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.

(a)
(b)

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: https://carma.newcastle.edu.au/meetings/ium/ 

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

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, *)

Organisers

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

For more information, visit https://www.uni-muenster.de/MathematicsMuenster/events/2021/mrt-2021.shtml

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:
https://careers.adelaide.edu.au/cw/en/job/505815/associate-professorprofessor-in-mathematical-sciences

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
Melbourne

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.

Australian Mathematical Society expresses concerns about the proposed new mathematics curriculum

The Australian Curriculum, Assessment and Reporting Authority (ACARA) is currently developing a new national school curriculum, including for mathematics. The public consultation period is drawing to a close, finishing on the 8th July.

On the 2nd of July the President of the AustMS, Prof. Ole Warnaar, contacted David de Carvalho, CEO of ACARA, asking for an extension of the consultation period, and further details about the design process and evidence base for the proposed mathematics curriculum. This letter, along with Mr de Carvalho’s response, can be seen at this page.

The exchange of letters was followed up with a meeting on the 5th of July between Mr de Carvalho, Prof. Warnaar, and Prof. Geoff Prince, Vice-President of AustMS. One result is that “The meeting confirmed that mathematical scientists were not involved in any official capacity in the preparation of the revised curriculum.”

It is deeply concerning that the mathematics profession has been left out of the revision process and design of the new National Curriculum in Mathematics.

Prof Ole Warnaar

Prof. Warnaar’s full summary of the situation can also be seen at the letter page. At the time of posting there is to be no change to the consultation timeline.

Lecturer/Senior Lecturer in Statistics, Data Science, Stochastic Modelling

School of Mathematical Sciences
University of Adelaide

Closing date: 1st August 2021

(Level B, Lecturer) $100,933 to $119,391 or (Level C, Senior Lecturer) $123,075 to $141,537 per annum plus an employer contribution of up to 17% superannuation may apply. 

Three-year fixed term position available from December 2021.  On conclusion of the three-year term, the position may be converted to a continuing position under the provisions of the University’s Enterprise Agreement.  

Two full-time positions are available.

The University of Adelaide is seeking to grow the statistics, data science, and stochastic modelling team in the School of Mathematical Sciences. This is an opportunity for a highly motivated researcher and committed educator to join a School that is a leader in pedagogical innovation and 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.

The School has identified data science, broadly construed, as one of its strategic priorities. We are seeking an enthusiastic colleague to work with us to expand our research and educational offerings in statistics, data science, and stochastic modelling. Willingness to engage with industry would be an asset. 

The School is strongly committed to increasing the diversity of its staff and students. These two available positions are directed at applicants who are able to contribute to the diversity of the School community.

For more information and to apply, click here.

Contribution of mathematical modelling to COVID-19 response strategies in regional and remote Australian Aboriginal and Torres Strait Islander communities

(This is a guest post by Dr Rebecca Chisholm, Dr Ben Hui and Associate Professor David Regan 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.)

The health and science communities recognised early on in the SARS-CoV-2 pandemic that Aboriginal and Torres Strait Islander Australians were likely to be at high risk of COVID-19 infection and severe outcomes, due to high rates of comorbidities associated with severe outcomes [1,2], and multiple factors predisposing to increased SARS-CoV-2 transmission [2,3,4].  In March 2020, the Australian Government convened the Aboriginal and Torres Strait Islander Advisory Group on COVID-19 (IAG), co-chaired by the Department of Health and the National Aboriginal Community Controlled Health Organisation. The role of the IAG was to develop and deliver a National Management Plan to protect Aboriginal and Torres Strait Islander communities.  Our research groups—located at the Doherty Institute, the Kirby Institute and La Trobe University—were commissioned to carry out modelling, under the guidance of the IAG, to help inform aspects of this plan related to regional and remote communities.  

Our prior research and existing modelling frameworks enabled us to quickly begin the process of responding to the questions of interest to the IAG which included:

  • How important is a timely response to the first identified case of COVID-19? 
  • Who should be quarantined and/or tested in communities?
  • How important is it to test people when they are in quarantine and prior to exit from quarantine?
  • Is there a role for community-wide lockdown in initial containment? 

