School of Mathematics and Statistics - Research Publications

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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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    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 Multiscale Mathematical Model of Plasmodium Vivax Transmission
    Anwar, MN ; Hickson, RI ; Mehra, S ; McCaw, JM ; Flegg, JA (SPRINGER, 2022-08)
    Malaria is caused by Plasmodium parasites which are transmitted to humans by the bite of an infected Anopheles mosquito. Plasmodium vivax is distinct from other malaria species in its ability to remain dormant in the liver (as hypnozoites) and activate later to cause further infections (referred to as relapses). Mathematical models to describe the transmission dynamics of P. vivax have been developed, but most of them fail to capture realistic dynamics of hypnozoites. Models that do capture the complexity tend to involve many governing equations, making them difficult to extend to incorporate other important factors for P. vivax, such as treatment status, age and pregnancy. In this paper, we have developed a multiscale model (a system of integro-differential equations) that involves a minimal set of equations at the population scale, with an embedded within-host model that can capture the dynamics of the hypnozoite reservoir. In this way, we can gain key insights into dynamics of P. vivax transmission with a minimum number of equations at the population scale, making this framework readily scalable to incorporate more complexity. We performed a sensitivity analysis of our multiscale model over key parameters and found that prevalence of P. vivax blood-stage infection increases with both bite rate and number of mosquitoes but decreases with hypnozoite death rate. Since our mathematical model captures the complex dynamics of P. vivax and the hypnozoite reservoir, it has the potential to become a key tool to inform elimination strategies for P. vivax.
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    Estimation of the probability of epidemic fade-out from multiple outbreak data
    Alahakoon, P ; McCaw, JM ; Taylor, PG (ELSEVIER, 2022-03)
    Deterministic epidemic models that allow for replenishment of susceptibles typically display damped oscillatory behaviour. If the population is initially fully susceptible, once an epidemic takes off a distinct trough will exist between the first and second waves of infection. Epidemic dynamics are, however, influenced by stochastic effects, particularly when the prevalence is low. At the beginning of an epidemic, stochastic die-out is possible and well characterised through use of a branching process approximation. Conditional on an epidemic taking off, stochastic extinction is highly unlikely during the first epidemic wave, but the probability of extinction increases again as the wave declines. Extinction during this period, prior to a potential second wave of infection, is defined as 'epidemic fade-out'. We consider a set of observed epidemics, each distinct and having evolved independently, in which some display fade-out and some do not. While fade-out is necessarily a stochastic phenomenon, the probability of fade-out will depend on the model parameters associated with each epidemic. Accordingly, we ask whether time-series data for the epidemics contain sufficient information to identify the key driver(s) of different outcomes-fade-out or otherwise-across the sub-populations supporting each epidemic. We apply a Bayesian hierarchical modelling framework to synthetic data from an SIRS model of epidemic dynamics and demonstrate that we can (1) identify when the sub-population specific model parameters supporting each epidemic have significant variability and (2) estimate the probability of epidemic fade-out for each sub-population. We demonstrate that a hierarchical analysis can provide precise estimates of the probability of fade-out than is possible if considering each epidemic in isolation. Our methods may be applied to both epidemiological and other biological data to identify where differences in outcome-fade-out or recurrent infection/waves are purely due to chance or driven by underlying changes in the parameters driving the dynamics.
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    Rapid assessment of the risk of SARS-CoV-2 importation: case study and lessons learned
    Shearer, FM ; Walker, J ; Tellioglu, N ; McCaw, JM ; McVernon, J ; Black, A ; Geard, N (ELSEVIER, 2022-03)
    During the early stages of an emerging disease outbreak, governments are required to make critical decisions on how to respond, 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. Here we describe a rapid risk assessment framework that was developed in February 2020 to support time-critical decisions on the risk of SARS-CoV-2 importation into Australia. We briefly describe the context in which our framework was developed, the framework itself, and provide an example of the type of decision support provided to the Australian government. We then report a critical evaluation of the modelling choices made in February 2020, assessing the impact of our assumptions on estimated rates of importation, and provide a summary of "lessons learned". The framework presented and evaluated here provides a flexible approach to rapid assessment of importation risk, of relevance to current and future pandemic scenarios.
