Informing the COVID-19 response: mathematicians’ contributions to pandemic planning and response

(This is a guest post by Professor James McCaw, 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.)

COVID-19 has changed how we live our lives, and will continue to do so for some time yet. Australia has been fortunate in many ways. We have clearly defined borders which are able to be managed effectively. We have a highly functional public health system. Despite the challenges in Victoria in mid-2020, ultimately we increased testing and contact tracing capacity enough to suppress transmission. We have, for the most part, seen coherent leadership from our state and Commonwealth political leaders.

The ‘science’—from clinical and lab-based research to mathematical modelling—has been listened to and, again for the most part, acted upon.

But world class research is clearly not sufficient to manage the pandemic. The United Kingdom—the ‘home’, and I would argue ‘intellectual powerhouse’, of mathematical epidemiology—has suffered greatly. As has the United States and much of Europe.

In Australia, the field of mathematical epidemiology is still in development. It was only 2005 when Australia’s National Health and Medical Research Council made its first major investment, funding a ‘Capacity Building Grant’ in infectious diseases modelling to support public health. I was fortunate to be appointed as a post-doctoral research fellow under the scheme, as were a number of other now well-known mathematical epidemiologists including Professor Jodie McVernon (Doherty Institute) and A/Prof James Wood (UNSW), who trained in infectious disease modelling and mathematical physics respectively. The grant was led by Professor Raina MacIntyre, a prominent epidemiologist and media figure in Australia’s COVID-19 response.

From the outset, we were engaged with the Australian Government Department of Health’s Office of Health Protection, the body responsible for preparedness and response to public health emergencies in Australia. At the time, the focus was on SARS and pandemic influenza.

As a mathematician, I have maintained an open dialogue with the Commonwealth for over 15 years. Through contractual research, we have developed stochastic models for border incursions, examined optimal distribution strategies for limited supplies of antivirals, estimated the volume of Personal Protection Equipment (PPE) required in a response and examined optimal strategies for vaccination. These analyses informed the development and multiple revisions of the Australian Health Management Plan for Pandemic Influenza (AHMPPI). In February 2020, with input from me and colleagues, the AHMPPI was rapidly adapted for COVID-19.

Throughout this 15 year period, we regularly visited Canberra to sit around the table with Health leadership, including four different Chief Medical Officers of Australia and their advisors. Both parties learnt a lot through that collaboration. As a mathematician I learnt how to communicate the purpose, limitations and relevance of our models. The government learnt to appreciate what models could and could not do. What policy decisions they could and could not inform. We gained a shared understanding that deeply quantitative work primarily delivered qualitative insights. And we learnt to trust each other.

Trust—not just in the science, but in the people conveying that science—is, in my view, the most fundamental requirement for the effective contribution of scientific knowledge to policy and response.

As a qualified and trusted advisor, I have contributed in two ways. With my team, we have undertaken mathematical analyses and delivered those results to government. But my responsibilities also include interpretation and evaluation of the (global and emerging) literature. Can Imperial College’s COVID-19 modelling on ‘lockdowns’ be applied to Australia? Are optimal vaccination strategies developed for other countries applicable here? Are real-time analysis methods for a well-established outbreak—like those developed at the London School of Hygiene and Tropical Medicine—applicable to Australian case data?

I believe that Australia benefited from the deep engagement and trust developed between academics and the Commonwealth over 15 years. The trust lies not just with the advisors, such as me. The trust extends through to a cultivated broader trust in the scientific research performed by others and interpreted and evaluated by those advisors.

And with that, where does mathematical analysis make a difference?

Often, it is in what we (as mathematicians) may perceive as surprisingly simple points.

Epidemic theory describes how a pathogen spreads through the community. Scaling out the average duration of infectiousness, and ignoring some biological subtleties, the rate of change in prevalence I (the proportion of individuals who are Infectious in the population) is described by a non-linear ordinary differential equation:

dI/dt = (R0S − 1)I

where R0 is the ‘basic Reproduction number’, the number of secondary cases arising from a single case in an otherwise fully susceptible population, and S is the proportion of the population that is Susceptible.

