PhD scholarship: Mathematical modeling in infection and immunity, Infection Analytics Program@Kirby Institute, UNSW Sydney

The Infection Analytics Program at the Kirby Institute is looking for talented students with a strong interest in applying quantitative approaches to solving major challenges in infectious diseases, health and immunity.

The Group and Projects

The Infection Analytics Program is a team of mathematicians, physicists and other quantitative specialists, working to understand infection and immunity. The group primarily works on HIV, malaria, and SARS-CoV-2 and has an outstanding track record of research, making a major contribution to the medical and biological sciences. These projects rely heavily on experimental data, and members of the Infection Analytics Program work closely with a number of experimental collaborators from across the globe. Students who join the group will be trained in interdisciplinary research with a strong emphasis on using mathematical and quantitative approaches, as well as experimental and clinical data to better understand topics in infection and immunity, such as how antimalarials alter the course of malaria infection, how to optimise treatment for HIV, how vaccines for SARS-CoV-2 boost immunity, and how immunity affects the progression of all three of these infections.

Scholarships

Applicants are sought for both domestic and international student scholarships for PhD studies commencing in 2022. Student scholarships of up to $38,000-41,000 p.a. are available for a duration of 3.5 years (depending on undergraduate performance).

Applicant Requirements

The Infection Analytics Program at Kirby Institute is an ideal group for students with a quantitative background (mathematics / physics / statistics) aiming to diversify their existing experience in mathematical biology or considering a career change from another quantitative science to mathematical biology.

The scholarships are highly competitive. For local students, first class honours is usually required. For international students, first class honours, a high GPA (>87%) and high ranking in graduate class (top 1-2 in year) in Bachelors degree as well as research experience (>6 month research project) is required. These criteria should be directly addressed in any enquiries on the scholarships.

How to apply

For students to commence in 2022 Term 3 (September), applications are due January 25th. Applications to commence Term 1 2023 (February) will be due April 29th.

Please apply by providing your academic transcripts, CV, and cover letter addressing the eligibility criteria (listed above) to Professor Miles Davenport (m.davenport@unsw.edu.au) or Dr. David Khoury (david.khoury@unsw.edu.au)

PhD scholarship on game theory and fundamental social and biological interactions@Victoria University of Wellington

  • Full tuition fees
  • Stipend of NZ$28,500 per year (tax free)
  • Due date: Applications will be considered until the position is filled. Applications received by Friday 21 January 2022 will receive full consideration.
  • Start date: Start date is flexible but would preferably be between January and June 2022.

Applications are invited for a fully funded PhD scholarship to examine fundamental social and biological interactions using game theory.

Do you want to know why fundamental aspects of social and biological interactions are the way they are? Such as why sexual reproduction nearly always requires two different sexes. And why money is pretty much ubiquitous in human societies.

We do! We see the world through the lens of evolutionary game theory with stochastic interacting agents. They all want to get the best for themselves, and somehow self-organise to find equilibria where nobody is too unhappy.

Constructing and analysing these games requires maths, computer science, and some knowledge of the system we are evolving, which might be the evolution of oogamy, or more generally cooperation within groups. Or something else that’s equally exciting… That’s where you might come in.

For more information and application details, please see this page.

PhD scholarship on modelling spreading processes on real-world networks@UAuckland

  • Full tuition fees
  • Stipend of NZ$28,500 per year (tax free)
  • Due date: Applications will be considered until the position is filled. Applications received by 15 January 2022 will receive full consideration.
  • Start date: Start date is flexible but would preferably be between March and June 2022

Applications are invited for a fully-funded PhD studentship to work on a project modelling and understanding spreading processes on multilayer and multiplex networks.

There is growing understanding that spreading processes on real-world networks are typically moderated or influenced by additional factors, which themselves occur on networks and with feedback loops between the processes on the two networks. These dual spreading processes can occur either across a single node set with multiple edge types (multiplex networks), or multiple distinct node sets, with different edge types within and between the node sets (multilayer networks).

This project aims to understand how the outcomes of spreading processes are affected by the multilayer and multiplex network structures and by different network topologies arising in different applications, for example, by considering how behavioural dynamics can affect contagion in networks of epidemic spread.

You will combine mathematical modelling and dynamical systems methods with practical applications using concrete data to understand the role of social factors in epidemic spread and to investigate the dynamics of these processes.

For more information and application details, please see this page.

Ph.D. position in topological/computational group theory@UNewcastle

A Ph.D. position is available to work with Dr Stephan Tornier and other members of the Zero-Dimensional Symmetry Research Group at The University of Newcastle on the ARC DECRA project “Effective classification of closed vertex-transitive groups acting on trees”.

Candidates with a strong interest and demonstrated skills in at least one of the following areas are encouraged to apply: (topological) group theory, computational algebra (e.g. with GAP), graph theory, combinatorics.