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    COVID-19 in low-tolerance border quarantine systems: Impact of the Delta variant of SARS-CoV-2
    Zachreson, C ; Shearer, FM ; Price, DJ ; Lydeamore, MJ ; McVernon, J ; McCaw, J ; Geard, N (AMER ASSOC ADVANCEMENT SCIENCE, 2022-04)
    In controlling transmission of coronavirus disease 2019 (COVID-19), the effectiveness of border quarantine strategies is a key concern for jurisdictions in which the local prevalence of disease and immunity is low. In settings like this such as China, Australia, and New Zealand, rare outbreak events can lead to escalating epidemics and trigger the imposition of large-scale lockdown policies. Here, we develop and apply an individual-based model of COVID-19 to simulate case importation from managed quarantine under various vaccination scenarios. We then use the output of the individual-based model as input to a branching process model to assess community transmission risk. For parameters corresponding to the Delta variant, our results demonstrate that vaccination effectively counteracts the pathogen's increased infectiousness. To prevent outbreaks, heightened vaccination in border quarantine systems must be combined with mass vaccination. The ultimate success of these programs will depend sensitively on the efficacy of vaccines against viral transmission.
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    From Climate Change to Pandemics: Decision Science Can Help Scientists Have Impact
    Baker, CM ; Campbell, PT ; Chades, I ; Dean, AJ ; Hester, SM ; Holden, MH ; McCaw, JM ; McVernon, J ; Moss, R ; Shearer, FM ; Possingham, HP (FRONTIERS MEDIA SA, 2022-02-14)
    Scientific knowledge and advances are a cornerstone of modern society. They improve our understanding of the world we live in and help us navigate global challenges including emerging infectious diseases, climate change and the biodiversity crisis. However, there is a perpetual challenge in translating scientific insight into policy. Many articles explain how to better bridge the gap through improved communication and engagement, but we believe that communication and engagement are only one part of the puzzle. There is a fundamental tension between science and policy because scientific endeavors are rightfully grounded in discovery, but policymakers formulate problems in terms of objectives, actions and outcomes. Decision science provides a solution by framing scientific questions in a way that is beneficial to policy development, facilitating scientists’ contribution to public discussion and policy. At its core, decision science is a field that aims to pinpoint evidence-based management strategies by focussing on those objectives, actions, and outcomes defined through the policy process. The importance of scientific discovery here is in linking actions to outcomes, helping decision-makers determine which actions best meet their objectives. In this paper we explain how problems can be formulated through the structured decision-making process. We give our vision for what decision science may grow to be, describing current gaps in methodology and application. By better understanding and engaging with the decision-making processes, scientists can have greater impact and make stronger contributions to important societal problems.
