School of Mathematics and Statistics - Research Publications
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ItemNo Preview AvailableEstimating measures to reduce the transmission of SARS-CoV-2 in Australia to guide a 'National Plan' to reopening.(Elsevier BV, 2024-03-19)The availability of COVID-19 vaccines promised a reduction in the severity of disease and relief from the strict public health and social measures (PHSMs) imposed in many countries to limit spread and burden of COVID-19. We were asked to define vaccine coverage thresholds for Australia's transition to easing restrictions and reopening international borders. Using evidence of vaccine effectiveness against the then-circulating Delta variant, we used a mathematical model to determine coverage targets. The absence of any COVID-19 infections in many sub-national jurisdictions in Australia posed particular methodological challenges. We used a novel metric called Transmission Potential (TP) as a proxy measure of the population-level effective reproduction number. We estimated TP of the Delta variant under a range of PHSMs, test-trace-isolate-quarantine (TTIQ) efficiencies, vaccination coverage thresholds, and age-based vaccine allocation strategies. We found that high coverage across all ages (≥70%) combined with ongoing TTIQ and minimal PHSMs was sufficient to avoid lockdowns. At lesser coverage (≤60%) rapid case escalation risked overwhelming of the health sector or the need to reimpose stricter restrictions. Maintaining low case numbers was most beneficial for health and the economy, and at higher coverage levels (≥80%) further easing of restrictions was deemed possible. These results directly informed easing of COVID-19 restrictions in Australia.
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ItemNo Preview AvailableEstimating the impact of test-trace-isolate-quarantine systems on SARS-CoV-2 transmission in Australia.(Elsevier BV, 2024-03-22)BACKGROUND: Australian states and territories used test-trace-isolate-quarantine (TTIQ) systems extensively in their response to the COVID-19 pandemic in 2020-2021. We report on an analysis of Australian case data to estimate the impact of test-trace-isolate-quarantine systems on SARS-CoV-2 transmission. METHODS: Our analysis uses a novel mathematical modelling framework and detailed surveillance data on COVID-19 cases including dates of infection and dates of isolation. First, we directly translate an empirical distribution of times from infection to isolation into reductions in potential for onward transmission during periods of relatively low caseloads (tens to hundreds of reported cases per day). We then apply a simulation approach, validated against case data, to assess the impact of case-initiated contact tracing on transmission during a period of relatively higher caseloads and system stress (up to thousands of cases per day). RESULTS: We estimate that under relatively low caseloads in the state of New South Wales (tens of cases per day), TTIQ contributed to a 54% reduction in transmission. Under higher caseloads in the state of Victoria (hundreds of cases per day), TTIQ contributed to a 42% reduction in transmission. Our results also suggest that case-initiated contact tracing can support timely quarantine in times of system stress (thousands of cases per day). CONCLUSION: Contact tracing systems for COVID-19 in Australia were highly effective and adaptable in supporting the national suppression strategy from 2020-21, prior to the emergence of the Omicron variant in November 2021. TTIQ systems were critical to the maintenance of the strong suppression strategy and were more effective when caseloads were (relatively) low.
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ItemNo Preview AvailableMathematical models of Plasmodium vivax transmission: A scoping review(PUBLIC LIBRARY SCIENCE, 2024-03)Plasmodium vivax is one of the most geographically widespread malaria parasites in the world, primarily found across South-East Asia, Latin America, and parts of Africa. One of the significant characteristics of the P. vivax parasite is its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. Models that capture P. vivax dynamics differ from those that capture P. falciparum dynamics, as they must account for relapses caused by the activation of hypnozoites. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023. The primary objective of this work is to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. In doing so, we aim to assist researchers working on mathematical epidemiology, disease transmission, and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where further model development is required. We categorise P. vivax models according to whether a deterministic or agent-based approach was used. We provide an overview of the different strategies used to incorporate the parasite's biology, use of multiple scales (within-host and population-level), superinfection, immunity, and treatment interventions. In most of the published literature, the rationale for different modelling approaches was driven by the research question at hand. Some models focus on the parasites' complicated biology, while others incorporate simplified assumptions to avoid model complexity. Overall, the existing literature on mathematical models for P. vivax encompasses various aspects of the parasite's dynamics. We recommend that future research should focus on refining how key aspects of P. vivax dynamics are modelled, including spatial heterogeneity in exposure risk and heterogeneity in susceptibility to infection, the accumulation of hypnozoite variation, the interaction between P. falciparum and P. vivax, acquisition of immunity, and recovery under superinfection.
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ItemSuperinfection and the hypnozoite reservoir for Plasmodium vivax: a general framework(SPRINGER HEIDELBERG, 2024-01)A characteristic of malaria in all its forms is the potential for superinfection (that is, multiple concurrent blood-stage infections). An additional characteristic of Plasmodium vivax malaria is a reservoir of latent parasites (hypnozoites) within the host liver, which activate to cause (blood-stage) relapses. Here, we present a model of hypnozoite accrual and superinfection for P. vivax. To couple host and vector dynamics for a homogeneously-mixing population, we construct a density-dependent Markov population process with countably many types, for which disease extinction is shown to occur almost surely. We also establish a functional law of large numbers, taking the form of an infinite-dimensional system of ordinary differential equations that can also be recovered by coupling expected host and vector dynamics (i.e. a hybrid approximation) or through a standard compartment modelling approach. Recognising that the subset of these equations that model the infection status of the human hosts has precisely the same form as the Kolmogorov forward equations for a Markovian network of infinite server queues with an inhomogeneous batch arrival process, we use physical insight into the evolution of the latter process to write down a time-dependent multivariate generating function for the solution. We use this characterisation to collapse the infinite-compartment model into a single integrodifferential equation (IDE) governing the intensity of mosquito-to-human transmission. Through a steady state analysis, we recover a threshold phenomenon for this IDE in terms of a parameter [Formula: see text] expressible in terms of the primitives of the model, with the disease-free equilibrium shown to be uniformly asymptotically stable if [Formula: see text] and an endemic equilibrium solution emerging if [Formula: see text]. Our work provides a theoretical basis to explore the epidemiology of P. vivax, and introduces a strategy for constructing tractable population-level models of malarial superinfection that can be generalised to allow for greater biological realism in a number of directions.
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ItemNo Preview AvailableCOVID-19 vaccine coverage targets to inform reopening plans in a low incidence setting(ROYAL SOC, 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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ItemNo Preview AvailableIndividual variation in vaccine immune response can produce bimodal distributions of protection(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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ItemChoice of spatial discretisation influences the progression of viral infection within multicellular tissues(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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ItemNo Preview AvailableStochastic Modeling of Within-Host Dynamics of Plasmodium Falciparum(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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ItemNo Preview AvailableForecasting COVID-19 activity in Australia to support pandemic response: May to October 2020(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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ItemNo Preview AvailableHypnozoite dynamics for Plasmodium vivax malaria: The epidemiological effects of radical cure(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.