Please direct expressions of interest to stephan.tornier@newcastle.edu.au by January 31, 2021

See https://zerodimensional.group/news/phd_advert.html for further details.

PhD Top-up Scholarships: Ocean and Sea Ice Modelling

Closing date: 30 November 2021

Are you interested in understanding ocean physics, and do you have skills in computational/mathematical modelling?

The Consortium for Ocean-Sea Ice Modelling in Australia (COSIMA) is providing opportunities for PhD
students to work at the intersection of high-performance computing and ocean-climate dynamics.
Projects are available focusing on a wide range of topics, including:

  1. The role of sea ice in the climate system;
  2. Modelling biogeochemical cycles in the global ocean;
  3. Coupling between surface waves and large-scale currents;
  4. Antarctic ice shelves and their interaction with the Southern Ocean; and
  5. The sensitivity of ocean dynamics to vertical coordinate systems in ocean models.

These scholarships are valued at $7,500 per year for 3.5 years. Successful applicants will also need to be
successful in receiving a Research Training Program (RTP) scholarship, or equivalent primary scholarship,
at a COSIMA partner university (ANU, UNSW, UTas, USyd, UniMelb or U Adelaide).

To Apply, you should submit a package to Ms Alina Bryleva including:

  • A half-page statement explaining your research interests and your planned work with COSIMA.
  • Your CV and academic transcripts.
  • Provide amount and source of any existing scholarships, both top-ups and a primary stipend.

These top-up scholarships are intended primarily for new students, however existing students working on one of the COSIMA models will also be considered. Preference will be given to competitive applicants who do not already receive a top-up scholarship from another source.

Enquiries: Please contact Professor Andrew Hogg

4-year industry PhD scholarship+top-up on online misinformation detection@Uni Adelaide

School of Mathematical Sciences, University of Adelade

Closing date: COB 28 October 2021

The spread of misinformation online is believed to be driven in part by non­human actors: algorithms and bots, often coordinated offshore. Recent research has developed algorithms for identifying such bots through measures of coordination: accounts that post to social media at similar times, or with similar, recognisable patterns of behaviour. State-of-the-art approaches to bot detection nonetheless use relatively naive social media analytics and measures, and not using the full extent of information (e.g., network structure and full post content) available. This project will develop new measures of social information flow to understand the extent of online social influence, and build new tools to counter malicious coordinated behavior, in real time.

4-year PhD stipend ($28,597 p/a) plus $12,500 p/a (Supplementary Scholarship, indexed annually); includes internship with Defence Science and Technology Group (DSTG). Applicants must be Australian citizens able to obtain security clearance. Applications for this UAiPhD project should be submitted to Associate Professor Lewis Mitchell by no later than COB 28 October 2021.

https://scholarships.adelaide.edu.au/Scholarships/postgraduate-research/faculty-of-engineering-computer-and-mathematical-sciences-35

PhD top-up scholarship suitable for applied maths/stats@ANU

Computational methods for pupil-based disease diagnostics

Pupils are a diagnostic window onto the eye and brain circuits that govern their movements and hold the promise of contactless disease screening. However, the journey from pupil response to disease biomarker is a challenging road paved with complicated computational methods and ingenious visual stimulus design. A biomarker refers to a characteristic that is objectively measured and evaluated as an indicator of normal biological processes, pathogenic processes, or pharmacologic responses to a therapeutic intervention (US National Institutes of Health. Biomarkers Definitions Working Group, 1998). When combined with computational methods to allow systematic data analyses at scale to discover disease, immune, and treatment-response signatures, biomarkers can be used to develop novel diagnostics.We seek a PhD candidate with a background in computer science, computational neuroscience, or applied mathematics to join a multidisciplinary team developing novel algorithms that transform pupil-diameter time series to biomarkers for disease. Students with strong analytic and programming abilities combined with an interest in solving big health problems through engineering are encouraged to apply.The position would jointly supervised by Dr Elena Daskalaki and Dr Josh van Kleef and attract a generous top-up scholarship of $10K p.a. for 3 years provided by our commercial partner (Konan Medical USA). It is expected that suitable candidates would have qualified for an Australian Postgraduate Award or equivalent scholarship for international candidates.This research will be delivered in partnership with Our Health in Our Hands (OHIOH), a strategic initiative of the Australian National University, which aims to transform healthcare by developing new personalised health technologies and solutions in collaboration with patients, clinicians, and health care providers. Research undertaken by the group has already resulted in a number of patents, so there is strong potential for commercial applications arising from this project.