With R0 > 1 and S sufficiently large (as it is at the beginning of an epidemic), prevalence (that is, I) grows exponentially and S decreases (as dS/dt = −R0SI).

Eventually, depletion of the susceptible pool (S) modified the dynamics. The resultant non-linear dynamics are what make infectious diseases both mathematically interesting, and conceptually challenging for public health policy makers to respond to.

In early 2020, my team delivered a report to government which explored the possible change in the total number of infections over the course of an epidemic due to various percentage reductions in transmissibility. For our purposes here, this is as simple as considering how the size of an epidemic depends upon R0, although we did not report the analysis in this way to government.

A textbook analysis yields the ‘final size equation’, which relates R0 to the size (as t→∞) of the epidemic, Z = 1 − S(t→∞):

Z = 1 − eR0 Z

This is a non-linear relationship. By February 2020, we suspected the R0 for COVID-19 was in the range 1.5–3. At the upper end of this range, a 50% reduction (due to say, some level of physical distancing) has an important but fundamentally challenging effect—an epidemic with a modified reproduction number of 3/2 = 1.5 still spreads explosively, resulting in a vast number of infections. But if COVID-19’s reproduction number was at the lower end, a 50% reduction would prevent the virus from spreading entirely as 1.5/2 = 0.75 < 1 and transmission cannot be sustained.

Such results are entirely unsurprising to us as mathematicians. We understand the importance of non-linearities and of features such as bifurcations. It is natural for us to view the transmission of an infectious disease as a dynamical system. But these important points are anything but intuitive and easily missed by decision makers.

With trust and open communication channels, important findings, as well as viewing the entire pandemic and our response to it as a dynamical system, proved influential in Australia’s early response.

Simple analyses emphasised the value of mathematical reasoning. They highlighted the risks of ‘intuitive linear thinking’ but they also demonstrated how mathematical analysis can overcome that limitation. Models can be used to anticipate or reason on the (positive or negative) impacts of alternative response strategies.

Subsequent scenario analyses (with more ‘realistic’ and nuanced models calibrated to COVID-19 epidemiology) laid the groundwork for our initial response and for the monitoring and evaluation of the ‘effective reproduction number’ of COVID-19 throughout 2020 and into 2021. Collectively, these mathematical capabilities have contributed to the Australian government’s risk-assessment process for managing the pandemic.

National policy guidance relies upon in-depth mathematical modelling and analyses, conducted both in-house, nationally and around the world. But while necessary, the existence of that research is not sufficient to have impact. To have impact, to be effective, also requires relationships, ‘translators’ and, above all, (mutual) trust.

Abel Prize: call for nominations

The Norwegian Academy of Science and Letters hereby calls for nominations of candidates for the Abel Prize 2021.

The Abel Prize recognizes outstanding scientific work in the field of mathematics, including mathematical aspects of computer science, mathematical physics, probability, numerical analysis and scientific computing, statistics and applications of mathematics in the sciences.

The Abel Prize amounts to NOK 7,5 million.

The Abel Prize may be awarded to one single person, or shared for closely related fundamental contributions. The first instalment of the Abel Prize was in 2003. For laureates up until 2021, please consult

The Norwegian Academy of Science and Letters awards the Abel Prize on the basis of a recommendation from the Academy’s Abel Committee, chaired by an Academy member and consisting of four further members elected amongst names put forward by the International Mathematical Union and the European Mathematical Society. The Abel Committee receives all nominations and may itself nominate candidates for the Abel Prize. The name of the Abel Laureate will be announced in March 2022. The award ceremony will take place in Oslo in May 2022.

We hereby invite you (or your society or institution) to nominate candidate(s) for the Abel Prize. Your nomination should be accompanied by a description of the work and impact of the nominee/nominees, together with names of distinguished specialists in the field of the nominee/nominees who can be contacted for an independent opinion. When nominating it is a requirement to take into account that the nominee has adhered to general guidelines for research ethics.

Your letter of nomination should be sent no later than September 15, 2021.

For further information and the nomination form, please consult

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.

SMRI International Visitor Program (NZ only)

The SMRI International Visitor Program is now open again, for visitors travelling from
New Zealand only. This program funds researchers in the mathematical sciences to travel
to Australia for research collaborations at Australian universities. If you have
existing or potential collaborators working in New Zealand, please encourage them to
make use of this opportunity.