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    Development and Validation of an In Silico Decision Tool To Guide Optimization of Intravenous Artesunate Dosing Regimens for Severe Falciparum Malaria Patients
    Zaloumis, SG ; Whyte, JM ; Tarning, J ; Krishna, S ; McCaw, JM ; Cao, P ; White, MT ; Dini, S ; Fowkes, FJ ; Maude, RJ ; Kremsner, P ; Dondorp, A ; Price, RN ; White, NJ ; Simpson, JA (AMER SOC MICROBIOLOGY, 2021-06)
    Most deaths from severe falciparum malaria occur within 24 h of presentation to a hospital. Intravenous (i.v.) artesunate is the first-line treatment for severe falciparum malaria, but its efficacy may be compromised by delayed parasitological responses. In patients with severe malaria, the life-saving benefit of the artemisinin derivatives is their ability to clear circulating parasites rapidly, before they can sequester and obstruct the microcirculation. To evaluate the dosing of i.v. artesunate for the treatment of artemisinin-sensitive and reduced ring stage sensitivity to artemisinin severe falciparum malaria infections, Bayesian pharmacokinetic-pharmacodynamic modeling of data from 94 patients with severe malaria (80 children from Africa and 14 adults from Southeast Asia) was performed. Assuming that delayed parasite clearance reflects a loss of ring stage sensitivity to artemisinin derivatives, the median (95% credible interval) percentage of patients clearing ≥99% of parasites within 24 h (PC24≥99%) for standard (2.4 mg/kg body weight i.v. artesunate at 0 and 12 h) and simplified (4 mg/kg i.v. artesunate at 0 h) regimens was 65% (52.5% to 74.5%) versus 44% (25% to 61.5%) for adults, 62% (51.5% to 74.5%) versus 39% (20.5% to 58.5%) for larger children (≥20 kg), and 60% (48.5% to 70%) versus 36% (20% to 53.5%) for smaller children (<20 kg). The upper limit of the credible intervals for all regimens was below a PC24≥99% of 80%, a threshold achieved on average in clinical studies of severe falciparum malaria infections. In severe falciparum malaria caused by parasites with reduced ring stage susceptibility to artemisinin, parasite clearance is predicted to be slower with both the currently recommended and proposed simplified i.v. artesunate dosing regimens.
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    Development of an influenza pandemic decision support tool linking situational analytics to national response policy.
    Shearer, FM ; Moss, R ; Price, DJ ; Zarebski, AE ; Ballard, PG ; McVernon, J ; Ross, JV ; McCaw, JM (Elsevier, 2021-06-19)
    National influenza pandemic plans have evolved substantially over recent decades, as has the scientific research that underpins the advice contained within them. While the knowledge generated by many research activities has been directly incorporated into the current generation of pandemic plans, scientists and policymakers are yet to capitalise fully on the potential for near real-time analytics to formally contribute to epidemic decision-making. Theoretical studies demonstrate that it is now possible to make robust estimates of pandemic impact in the earliest stages of a pandemic using first few hundred household cohort (FFX) studies and algorithms designed specifically for analysing FFX data. Pandemic plans already recognise the importance of both situational awareness i.e., knowing pandemic impact and its key drivers, and the need for pandemic special studies and related analytic methods for estimating these drivers. An important next step is considering how information from these situational assessment activities can be integrated into the decision-making processes articulated in pandemic planning documents. Here we introduce a decision support tool that directly uses outputs from FFX algorithms to present recommendations on response options, including a quantification of uncertainty, to decision makers. We illustrate this approach using response information from within the Australian influenza pandemic plan.
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    Modelling the Effect of MUC1 on Influenza Virus Infection Kinetics and Macrophage Dynamics
    Li, K ; Cao, P ; McCaw, JM (MDPI, 2021-05)
    MUC1 belongs to the family of cell surface (cs-) mucins. Experimental evidence indicates that its presence reduces in vivo influenza viral infection severity. However, the mechanisms by which MUC1 influences viral dynamics and the host immune response are not yet well understood, limiting our ability to predict the efficacy of potential treatments that target MUC1. To address this limitation, we use available in vivo kinetic data for both virus and macrophage populations in wildtype and MUC1 knockout mice. We apply two mathematical models of within-host influenza dynamics to this data. The models differ in how they categorise the mechanisms of viral control. Both models provide evidence that MUC1 reduces the susceptibility of epithelial cells to influenza virus and regulates macrophage recruitment. Furthermore, we predict and compare some key infection-related quantities between the two mice groups. We find that MUC1 significantly reduces the basic reproduction number of viral replication as well as the number of cumulative macrophages but has little impact on the cumulative viral load. Our analyses suggest that the viral replication rate in the early stages of infection influences the kinetics of the host immune response, with consequences for infection outcomes, such as severity. We also show that MUC1 plays a strong anti-inflammatory role in the regulation of the host immune response. This study improves our understanding of the dynamic role of MUC1 against influenza infection and may support the development of novel antiviral treatments and immunomodulators that target MUC1.