4):58–75, Oct. 2013.

[2] P. Diggle, A. Chetwynd, R. Häggkvist, and S. Morris. Second-order analysis of space- time clustering. Statistical Methods in Medical Research, 4(2):124–136, June 1995.

[3] A. C. Gatrell, T. C. Bailey, P. J. Diggle, and B. S. Rowlingson. Spatial Point Pattern Analysis and Its Application in Geographical Epidemiology. Transactions of the Institute of British Geographers, 21(1):256–274, 1996.

[4] C. Guinat, G. Nicolas, T. Vergne, A. Bronner, B. Durand, A. Courcoul, M. Gilbert, J.-L. Guérin, and M. C. Paul. Spatio-temporal patterns of highly pathogenic avian influenza virus subtype H5N8 spread, France, 2016 to 2017. Eurosurveillance, 23(26):1700791, June 2018.

[5] L. Loth, L. T. Pham, and M. A. Stevenson. Spatio-temporal distribution of outbreaks of highly pathogenic avian influenza virus subtype H5N1 in Vietnam, 2015–2018. Transboundary and Emerging Diseases, 68(1):13–20, 2019.

[6] R. Métras, T. Porphyre, D. U. Pfeiffer, A. Kemp, P. N. Thompson, L. M. Collins, and R. G. White. Exploratory Space-Time Analyses of Rift Valley Fever in South Africa in 2008–2011. PLOS Neglected Tropical Diseases, 6(8):e1808, Aug. 2012.

[7] B. D. Ripley. The Second-Order Analysis of Stationary Point Processes. Journal of Applied Probability, 13(2):255–266, 1976.

[8] J. W. Wilesmith, M. A. Stevenson, C. B. King, and R. S. Morris. Spatio-temporal epidemiology of foot-and-mouth disease in two counties of Great Britain in 2001. Preventive Veterinary Medicine, 61(3):157–170, Nov. 2003.

Indigenising University Mathematics 20-21 Sept: registration open – all welcome

Dear Colleagues,

You are warmly invited to register for “Indigenising University Mathematics” 20-21 Sept 2021, being held simultaneously online via Zoom and in-person at the Wollotuka Institute, University of Newcastle: 

This symposium is being put together to provide support, learning and collaborative opportunities around Indigenising our practices and teaching in University Mathematics and Statistics.  Increasingly, this is a responsibility that individual academics and University departments are feeling, but we do not necessarily know where to start. In some discipline areas, such as Food Science or Astronomy, the task may seem easier due to more obvious links between traditional Indigenous knowledge and course content.  In Mathematics and Statistics, the task may initially seem harder.  The purpose of this Symposium is to help.

It turns out that the challenges presented by Mathematics and Statistics may mean we may have an opportunity to do things which are deeper and more meaningful than simply incorporating isolated fragments of content, and we can do this in multiple ways.   We can utilise Indigenous pedagogies, for example using stories, symbols, maps and relationships.  We can promote inclusion and recognition.  We can compare with and learn from Indigenous ways of organising the world through structures such as kinship, that relate to graph theory and group theory and so on. And we can begin to (learn and) apply Indigenous perspectives to our own traditional content.  There is a lot to discover. 

In this symposium, we will utilise the traditional Indigenous practice of “yarning circles” to help us all get together and think through opportunities around all these and more.  To support this, the Symposium is organised around a number of themes, each of which is led by a small team of 2 or 3 Mathematicians/Statisticians/Indigenous practitioners. A presentation on each theme – see the Symposium webpage for more details – will precede the yarning sessions.  We hope to have broad representation from our Mathematics/Statistics and Indigenous communities, to facilitate sharing and the development of relationships and partnerships to support ongoing work in this area.

If you’d like to attend in person, please register soon, since places are limited to about 40 for in-person attendance, due to covid.  If you do register for in-person attendance and then cannot come in person, and you let us know by the week before, we will happily refund the difference and convert your registration to online. 

Feel free to contact me if you have any questions.

best wishes,

Judy-anne and all the organising committee.

