School of Mathematics and Statistics - Research Publications

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    COVID-19 vaccine coverage targets to inform reopening plans in a low incidence setting.
    Conway, E ; Walker, CR ; Baker, C ; Lydeamore, MJ ; Ryan, GE ; Campbell, T ; Miller, JC ; Rebuli, N ; Yeung, M ; Kabashima, G ; Geard, N ; Wood, J ; McCaw, JM ; McVernon, J ; Golding, N ; Price, DJ ; Shearer, FM (The Royal Society, 2023-08-30)
    Since the emergence of SARS-CoV-2 in 2019 through to mid-2021, much of the Australian population lived in a COVID-19-free environment. This followed the broadly successful implementation of a strong suppression strategy, including international border closures. With the availability of COVID-19 vaccines in early 2021, the national government sought to transition from a state of minimal incidence and strong suppression activities to one of high vaccine coverage and reduced restrictions but with still-manageable transmission. This transition is articulated in the national 're-opening' plan released in July 2021. Here, we report on the dynamic modelling study that directly informed policies within the national re-opening plan including the identification of priority age groups for vaccination, target vaccine coverage thresholds and the anticipated requirements for continued public health measures-assuming circulation of the Delta SARS-CoV-2 variant. Our findings demonstrated that adult vaccine coverage needed to be at least 60% to minimize public health and clinical impacts following the establishment of community transmission. They also supported the need for continued application of test-trace-isolate-quarantine and social measures during the vaccine roll-out phase and beyond.
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    Individual variation in vaccine immune response can produce bimodal distributions of protection
    Zachreson, C ; Tobin, R ; Szanyi, J ; Walker, C ; Cromer, D ; Shearer, FM ; Conway, E ; Ryan, G ; Cheng, A ; McCaw, JM ; Geard, N (ELSEVIER SCI LTD, 2023-10-26)
    The ability for vaccines to protect against infectious diseases varies among individuals, but computational models employed to inform policy typically do not account for this variation. Here we examine this issue: we implement a model of vaccine efficacy developed in the context of SARS-CoV-2 in order to evaluate the general implications of modelling correlates of protection on the individual level. Due to high levels of variation in immune response, the distributions of individual-level protection emerging from this model tend to be highly dispersed, and are often bimodal. We describe the specification of the model, provide an intuitive parameterisation, and comment on its general robustness. We show that the model can be viewed as an intermediate between the typical approaches that consider the mode of vaccine action to be either "all-or-nothing" or "leaky". Our view based on this analysis is that individual variation in correlates of protection is an important consideration that may be crucial to designing and implementing models for estimating population-level impacts of vaccination programs.
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    Choice of spatial discretisation influences the progression of viral infection within multicellular tissues
    Williams, T ; McCaw, JM ; Osborne, JM (ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2023-09-21)
    There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are simulated by discretising the viral surface and depending on the rate of viral diffusion and other considerations, a finer or coarser discretisation may be used. The impact that this choice may have on the behaviour of the system has not been studied. Here we demonstrate that under realistic parameter regimes - where viral diffusion is small enough to support the formation of familiar ring-shaped infection plaques - the choice of spatial discretisation of the viral surface can qualitatively change key model outcomes including the time scale of infection. Importantly, we show that the choice between implementing viral spread as a cell-scale process, or as a high-resolution converged PDE can generate distinct model outcomes, which raises important conceptual questions about the strength of assumptions underpinning the spatial structure of the model. We investigate the mechanisms driving these discretisation artefacts, the impacts they may have on model predictions, and provide guidance on the design and implementation of spatial and especially multicellular models of viral dynamics. We obtain our results using the simplest TIV construct for the viral dynamics, and therefore anticipate that the important effects we describe will also influence model predictions in more complex models of virus-cell-immune system interactions. This analysis will aid in the construction of models for robust and biologically realistic modelling and inference.
