School of Mathematics and Statistics - Research Publications
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ItemNo Preview AvailableSpatio-temporal spread of artemisinin resistance in Southeast Asia(PUBLIC LIBRARY SCIENCE, 2024-04)Current malaria elimination targets must withstand a colossal challenge-resistance to the current gold standard antimalarial drug, namely artemisinin derivatives. If artemisinin resistance significantly expands to Africa or India, cases and malaria-related deaths are set to increase substantially. Spatial information on the changing levels of artemisinin resistance in Southeast Asia is therefore critical for health organisations to prioritise malaria control measures, but available data on artemisinin resistance are sparse. We use a comprehensive database from the WorldWide Antimalarial Resistance Network on the prevalence of non-synonymous mutations in the Kelch 13 (K13) gene, which are known to be associated with artemisinin resistance, and a Bayesian geostatistical model to produce spatio-temporal predictions of artemisinin resistance. Our maps of estimated prevalence show an expansion of the K13 mutation across the Greater Mekong Subregion from 2000 to 2022. Moreover, the period between 2010 and 2015 demonstrated the most spatial change across the region. Our model and maps provide important insights into the spatial and temporal trends of artemisinin resistance in a way that is not possible using data alone, thereby enabling improved spatial decision support systems on an unprecedented fine-scale spatial resolution. By predicting for the first time spatio-temporal patterns and extents of artemisinin resistance at the subcontinent level, this study provides critical information for supporting malaria elimination goals in Southeast Asia.
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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 AvailableOn the rate of normal approximation for Poisson continuum percolation(Elsevier BV, 2024-07-01)
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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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Itemβ-Ensembles and higher genera Catalan numbers(SPRINGER, 2024-02-05)Abstract We propose formulas for the large N expansion of the generating function of connected correlators of the $$\beta $$ β -deformed Gaussian and Wishart–Laguerre matrix models. We show that our proposal satisfies the known transformation properties under the exchange of $$\beta $$ β with $$1/\beta $$ 1 / β and, using Virasoro constraints, we derive a recursion formula for the coefficients of the expansion. In the undeformed limit $$\beta =1$$ β = 1 , these coefficients are integers and they have the combinatorial interpretation of generalized Catalan numbers. For generic $$\beta $$ β , we define the higher genus Catalan polynomials $$C_{g,\nu }(\beta )$$ C g , ν ( β ) whose coefficients are integer numbers.
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ItemExpanding the Fourier Transform of the Scaled Circular Jacobi β Ensemble Density(SPRINGER, 2023-10-18)Abstract The family of circular Jacobi $$\beta $$ β ensembles has a singularity of a type associated with Fisher and Hartwig in the theory of Toeplitz determinants. Our interest is in the Fourier transform of the corresponding $$N \rightarrow \infty $$ N → ∞ bulk scaled spectral density about this singularity, expanded as a series in the Fourier variable. Various integrability aspects of the circular Jacobi$$\beta $$ β ensemble are used for this purpose. These include linear differential equations satisfied by the scaled spectral density for $$\beta = 2$$ β = 2 and $$\beta = 4$$ β = 4 , and the loop equation hierarchy. The polynomials in the variable $$u=2/\beta $$ u = 2 / β which occur in the expansion coefficents are found to have special properties analogous to those known for the structure function of the circular $$\beta $$ β ensemble, specifically in relation to the zeros lying on the unit circle $$|u|=1$$ | u | = 1 and interlacing. Comparison is also made with known results for the expanded Fourier transform of the density about a guest charge in the two-dimensional one-component plasma.
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ItemComparison of new computational methods for spatial modelling of malaria.(Springer Science and Business Media LLC, 2023-11-21)BACKGROUND: Geostatistical analysis of health data is increasingly used to model spatial variation in malaria prevalence, burden, and other metrics. Traditional inference methods for geostatistical modelling are notoriously computationally intensive, motivating the development of newer, approximate methods for geostatistical analysis or, more broadly, computational modelling of spatial processes. The appeal of faster methods is particularly great as the size of the region and number of spatial locations being modelled increases. METHODS: This work presents an applied comparison of four proposed 'fast' computational methods for spatial modelling and the software provided to implement them-Integrated Nested Laplace Approximation (INLA), tree boosting with Gaussian processes and mixed effect models (GPBoost), Fixed Rank Kriging (FRK) and Spatial Random Forests (SpRF). The four methods are illustrated by estimating malaria prevalence on two different spatial scales-country and continent. The performance of the four methods is compared on these data in terms of accuracy, computation time, and ease of implementation. RESULTS: Two of these methods-SpRF and GPBoost-do not scale well as the data size increases, and so are likely to be infeasible for larger-scale analysis problems. The two remaining methods-INLA and FRK-do scale well computationally, however the resulting model fits are very sensitive to the user's modelling assumptions and parameter choices. The binomial observation distribution commonly used for disease prevalence mapping with INLA fails to account for small-scale overdispersion present in the malaria prevalence data, which can lead to poor predictions. Selection of an appropriate alternative such as the Beta-binomial distribution is required to produce a reliable model fit. The small-scale random effect term in FRK overcomes this pitfall, but FRK model estimates are very reliant on providing a sufficient number and appropriate configuration of basis functions. Unfortunately the computation time for FRK increases rapidly with increasing basis resolution. CONCLUSIONS: INLA and FRK both enable scalable geostatistical modelling of malaria prevalence data. However care must be taken when using both methods to assess the fit of the model to data and plausibility of predictions, in order to select appropriate model assumptions and parameters.
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ItemOpen networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals(SPRINGER, 2023-12)Abstract In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution.
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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.