Representation theory’s hidden motives: Conference at Münster and Sydney

The workshop takes place in-person at the University of Münster and at the University of Sydney, on 27 September – 1 October 2021. It can also be attended online. Workshop participation is free of charge. However, a registration is required. 

In recent years, motivic techniques have been applied in several branches of representation theory, for example in geometric and modular representation theory. The goal of this workshop is to bring together researchers in these areas in order to foster new synergies in topics such as foundational aspects of the theory of motives, Tate motives on varieties of representation-theoretic origin, motivic aspects of the Langlands program, and motives of classifying spaces.


Speakers marked (*) will speak in Münster, (**) will speak in Sydney.

Angeltveit, Vigleik (Canberra, **)
Cass, Robert (Harvard, *)
Coulembier, Kevin (Sydney, **)
Eberhardt, Jens (Bonn, *)
Fu, Lie (Lyon, *)
Haesemeyer, Christian (Melbourne, **)
Hoskins, Victoria (Nijmegen, *)
Kamgarpour, Masoud (UQ, **)
Lanini, Martina (Roma, *)
Levine, Marc (Essen, *)
Richarz, Timo (Darmstadt, *)
Semenov, Nikita (Munich, *)
Soergel, Wolfgang (Freiburg, *)
Spitzweck, Markus (Osnabrück, *)
Treumann, David (Boston College, *)
Vilonen, Kari (Melbourne, **)
Xue, Ting (Melbourne, **)
Yang, Yaping (Melbourne, **)
Zhao, Gufang (Melbourne, **)
Zhong, Changlong (Albany, *)


Nora Ganter (Melbourne)
Jakob Scholbach (Münster)
Matthias Wendt (Wuppertal)
Geordie Williamson (Sydney)

For more information, visit

Postdoctoral Research Fellow/Research Fellow

The School of Mathematics and Physics
University of Queensland

Closing Date: 3rd August 2021

The primary purpose of this position is to carry out high-quality mathematical research in the general area of Geometric and Nonlinear Analysis. Some contribution to undergraduate and/or postgraduate coursework teaching may be expected.

The position reports to the Head of School, Professor Joseph Grotowski.

This position is located at our picturesque St Lucia campus, renowned as one of Australia’s most attractive university campuses, and located just 7km from Brisbane’s city centre. Bounded by the Brisbane River on three sides, and with outstanding public transport connections, our 114-hectare site provides a perfect work environment – you can enjoy the best of both worlds: a vibrant campus with the tradition of an established university.

For more information and to apply, click here.

Associate Professor/Professor in Statistics or Data Science

School of Mathematical Sciences
The University of Adelaide

Closing Date: 12th August 2021

(Level D/E) $147,685 to $189,518 per annum plus an employer contribution of up to 17% superannuation may apply. 

Continuing position available from 1 January 2022.

The University of Adelaide is seeking a senior academic to lead the Discipline of Statistics in the School of Mathematical Sciences and contribute to the School’s strategic priority of expanding its research and educational offerings in data science, broadly construed.

This is an opportunity for an emerging or current academic leader to join a top-ranked team with ambitious plans for the future. The University of Adelaide received the highest possible rating of research quality in the mathematical sciences overall and in each of its disciplines in the two most recent ERA assessments. It was the only Australian university to receive top ratings for engagement and impact in the mathematical sciences in the 2018 Engagement and Impact Assessment.

The School is committed to pedagogical innovation and is currently working with its Industry Advisory Board to strengthen its external engagement as a strategic priority.

The School is strongly committed to increasing the diversity of its staff and students. We encourage and warmly welcome applications from academics who are able to contribute to the diversity of the School community. For more information and to apply, go to:

Mathematical modelling of Australian COVID-19 response: A PhD student perspective

(This is a guest post by Dennis Liu as part of our miniseries of articles/essays by Australian mathematicians involved in the pandemic response. A pdf version of this article is available here.)

It has been a little over 12 months since COVID-19 became a regular headline in the Australian media, but I would not be alone in saying it has definitely felt longer. At the time I was entering the third year of my PhD in mathematics and epidemiology, so when news broke of the new virus in late 2019, I was certainly paying attention. Little did I know it would affect not only my life as a researcher in the field, but everyone across the world.