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    Stochastic Modeling of Within-Host Dynamics of Plasmodium Falciparum
    Sun, X ; McCaw, JM ; Cao, P (MDPI, 2022-11)
    Malaria remains a major public health burden in South-East Asia and Africa. Mathematical models of within-host infection dynamics and drug action, developed in support of malaria elimination initiatives, have significantly advanced our understanding of the dynamics of infection and supported development of effective drug-treatment regimens. However, the mathematical models supporting these initiatives are predominately based on deterministic dynamics and therefore cannot capture stochastic phenomena such as extinction (no parasitized red blood cells) following treatment, with potential consequences for our interpretation of data sets in which recrudescence is observed. Here we develop a stochastic within-host infection model to study the growth, decline and possible stochastic extinction of parasitized red blood cells in malaria-infected human volunteers. We show that stochastic extinction can occur when the inoculation size is small or when the number of parasitized red blood cells reduces significantly after an antimalarial treatment. We further show that the drug related parameters, such as the maximum killing rate and half-maximum effective concentration, are the primary factors determining the probability of stochastic extinction following treatment, highlighting the importance of highly-efficacious antimalarials in increasing the probability of cure for the treatment of malaria patients.
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    Forecasting COVID-19 activity in Australia to support pandemic response: May to October 2020
    Moss, R ; Price, DJ ; Golding, N ; Dawson, P ; McVernon, J ; Hyndman, RJ ; Shearer, FM ; McCaw, JM (NATURE PORTFOLIO, 2023-05-30)
    As of January 2021, Australia had effectively controlled local transmission of COVID-19 despite a steady influx of imported cases and several local, but contained, outbreaks in 2020. Throughout 2020, state and territory public health responses were informed by weekly situational reports that included an ensemble forecast of daily COVID-19 cases for each jurisdiction. We present here an analysis of one forecasting model included in this ensemble across the variety of scenarios experienced by each jurisdiction from May to October 2020. We examine how successfully the forecasts characterised future case incidence, subject to variations in data timeliness and completeness, showcase how we adapted these forecasts to support decisions of public health priority in rapidly-evolving situations, evaluate the impact of key model features on forecast skill, and demonstrate how to assess forecast skill in real-time before the ground truth is known. Conditioning the model on the most recent, but incomplete, data improved the forecast skill, emphasising the importance of developing strong quantitative models of surveillance system characteristics, such as ascertainment delay distributions. Forecast skill was highest when there were at least 10 reported cases per day, the circumstances in which authorities were most in need of forecasts to aid in planning and response.
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    Hypnozoite dynamics for Plasmodium vivax malaria: The epidemiological effects of radical cure
    Mehra, S ; Stadler, E ; Khoury, D ; McCaw, JM ; Flegg, JA (ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2022-03-21)
    Malaria is a mosquito-borne disease with a devastating global impact. Plasmodium vivax is a major cause of human malaria beyond sub-Saharan Africa. Relapsing infections, driven by a reservoir of liver-stage parasites known as hypnozoites, present unique challenges for the control of P. vivax malaria. Following indeterminate dormancy periods, hypnozoites may activate to trigger relapses. Clearance of the hypnozoite reservoir through drug treatment (radical cure) has been proposed as a potential tool for the elimination of P. vivax malaria. Here, we introduce a stochastic, within-host model to jointly characterise hypnozoite and infection dynamics for an individual in a general transmission setting, allowing for radical cure. We begin by extending an existing activation-clearance model for a single hypnozoite, adapted to both short- and long-latency strains, to include drug treatment. We then embed this activation-clearance model in an epidemiological framework accounting for repeated mosquito inoculation and the administration of radical cure. By constructing an open network of infinite server queues, we derive analytic expressions for several quantities of epidemiological significance, including the size of the hypnozoite reservoir; the relapse rate; the relative contribution of relapses to the infection burden; the distribution of multiple infections; the cumulative number of recurrences over time, and the time to first recurrence following drug treatment. We derive from first principles the functional dependence between within-host and transmission parameters and patterns of blood- and liver-stage infection, whilst allowing for treatment under a mass drug administration regime. To yield population-level insights, our analytic within-host distributions can be embedded in multiscale models. Our work thus contributes to the epidemiological understanding of the effects of radical cure on P. vivax malaria.