Together, we repurposed a stochastic, individual-based modelling framework which had previously been developed at the Kirby Institute to examine the dynamics of sexually transmitted infections in remote communities [5].  Within this framework, we incorporated a model of population mobility and household structure relevant to disease spread via close contact in remote communities. This model was originally developed at La Trobe University and the Doherty Institute as part of a research program focused on understanding the drivers of high prevalence of Group A Streptococcus disease in these communities [4].  We also integrated a COVID-19-specific disease transmission model and the effects of various public health responses.  Throughout this model building process, we regularly engaged with the IAG and representatives from other peak bodies and public health units to iteratively refine details and assumptions (described in Box 1 and Figure 1).  

To address the questions of interest to the IAG, we used the model to simulate and analyse a number of outbreak response scenarios. We designed the scenarios in consultation with public health service providers working closely with communities (with options varying by jurisdiction and community). These included:

  • Case isolation, with or without an exit test, and with various expected delays between case identification and response;
  • Case isolation and quarantining the contacts of a case (based on different definitions of contacts), with or without exit tests, and with or without tests on entry to quarantine;
  • Case isolation and population lockdown (entire community quarantined), with or without exit tests, and with various levels of assumed compliance to lockdown.

Box 1. Brief model summary. The individual-based, computational model we designed simulated the “silent” introduction of SARS-CoV-2 into a remote community of either 100, 500, 1000 or 3500 people, the subsequent transmission of SARS-CoV-2 within the community, and the public health response. The model explicitly represented the infection status of each community member, as well as their age and place of residence within the community, which were tracked and updated daily.  Community members were assumed to have close family connections across multiple dwellings in the community (their so-called “extended household”), between which their time at home was distributed, and within which they were at higher transmission risk compared to individuals staying in different dwellings (Figure 1a).  Infected community members were further classified according to whether or not they would present to healthcare services for testing (if symptoms developed and were recognized, and fear/stigma did not prevent individuals from presenting, Figure 1b). At the time we developed our model, there had been no  SARS-CoV-2 transmission in Australian Aboriginal and Torres Strait Islander communities.  Therefore, our model was parameterized based on the experience of SARS-CoV-2 in other populations [6], but accounting for the expected increase in transmission due to enhanced mixing anticipated in interconnected and overcrowded households [2,3].  

Two images: a) graphic showing population model with infectious and not infections people in various types of households in the community
b) flowchart with details on internal state of the disease model in the Infected phase
Figure 1. Schematic representation of the individual-based model. The model simulates the “silent” introduction of SARS-CoV-2 into a remote community, the subsequent transmission of SARS-CoV-2, and the public health response.  Here we illustrate the structure of the (a) population model; and (b) disease model.

To gain an understanding of the range of possible epidemic outcomes, we used our model to run 100 simulations of each outbreak response scenario  (defined by a set of parameters controlling the transmission of SARS-CoV-2, the public health response, and the assumed response of community members to the response).  For different response scenarios, we compared and reported the median and interquartile range of several model outputs of interest, including the percentage of the community who were infected at the peak of the outbreak (peak infection prevalence) and by the end of the outbreak (the attack rate), the number of cases identified versus the number of cumulative infections over time, the total number of person-days community members were in quarantine for, and the number of tests performed.  

We sought regular feedback on the response scenarios considered, and our interpretation and communication of model outputs.  This ensured we were always addressing relevant questions and faithfully relaying our findings (summarised in Box 2 and Figure 2). 

Our work informed both the CDNA National Guidance for remote Aboriginal and Torres Strait Islander Communities for COVID-19 [7] and the Australian Health Sector Emergency Response Plan for Novel Coronavirus (COVID-19) [8].  We have since submitted a publication for peer-review describing our work, currently available as a pre-print [9].  We also worked together with the IAG to develop a plain-language document containing key messages for health services [10], and a plain-language presentation [11] containing key messages for Health service decision makers and community leaders to consider when deciding how a remote community will respond to a COVID‐19 outbreak.   

To date, efforts to protect Australian Aboriginal and Torres Strait Islander peoples from COVID-19 are working – there have been no incursions of SARS-CoV-2 into remote Australian Aboriginal and Torres Strait Islander communities, and the incidence of locally-acquired cases among all Australian Aboriginal and Torres Strait Islander peoples is six-times lower than the Australia-wide incidence [12].  