Although COVID-19 restrictions have disrupted my study and research like many other HDR students, I have been fortunate that my work in modelling COVID-19 made progress towards my thesis.

In late February 2020 I was asked if I could help in the modelling effort, and at first this was supporting Dr Andrew Black and Dr James Walker in examining Australia’s pandemic preparedness and border closures. This modelling work by Andrew and James formed part of the advice on closing the international border. It was a frantic period of time, with a rapidly evolving situation.  Seeing this body of work influence policy was the first of many instances 

It wasn’t long after that my supervisor Prof. Joshua V. Ross asked if I was interested in developing and providing a forecast of COVID-19 cases to the COVID-19 response. I would be lying if I didn’t say Imposter Syndrome didn’t tell me to run the other way. Fortunately, and with encouragement from my supervisors and the wider COVID-19 modelling group, I didn’t give in and dived into the work.

To better describe our model, I will briefly introduce some important epidemiological concepts. An important epidemiological parameter is the effective reproduction number Reff, which can be defined as the average secondary number of infections from an infectious individual. This can vary through time, as behaviour changes through the epidemic, through social distancing and public health policy changes.

Reff can be retrospectively estimated through examining the number of cases over time, but to forecast cases using a mechanistic model, it must incorporate some estimate of the future transmission potential and/or arrival of infected cases. The relatively low number of cases in Australia also creates difficulties in utilising methods that rely on historical case incidence. Measures of mobility of each Australian jurisdiction provided by Google and survey results of the public’s behaviour in adhering to personal distancing measures provides the ability to link these indicators to an estimate of the effective reproduction number. This allows for a mechanistic model to forecast cases.

Figure 1: A schematic of the probabilistic COVID-19 forecasting model.

We estimated Reff using historical case incidence and an established method from the literature. To forecast Reff forward, we calibrated a model that links social mobility and personal distancing measures to these estimates of Reff

Within Australia, there have been jurisdictional level differences in policy and response to social distancing, but the underlying culture and mobility patterns may have commonalities. As such, we employed a hierarchical model to partially pool information between jurisdictions, while allowing for inferred differences where they may occur.

After calibrating the model and using Bayesian inference to learn the parameters, we then forecast the social mobility and distancing metrics using a random walk with drift in each jurisdiction. The model then gives a posterior predictive distribution on the Reff over time. 

The relatively few cases of local transmission in Australia, in conjunction with strict border control measures internationally and domestically, makes it natural to forecast the number of cases in each jurisdiction using a stochastic branching model. This generative model, using estimates from the literature for epidemiological parameters, can be paired with the time varying effective reproduction number to forecast COVID-19 cases in Australian jurisdictions. This framework adapts to changing public health policies and responses to the ongoing pandemic, particularly during small outbreaks and the irregular but frequent responses to outbreaks seen in Australia.

This forecasting model was run every week, and the results contributed to an ensemble forecast that was provided to various bodies in the Australian Government. This ensemble forecast was often considered by Chief Health Officers in determining the appropriate course of action, and was even shown a few times at media press conferences.

As mathematicians, it is rare that we get to personally observe the impacts of our research, let alone at my level as a PhD candidate. While the pressure and high stakes definitely gave me some sleepless nights, to see policy and action consider my work was incredibly fulfilling, and I highly recommend any HDR student take any opportunity to work on research with direct and immediate impacts like the COVID-19 response. Don’t let your Imposter Syndrome dissuade you from contributing, as every effort, however minor, helps. Your unique perspective will always be valuable in discussions, and you will almost certainly be supported by an amazing and dedicated team as well as your supervisors, as I did in my work!

Senior Mathematical Modeller

Burnet Institute

Closing Date: 18th July 2021

Burnet Institute have an opportunity for a Senior Research Officer / Senior Research Fellow to join our fantastic Modelling & Biostatistics team. This is a unique opportunity to develop and apply epidemiological and costing models around the world across a range of disease areas, including COVID-19, HIV, TB, malaria, viral hepatitis, maternal and child health.

This position is initially for a 2 year period.

Refer to the attached position description for full details.

Click here to apply.