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    A model for malaria treatment evaluation in the presence of multiple species
    Walker, CR ; Hickson, RI ; Chang, E ; Ngor, P ; Sovannaroth, S ; Simpson, JA ; Price, DJ ; McCaw, JM ; Price, RN ; Flegg, JA ; Devine, A (ELSEVIER, 2023-09)
    Plasmodium falciparum and P. vivax are the two most common causes of malaria. While the majority of deaths and severe morbidity are due to P. falciparum, P. vivax poses a greater challenge to eliminating malaria outside of Africa due to its ability to form latent liver stage parasites (hypnozoites), which can cause relapsing episodes within an individual patient. In areas where P. falciparum and P. vivax are co-endemic, individuals can carry parasites of both species simultaneously. These mixed infections complicate dynamics in several ways: treatment of mixed infections will simultaneously affect both species, P. falciparum can mask the detection of P. vivax, and it has been hypothesised that clearing P. falciparum may trigger a relapse of dormant P. vivax. When mixed infections are treated for only blood-stage parasites, patients are at risk of relapse infections due to P. vivax hypnozoites. We present a stochastic mathematical model that captures interactions between P. falciparum and P. vivax, and incorporates both standard schizonticidal treatment (which targets blood-stage parasites) and radical cure treatment (which additionally targets liver-stage parasites). We apply this model via a hypothetical simulation study to assess the implications of different treatment coverages of radical cure for mixed and P. vivax infections and a "unified radical cure" treatment strategy where P. falciparum, P. vivax, and mixed infections all receive radical cure after screening glucose-6-phosphate dehydrogenase (G6PD) normal. In addition, we investigated the impact of mass drug administration (MDA) of blood-stage treatment. We find that a unified radical cure strategy leads to a substantially lower incidence of malaria cases and deaths overall. MDA with schizonticidal treatment was found to decrease P. falciparum with little effect on P. vivax. We perform a univariate sensitivity analysis to highlight important model parameters.
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    Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration
    Anwar, MN ; Hickson, RI ; Mehra, S ; Price, DJ ; McCaw, JM ; Flegg, MB ; Flegg, JA (SPRINGER, 2023-06)
    Plasmodium vivax is the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. One of the factors driving this widespread phenomenon is the ability of the parasites to remain dormant in the liver. Known as 'hypnozoites', they reside in the liver following an initial exposure, before activating later to cause further infections, referred to as 'relapses'. As around 79-96% of infections are attributed to relapses from activating hypnozoites, we expect it will be highly impactful to apply treatment to target the hypnozoite reservoir (i.e. the collection of dormant parasites) to eliminate P. vivax. Treatment with radical cure, for example tafenoquine or primaquine, to target the hypnozoite reservoir is a potential tool to control and/or eliminate P. vivax. We have developed a deterministic multiscale mathematical model as a system of integro-differential equations that captures the complex dynamics of P. vivax hypnozoites and the effect of hypnozoite relapse on disease transmission. Here, we use our multiscale model to study the anticipated effect of radical cure treatment administered via a mass drug administration (MDA) program. We implement multiple rounds of MDA with a fixed interval between rounds, starting from different steady-state disease prevalences. We then construct an optimisation model with three different objective functions motivated on a public health basis to obtain the optimal MDA interval. We also incorporate mosquito seasonality in our model to study its effect on the optimal treatment regime. We find that the effect of MDA interventions is temporary and depends on the pre-intervention disease prevalence (and choice of model parameters) as well as the number of MDA rounds under consideration. The optimal interval between MDA rounds also depends on the objective (combinations of expected intervention outcomes). We find radical cure alone may not be enough to lead to P. vivax elimination under our mathematical model (and choice of model parameters) since the prevalence of infection eventually returns to pre-MDA levels.