Box 2. Brief summary of findings. Our analysis indicated that without an effective public health response, an introduction of SARS-CoV-2 into a regional or remote Australian Aboriginal and Torres Strait Islander community would likely result in rapid spread.  Furthermore, multiple secondary cases would likely be present in a community by the time the first case is identified, indicating that capacity for early case detection and a prompt response would be crucial in constraining an outbreak.  A response involving case isolation and quarantining of close contacts of cases defined by extended household membership was found to significantly reduce peak infection prevalence compared to the non-response scenario, but subsequent waves of infection consistently led to unacceptably high attack rates in excess of 80% in modelled scenarios.  Rapidly initiating an additional 14-day, community-wide lockdown of non-quarantined households could reduce the attack rate to less than 10%, but only if compliance with the lockdown was at least 80% (Figure 2).

Chart showing comparisons of epidemic curves based on different model assumptions
Figure 2. Impact of initiating a 14-day lockdown in addition to case isolation and quarantining of contacts with entry and exit testing on epidemic control. Epidemic curves for a community of 1000 individuals with various levels of individual compliance with community lockdown [9]

References

[1] Chen T, Wu D, Chen H, Yan W, Yang D, Chen G, Ma K, Xu D, Yu H, Wang H: Clinical characteristics of 113 deceased patients with coronavirus disease 2019: retrospective study. Bmj 2020, 368. https://doi.org/10.1136/bmj.m1295

[2] Australian Institute of Health and Welfare: The health and welfare of Australia’s Aboriginal and Torres Strait Islander peoples: 2015. In. Canberra: AIHW; 2015. https://doi.org/10.25816/5ebcbd26fa7e4

[3] Koh D: Migrant workers and COVID-19. Occupational and Environmental Medicine 2020:oemed-2020-106626. https://doi.org/10.1136/oemed-2020-106626

[4] Chisholm RH, Crammond B, Wu Y, Bowen A, Campbell PT, Tong SY, McVernon J, Geard N: A model of population dynamics with complex household structure and mobility: implications for transmission and control of communicable diseases. PeerJ 2020, 8:e10203. https://doi.org/10.7717/peerj.10203

[5] Hui BB, Gray RT, Wilson DP, Ward JS, Smith AMA, Philp DJ, Law MG, Hocking JS, Regan DG: Population movement can sustain STI prevalence in remote Australian indigenous communities. BMC Infectious Diseases 2013, 13:188. https://doi.org/10.1186/1471-2334-13-188

[6] Sanche S, Lin YT, Xu C, Romero-Severson E, Hengartner N, Ke R: High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerg Infect Dis 2020, 26(7). https://doi.org/10.3201/eid2607.200282

[7] Communicable Disease Network Australia: National Guidance for remote Aboriginal and Torres Strait Islander Communities for COVID-19. 2020, Department of Health, Commonwealth of Australia [https://www.health.gov.au/resources/publications/cdna-national-guidance-for-remote-aboriginal-and-torres-strait-islander-communities-for-covid-19]

[8] Department of Health, Commonwealth of Australia. Australian Health Sector Emergency Response Plan for Novel Coronavirus (COVID-19). 2020, Department of Health, Commonwealth of Australia [https://www.health.gov.au/resources/publications/australian-health-sector-emergency-response-plan-for-novel-coronavirus-covid-19]

[9] Hui BB, Brown D, Chisholm RH, Geard N, McVernon J, Regan DG: Modelling testing and response strategies for COVID-19 outbreaks in remote Australian Aboriginal communities. medRxiv 2020, 2020.10.07.20208819. https://doi.org/10.1101/2020.10.07.20208819

[10] Department of Health, Commonwealth of Australia. COVID-19 Testing and Response Strategies in Regional and Remote Indigenous Communities: Key Messages for Health Services. 2020, Department of Health, Commonwealth of Australia [https://www.health.gov.au/resources/publications/covid-19-testing-and-response-strategies-in-regional-and-remote-indigenous-communities-key-messages-for-health-services]

[11] Department of Health, Commonwealth of Australia. Impact of COVID-19 in remote and regional settings. 2020, Department of Health, Commonwealth of Australia [https://www.health.gov.au/resources/publications/impact-of-covid-19-in-remote-and-regional-settings]

[12] Aboriginal and Torres Strait Islander Advisory Group on COVID-19. Aboriginal and Torres Strait Islander Advisory Group on COVID-19 Communique Update: 14 December 2020. Department of Health, Commonwealth of Australia [https://www.health.gov.au/resources/publications/aboriginal-and-torres-strait-islander-advisory-group-on-covid-19-communiques]