Please direct any potential applicants to the SMRI website for the full terms and conditions,
and instructions on how to apply. Any further questions about the scheme can be
addressed to this email address.

At least initially, applications for this NZ-only IVP will be on a rolling basis as with
our Domestic Visitor Program. For Aus or NZ citizens or Aus permanent residents, the
application deadline is 2-6 months before the start of the proposed visit; for other NZ
residents, 4-6 months before the start of the proposed visit.

Terms and conditions for the IVP will be updated when travel to Australia from other
source countries becomes possible.

Anthony Henderson

Executive Director, SMRI

Workshop on the Intersections of Computation and Optimisations

MoCaO (Mathematics of Computation and Optimisation) is planning a new workshop for late 2021 which is sponsored by the ANU, UNSW and AMSI. This workshop intends to bring together researchers from the areas of computation, optimisation, computing sciences and engineering interested in the cross-fertilization of ideas around the following theme:

 Optimisation often faces unique issues when there is a need to efficiently compute. On the other hand, computational techniques at times utilise optimisation within their algorithms. Both areas fundamentally need to understand approximation in all its facets which is also fundamental to computation as are the associated notions of convergence. Indeed, recent research has blurred the boundaries between optimisation (continuous and discrete), computation and areas of computing science. The area of machine learning has crept into relevance everywhere. Recently research has turned to its use in computational techniques including the enhancement of optimisation algorithms and the cycle of cross fertilisation of ideas has continued to date.

Workshop Format

We intend to run the workshop in a blended format, involving a face to face component which will be held at the ANU mathematics school in conjunction with a simultaneous\parallel online format to which both group of participants will engage. Some keynotes will present in person (streamed online from ANU) and other will engage totally online in a remote format. We encourage local and international participants to take part in the online workshop. In addition to their keynote presentations, keynotes who will be invited to give a lectorial-discussion session that will promote research questions and engage emerging researchers in these areas.

Keynote Speakers

  • Prof Gerlind Plonka-Hoch (University of Goettingen, Germany)
  • Prof. Frances Kuo (UNSW)
  • Prof Stefan Wild (Argonne, USA)
  • Prof Stephen Wright (Wisconsin, USA) 
  • Prof. Ian Turner (QUT)
  • Prof. Claudia Sagastizabal (IMECC-Unicamp and CEMEAI, Brazil)
  • Prof Martin Berggren (Umeå University, Sweden)

Important dates:

Registration Opens: 07/06/2021
Workshop Dates: 22/11/2021 to 25/11/2021

Future Announcements and Grants:

We intend to follow up with regular announcements regarding workshop accommodation, details on format and software and funding opportunities for ECR, PHD and female participants. We also wish to draw female participants attention to the possibility of applying for the WIMSIG Cheryl E. Praeger Travel Award (support for attending conferences/visiting collaborators) and/or the WIMSIG Anne Penfold Street Awards (support for careering responsible while attending conferences/visiting collaborators).

Australian Institute of Tropical Health & Medicine course on disease modelling

The AITHM is running a short course on infectious disease modelling. Please circulate the below information and attached flyer to your networks, for any interested students and other parties.

What: Winter Short Course – Mathematical Modelling of Infectious Diseases
Date: 19th to 23rd July 2021
Location: Online and Townsville (great place to be in winter!)
Who for: Aimed at participants with a basic understanding of infectious disease modelling and some basic programming skills
Who by: The Australian Institute of Tropical Health and Medicine at James Cook University are running a short course
Duration: 5 days
Cost: $880, though there are up to 10 scholarships available.

For more information please see the attached flyer.

All applicants should contact the course organisers via email to express interest in attending either in person or online.