Team

  • A/Prof. Hanna Suominen (ANU School of Computing)
  • Prof. Ted Maddess (JCSMR)
  • Dr. Elena Daskalaki (ANU School of Computing)
  • Dr. Josh van Kleef (JCSMR)

References and Reading Recommendations

  • Carle, C.F., James, A.C., Kolic, M., Loh, Y.W. and Maddess, T., 2011. High-resolution multifocal pupillographic objective perimetry in glaucoma. Investigative Ophthalmology & Visual Science, 52(1), pp.604-610.
  • Carle, C.F., James, A.C., Rosli, Y. and Maddess, T., 2019. Localization of neuronal gain control in the pupillary response. Frontiers in neurology, 10, p.203.
  • James, A.C., Ruseckaite, R. and Maddess, T., 2005. Effect of temporal sparseness and dichoptic presentation on multifocal visual evoked potentials. Visual Neuroscience, 22(1), p.45.
  • Maddess, T.L., James, A.C. and Carle, C.F., Australian National University, 2017. Clustered volley method and apparatus. U.S. Patent 9,848,771.

ApplicationsTo express your interest in this PhD scholarship, please email the following documents to Josh van Kleef:

  • Current CV
  • Research proposal (max 2 pages)
  • Colour copies of all transcripts and completion certificates of prior study, in original language and  official English translations
  • Contact details for 3 referees.

https://cecs.anu.edu.au/research/student-research-projects/what-our-eyes-can-tell-about-our-health-0

COVID-19: vaccines and variants

(This is a guest post by Dr Freya Shearer, 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.)

In the latter part of 2020, two key events shifted the course of the COVID-19 pandemic: the availability of vaccines and the emergence of variants of concern. 

A key question that rose up the agenda for policy makers — to what extent can vaccines mitigate the impacts of COVID-19, especially in the context of variants of concern? 

Due to the many nuances and uncertainties in estimating the future impacts of vaccination, ongoing monitoring of SARS-CoV-2 epidemiology in Australia while vaccines continue to roll out is critical to adaptive policy making. 

One of my roles in the COVID-19 response is to help provide epidemic situational assessment to Australian states and territories. As part of this, I have been coordinating (with Dr David Price) weekly (at least) situation reports submitted to the Communicable Disease Network of Australia (CDNA) and the Australian Health Protection Principal Committee (AHPPC) since April 2020. Each week the content of these reports represents a huge team effort – led by Professor James McCaw, an expert member of AHPPC (see the first essay in this series). A large nationally distributed group of mathematical and statistical modellers conduct analyses of trends in population behaviours (using mobility data from technology companies and anonymous population surveys), the effective reproduction number (using case data) and forecasts of daily case counts and hospital occupancy. We also estimate the propensity for the virus to spread based on behavioural data and the biological characteristics of SARS-CoV-2 [1]. A weekly summary is published in the government’s Common Operating Picture.  

It has been an enormous privilege to develop new analyses and metrics alongside policymakers to meet information needs specific to our context — for example, understanding the risk of epidemic activity during sustained periods of zero cases and an ongoing risk of importation(s). 

Over the past six months, the situational assessment teams have been continually adapting and extending their models to account for the differential impacts of new variants and vaccine products, and multiple co-circulating variants. 

Vaccines can act on multiple elements of transmission and/or disease. They can reduce:

  • Susceptibility to infection
  • The probability of onward transmission from immunised infected individuals
  • The probability of developing symptoms given infection
  • The probability of developing severe disease and death given infection

The COVID-19 vaccines registered for use in Australia are highly effective at reducing susceptibility to infection and onward transmission from immunised infected individuals for the Alpha variant. The resulting overall reductions in transmissibility are estimated to be > 90%. 

These vaccines also dramatically reduce the probability that immunised infected individuals will develop severe disease (> 85% estimated reduction) or die from their infection (also > 85% estimated reduction). However, vaccine efficacy is specific to each vaccine product and pathogen strain. At the time of writing, the Delta variant was set to become the dominant circulating SARS-CoV-2 strain globally. Early data shows decreased efficacy of our vaccines against the Delta variant (more on this later). 

Above and beyond the direct benefits of vaccination, everyone—vaccinated and unvaccinated—indirectly benefits from reduced exposure because others are vaccinated. This protection is a consequence of the reduction in disease transmission brought by the depletion of fully susceptible people (see the first essay in this series by Professor James McCaw for an explanation on the role of susceptible depletion). 

This indirect protection is important because even highly effective vaccines are imperfect; there is still a chance of severe disease and death for fully vaccinated people. Further, some people are unable to be vaccinated, due to underlying health issues for example.  

The level of vaccination coverage required to prevent sustained disease transmission is the critical vaccination or ‘herd immunity’ threshold. This threshold will vary according to pathogen transmissibility, vaccine efficacy, the population groups prioritised for vaccination, and levels of population mixing, among other factors. Higher pathogen transmissibility will increase the required level of coverage, while higher vaccine efficacy will decrease the required level of coverage. 

