School of Mathematics and Statistics - Research Publications

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    Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields
    Lachieze-Rey, R ; Muirhead, S ( 2021-11-17)
    We study _ne properties of the convergence of a high intensity shot noise _eld towards the Gaussian _eld with the same covariance structure. In particular we (i) establish a strong invariance principle, i.e. a quantitative coupling between a high intensity shot noise _eld and the Gaussian limit such that they are uniformly close on large domains with high probability, and (ii) use this to derive an asymptotic expansion for the critical level above which the excursion sets of the shot noise _eld percolate.
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    Fluctuations of the number of excursion sets of planar Gaussian fields
    Beliaev, D ; McAuley, M ; Muirhead, S ( 2019-08-28)
    For a smooth, stationary, planar Gaussian field, we consider the number of connected components of its excursion set (or level set) contained in a large square of area R2. The mean number of components is known to be of order R2 for generic fields and all levels. We show that for certain fields with positive spectral density near the origin (including the Bargmann-Fock field), and for certain levels ℓ, these random variables have fluctuations of order at least R, and hence variance of order at least R2. In particular this holds for excursion sets when ℓ is in some neighbourhood of zero, and it holds for excursion/level sets when ℓ is sufficiently large. We prove stronger fluctuation lower bounds of order Rα, α ∈ [1, 2], in the case that the spectral density has a singularity at the origin. Finally we show that the number of excursion/level sets for the Random Plane Wave at certain levels has fluctuations of order at least R3/2, and hence variance of order at least R3. We expect that these bounds are of the correct order, at least for generic levels.
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    Assessing the risk of spread of COVID-19 to the Asia Pacific region
    Shearer, F ; Walker, J ; Tellioglu, N ; McCaw, J ; McVernon, J ; Black, A ; Geard, N ( 2020)
    During the early stages of an emerging disease outbreak, governments are required to make critical decisions on how to respond appropriately, despite limited data being available to inform these decisions. Analytical risk assessment is a valuable approach to guide decision-making on travel restrictions and border measures during the early phase of an outbreak, when transmission is primarily contained within a source country. Here we introduce a modular framework for estimating the importation risk of an emerging disease when the direct travel route is restricted and the risk stems from indirect importation via intermediary countries. This was the situation for Australia in February 2020. The framework was specifically developed to assess the importation risk of COVID-19 into Australia during the early stages of the outbreak from late January to mid-February 2020. The dominant importation risk to Australia at the time of analysis was directly from China, as the only country reporting uncontained transmission. However, with travel restrictions from mainland China to Australia imposed from February 1, our framework was designed to consider the importation risk from China into Australia via potential intermediary countries in the Asia Pacific region. The framework was successfully used to contribute to the evidence base for decisions on border measures and case definitions in the Australian context during the early phase of COVID-19 emergence and is adaptable to other contexts for future outbreak response.
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    Modelling the impact of COVID-19 in Australia to inform transmission reducing measures and health system preparedness
    Moss, R ; Wood, J ; Brown, D ; Shearer, F ; Black, AJ ; Cheng, AC ; McCaw, JM ; McVernon, J ( 2020)



    The ability of global health systems to cope with increasing numbers of COVID-19 cases is of major concern. In readiness for this challenge, Australia has drawn on clinical pathway models developed over many years in preparation for influenza pandemics. These models have been used to estimate health care requirements for COVID-19 patients, in the context of broader public health measures.


    An age and risk stratified transmission model of COVID-19 infection was used to simulate an unmitigated epidemic with parameter ranges reflecting uncertainty in current estimates of transmissibility and severity. Overlaid public health measures included case isolation and quarantine of contacts, and broadly applied social distancing. Clinical presentations and patient flows through the Australian health care system were simulated, including expansion of available intensive care capacity and alternative clinical assessment pathways.


    An unmitigated COVID-19 epidemic would dramatically exceed the capacity of the Australian health system, over a prolonged period. Case isolation and contact quarantine alone will be insufficient to constrain case presentations within a feasible level of expansion of health sector capacity. Overlaid social restrictions will need to be applied at some level over the course of the epidemic to ensure that systems do not become overwhelmed, and that essential health sector functions, including care of COVID-19 patients, can be maintained. Attention to the full pathway of clinical care is needed to ensure access to critical care.


    Reducing COVID-19 morbidity and mortality will rely on a combination of measures to strengthen and extend public health and clinical capacity, along with reduction of overall infection transmission in the community. Ongoing attention to maintaining and strengthening the capacity of health care systems and workers to manage cases is needed.


    Australian Government Department of Health Office of Health Protection, Australian Government National Health and Medical Research Council