Applications submitted to: this email address
EOI deadline: 10th June 2021
Payment deadline: 30th June 2021

Lecturer in Mathematics

University of Sydney
School of Mathematics and Statistics

Closing Date: 13th June 2021

We are currently seeking to appoint an accomplished academic to the position of Lecturer in Mathematics. To succeed, you will be a talented and well-qualified mathematician with a passion for teaching and research expertise in an area that strengthens the school’s profile and align with the research interests of SMRI’s director   Professor Geordie Williamson. This includes, but is not limited to algebra, geometry and representation theory. In particular, researchers with background in geometric representation theory, algebraic geometry or homotopy theory are particularly encouraged to apply. You will need to have appropriate skills and qualifications as outlined in the position description, including a PhD in Mathematics.

If appointed, you will be expected to undertake duties consistent with an appointment at the Lecturer level (Level B) on the Australian academic scale. This will include: publishing scholarly papers in international peer-reviewed journals and presenting at conferences; supervising undergraduate and postgraduate students; teaching a range of courses to undergraduate students; and applying for external funding.

For more information and to apply, click here.

PhD opportunity in multi-scale models in immuno-epidemiology

La Trobe University
Department of Mathematics and Statistics

Closing Date: 30th June 2021

We seek expressions of interest from prospective students to undertake a PhD in the research area: multi-scale models in immuno-epidemiology. The spread of a pathogen (for example, a virus or bacteria) through a population is a multi-scale phenomena, influenced by factors acting at both the population and within-host scales. At the population scale, transmission is influenced by how infectious an infected host is. Infectiousness in turn depends on the balance between pathogen replication within the host and immune/drug control mechanisms.  This project aims to develop new mathematical frameworks for simultaneously modelling these two scales. This will provide a platform for the rigorous study of complex biological interactions – such as the emergence and combat of drug-resistance – that shape society’s ability to control infectious diseases in human, animal and plant systems.

This PhD is funded by an Australian Research Council Discovery Project led by Prof James McCaw and A/Prof Nic Geard at the University of Melbourne, and Dr Rebecca Chisholm at La Trobe University. The successful applicant will be based at La Trobe Bundoora Campus and work closely with all investigators.

Graduates with a strong background in applied mathematics and with strong programming skills in either Python, Matlab, or R are encouraged to apply. Experience in infectious disease modelling is preferred, but not essential.

Further details:

How to apply

  • review details on how to apply for candidature at La Trobe University
  • contact Dr Rebecca Chisholm (, with any enquiries or to express an interest in the project.
  • when you have received in-principle agreement for supervision, complete and submit your application by 30 June 2021 for admission into La Trobe’s PhD program, indicating you wish to be considered for this scholarship on the application.

The University will carefully review your application and consider you for this scholarship. You will be advised of an outcome in July 2021.

Members are encouraged to nominate for the Australian Mathematical Society’s Teaching Excellence Awards

The AustMS annual Award for Teaching Excellence and the annual Award for Teaching Excellence (Early Career) have been established to encourage excellence in mathematics teaching in higher education. The AustMS Award for Teaching Excellence and Award for Teaching Excellence (Early Career) aim to recognise and reward outstanding contribution to teaching and student learning in the mathematical sciences at the tertiary level. With these awards the AustMS recognises the importance of quality of mathematics teaching and the impact it has on the training of a future mathematics workforce. Progressive teaching is essential to maintaining high standards across service courses for other disciplines, where high-quality mathematics teaching is of key importance.

Each year a Teaching Excellence Award and a Teaching Excellence Award (Early Career) will be presented at the Annual Meeting, with the prize money for each award set at $1000 per annum. Awardees will be invited to give a presentation on their work at the Annual Meeting and write a short classroom note for the Gazette. For more details see this page or email Chris Tisdell for clarification.

Nominations for these awards will close on 31 August 2021.

Applications for the 2021 Alf van der Poorten Travelling Fellowship now close on 16th June (closing date has been extended).

Prospective applicants should visit the Society’s web site here for an application template before submitting an application electronically to the selection committee before 16 June. The Alf van der Poorten Travelling Fellowship, of up to $10,000, is offered to early-career researchers who have obtained their PhD in pure mathematics from an Australian university.

To be eligible to apply, a candidate must have qualified for their PhD within five years of the closing date, allowing for career interruptions, and they cannot have previously been awarded the Alf van der Poorten Fellowship. Applicants must have been members of the Society for the consecutive twelve-month period immediately prior to the date of application. (Back dating of membership to the previous year is not sufficient.)