More specifically, the proportion of a homogeneously mixing population that would need to be vaccinated to prevent sustained transmission is given by (1–1/R0)/ε, where R0 is the “basic reproduction number”, the number of secondary cases arising from an index case in an otherwise fully susceptible population, and ε is the proportional vaccine efficacy at reducing transmission.  

Given an R0 value in many countries for wildtype SARS-CoV-2 of between 3 and 4, if we assume that vaccine efficacy is 90%, then the critical vaccination coverage becomes 75-85%. The Alpha variant is estimated to be around 50% more transmissible than wild type. This increases the critical vaccination threshold to 85–95%.

Early evidence suggests that the Delta variant is between 30 and 60% more transmissible than Alpha and may partially evade vaccine- and naturally-derived immunity. The critical vaccination threshold for a strain exhibiting such characteristics is nearing 100%, though we would expect significant population protection at lower vaccination levels and effective management of transmission. Due to the relatively short circulation period of Delta, very limited evidence is available on clinical severity and vaccine effectiveness against clinical outcomes. Early available data suggests lower vaccine effectiveness against the Delta variant compared to Alpha for most outcomes. 

The above simple calculations ignore important population heterogeneities that would make estimates higher or lower in specific settings. There are uncertainties in the transmissibility of Delta, indeed of any SARS-CoV-2 variant, including how it might vary geographically (even within Australia).  

An important part of our research is to adapt the above calculations to include a range of age-specific heterogeneities. The level of transmission reduction and protection against clinical outcomes achievable for a given population level of coverage depends on which sub-populations are prioritised for vaccination and differences in disease characteristics and social behaviours across different groups. 

The probability of hospitalisation, ICU admission and death given SARS-CoV-2 infection increases sharply with age, which is why vaccination programs in many countries have initially prioritised the oldest age groups.     

Groups at the highest risk of severe outcomes receive indirect protection through the vaccination of key transmitting population groups. Not all age groups contribute equally to transmission. Contributions vary because of different social contact rates, susceptibilities to infection and symptomatic fractions (which affect infectiousness) by age. For SARS-CoV-2, evidence suggests that susceptibility to infection and propensity to develop symptoms increases with age. Younger people and working age groups typically have more social contacts than older people.  

After accounting for all these factors, key transmitting ages for SARS-CoV-2 are estimated to be those aged 20–60 years. Whilst people under 20 have the highest numbers of contacts, they are less likely to spread SARS-CoV-2 to those contacts. People over 60 are more likely to spread SARS-CoV-2 to their contacts but typically have fewer contacts. People aged 20–60 have both relatively high numbers of contacts and ability to spread the disease. Thus, high coverage in these age groups is important for mitigating transmission and clinical outcomes. 

Future emerging variants are a key uncertainty in our ongoing management of COVID-19. With the emergence of each novel variant of concern, an early priority is to gather information on critical epidemiological indicators. What is its relative transmissibility compared to existing variants? What is the probability of severe illness given infection with the new variant? Does this vary by age group? What is the effectiveness of vaccines against the new variant? Does this differ by vaccine product? 

Estimating these quantities is extremely difficult in the early stages of variant emergence when information is scarce and detection efforts are highly varied and rapidly changing. Yet response planning/decisions are required before complete information is available. To support these decisions, analyses are made using the limited available data and must be continually reviewed and updated as evidence emerges.  

Ongoing global circulation of COVID-19, and global vaccine inequity mean that new variants will continue to emerge. Some of these variants will likely exhibit some combination of higher transmissibility, higher clinical severity and/or immune evasion. New vaccines/boosters will likely be needed to protect against such future variants. Response planning is designed to be adaptable to this continually evolving situation and many possible futures. For now, vaccination programs globally will continue to reduce transmission and harms related to COVID-19, together with public health and social measures.

Reference

[1] Nick Golding et al, Situational assessment of COVID-19 in Australia Technical Report 15 March 2021 (released 28 May 2021), https://www.doherty.edu.au/uploads/content_doc/Technical_Report_15_March_2021_RELEASED_VERSION.pdf

Scholarship opportunity: Kerry Landman Scholarship at the University of Melbourne

This scholarship will be available again in 2022, with applications opening on 1 October 2021, and I hope you may be able to assist in sharing this valuable opportunity through any appropriate channels you may have.

The Kerry Landman Scholarship supports high-achieving mathematics graduates that demonstrate a passion for education and wish to train as mathematics teachers. This scholarship is valued at up to $60,000 in total and students with a mathematics major who are enrolling in a Master of Teaching (Secondary) at the Melbourne Graduate School of Education are encouraged to apply. This scholarship aims to address the shortage of mathematically trained teachers who can passionately communicate the beauty and applications of mathematics to encourage, inspire and empower students to succeed. A successful candidate will have the potential to become a leader in a mathematics education.

Further detail regarding the scholarship can be found here.

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.