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    Real-time analysis of hospital length of stay in a mixed SARS-CoV-2 Omicron and Delta epidemic in New South Wales, Australia
    Tobin, RJJ ; Wood, JGG ; Jayasundara, D ; Sara, G ; Walker, CRR ; Martin, GEE ; McCaw, JMM ; Shearer, FMM ; Price, DJJ (BMC, 2023-01-17)
    BACKGROUND: The distribution of the duration that clinical cases of COVID-19 occupy hospital beds (the 'length of stay') is a key factor in determining how incident caseloads translate into health system burden. Robust estimation of length of stay in real-time requires the use of survival methods that can account for right-censoring induced by yet unobserved events in patient progression (e.g. discharge, death). In this study, we estimate in real-time the length of stay distributions of hospitalised COVID-19 cases in New South Wales, Australia, comparing estimates between a period where Delta was the dominant variant and a subsequent period where Omicron was dominant. METHODS: Using data on the hospital stays of 19,574 individuals who tested positive to COVID-19 prior to admission, we performed a competing-risk survival analysis of COVID-19 clinical progression. RESULTS: During the mixed Omicron-Delta epidemic, we found that the mean length of stay for individuals who were discharged directly from ward without an ICU stay was, for age groups 0-39, 40-69 and 70 +, respectively, 2.16 (95% CI: 2.12-2.21), 3.93 (95% CI: 3.78-4.07) and 7.61 days (95% CI: 7.31-8.01), compared to 3.60 (95% CI: 3.48-3.81), 5.78 (95% CI: 5.59-5.99) and 12.31 days (95% CI: 11.75-12.95) across the preceding Delta epidemic (1 July 2021-15 December 2021). We also considered data on the stays of individuals within the Hunter New England Local Health District, where it was reported that Omicron was the only circulating variant, and found mean ward-to-discharge length of stays of 2.05 (95% CI: 1.80-2.30), 2.92 (95% CI: 2.50-3.67) and 6.02 days (95% CI: 4.91-7.01) for the same age groups. CONCLUSIONS: Hospital length of stay was substantially reduced across all clinical pathways during a mixed Omicron-Delta epidemic compared to a prior Delta epidemic, contributing to a lessened health system burden despite a greatly increased infection burden. Our results demonstrate the utility of survival analysis in producing real-time estimates of hospital length of stay for assisting in situational assessment and planning of the COVID-19 response.
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    A modelling approach to estimate the transmissibility of SARS-CoV-2 during periods of high, low, and zero case incidence
    Golding, N ; Price, DJ ; Ryan, G ; McVernon, J ; McCaw, JM ; Shearer, FM (eLIFE SCIENCES PUBL LTD, 2023-01-20)
    Against a backdrop of widespread global transmission, a number of countries have successfully brought large outbreaks of COVID-19 under control and maintained near-elimination status. A key element of epidemic response is the tracking of disease transmissibility in near real-time. During major outbreaks, the effective reproduction number can be estimated from a time-series of case, hospitalisation or death counts. In low or zero incidence settings, knowing the potential for the virus to spread is a response priority. Absence of case data means that this potential cannot be estimated directly. We present a semi-mechanistic modelling framework that draws on time-series of both behavioural data and case data (when disease activity is present) to estimate the transmissibility of SARS-CoV-2 from periods of high to low - or zero - case incidence, with a coherent transition in interpretation across the changing epidemiological situations. Of note, during periods of epidemic activity, our analysis recovers the effective reproduction number, while during periods of low - or zero - case incidence, it provides an estimate of transmission risk. This enables tracking and planning of progress towards the control of large outbreaks, maintenance of virus suppression, and monitoring the risk posed by re-introduction of the virus. We demonstrate the value of our methods by reporting on their use throughout 2020 in Australia, where they have become a central component of the national COVID-19 response.