School of Mathematics and Statistics - Research Publications
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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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ItemNo Preview AvailableA multi-criteria framework for disease surveillance site selection: case study for Plasmodium knowlesi malaria in Indonesia(ROYAL SOC, 2024-01-10)Disease surveillance aims to collect data at different times or locations, to assist public health authorities to respond appropriately. Surveillance of the simian malaria parasite, Plasmodium knowlesi, is sparse in some endemic areas and the spatial extent of transmission is uncertain. Zoonotic transmission of Plasmodium knowlesi has been demonstrated throughout Southeast Asia and represents a major hurdle to regional malaria elimination efforts. Given an arbitrary spatial prediction of relative disease risk, we develop a flexible framework for surveillance site selection, drawing on principles from multi-criteria decision-making. To demonstrate the utility of our framework, we apply it to the case study of Plasmodium knowlesi malaria surveillance site selection in western Indonesia. We demonstrate how statistical predictions of relative disease risk can be quantitatively incorporated into public health decision-making, with specific application to active human surveillance of zoonotic malaria. This approach can be used in other contexts to extend the utility of modelling outputs.
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ItemNo Preview AvailableA spatio-temporal model of multi-marker antimalarial resistance(ROYAL SOC, 2024-01-17)The emergence and spread of drug-resistant Plasmodium falciparum parasites have hindered efforts to eliminate malaria. Monitoring the spread of drug resistance is vital, as drug resistance can lead to widespread treatment failure. We develop a Bayesian model to produce spatio-temporal maps that depict the spread of drug resistance, and apply our methods for the antimalarial sulfadoxine-pyrimethamine. We infer from genetic count data the prevalences over space and time of various malaria parasite haplotypes associated with drug resistance. Previous work has focused on inferring the prevalence of individual molecular markers. In reality, combinations of mutations at multiple markers confer varying degrees of drug resistance to the parasite, indicating that multiple markers should be modelled together. However, the reporting of genetic count data is often inconsistent as some studies report haplotype counts, whereas some studies report mutation counts of individual markers separately. In response, we introduce a latent multinomial Gaussian process model to handle partially reported spatio-temporal count data. As drug-resistant mutations are often used as a proxy for treatment efficacy, point estimates from our spatio-temporal maps can help inform antimalarial drug policies, whereas the uncertainties from our maps can help with optimizing sampling strategies for future monitoring of drug resistance.
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ItemUpdating estimates of Plasmodium knowlesi malaria risk in response to changing land use patterns across Southeast Asia(Public Library of Science (PLoS), 2024-01)BACKGROUND: Plasmodium knowlesi is a zoonotic parasite that causes malaria in humans. The pathogen has a natural host reservoir in certain macaque species and is transmitted to humans via mosquitoes of the Anopheles Leucosphyrus Group. The risk of human P. knowlesi infection varies across Southeast Asia and is dependent upon environmental factors. Understanding this geographic variation in risk is important both for enabling appropriate diagnosis and treatment of the disease and for improving the planning and evaluation of malaria elimination. However, the data available on P. knowlesi occurrence are biased towards regions with greater surveillance and sampling effort. Predicting the spatial variation in risk of P. knowlesi malaria requires methods that can both incorporate environmental risk factors and account for spatial bias in detection. METHODS & RESULTS: We extend and apply an environmental niche modelling framework as implemented by a previous mapping study of P. knowlesi transmission risk which included data up to 2015. We reviewed the literature from October 2015 through to March 2020 and identified 264 new records of P. knowlesi, with a total of 524 occurrences included in the current study following consolidation with the 2015 study. The modelling framework used in the 2015 study was extended, with changes including the addition of new covariates to capture the effect of deforestation and urbanisation on P. knowlesi transmission. DISCUSSION: Our map of P. knowlesi relative transmission suitability estimates that the risk posed by the pathogen is highest in Malaysia and Indonesia, with localised areas of high risk also predicted in the Greater Mekong Subregion, The Philippines and Northeast India. These results highlight areas of priority for P. knowlesi surveillance and prospective sampling to address the challenge the disease poses to malaria elimination planning.
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ItemNo Preview AvailableMathematical models of developmental vascular remodelling: A review.(Public Library of Science (PLoS), 2023-08)Over the past 40 years, there has been a strong focus on the development of mathematical models of angiogenesis, while developmental remodelling has received little such attention from the mathematical community. Sprouting angiogenesis can be seen as a very crude way of laying out a primitive vessel network (the raw material), while remodelling (understood as pruning of redundant vessels, diameter control, and the establishment of vessel identity and hierarchy) is the key to turning that primitive network into a functional network. This multiscale problem is of prime importance in the development of a functional vasculature. In addition, defective remodelling (either during developmental remodelling or due to a reactivation of the remodelling programme caused by an injury) is associated with a significant number of diseases. In this review, we discuss existing mathematical models of developmental remodelling and explore the important contributions that these models have made to the field of vascular development. These mathematical models are effectively used to investigate and predict vascular development and are able to reproduce experimentally observable results. Moreover, these models provide a useful means of hypothesis generation and can explain the underlying mechanisms driving the observed structural and functional network development. However, developmental vascular remodelling is still a relatively new area in mathematical biology, and many biological questions remain unanswered. In this review, we present the existing modelling paradigms and define the key challenges for the field.
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ItemNo Preview AvailableFree and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems(SPRINGER, 2023-11)Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.
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ItemNo Preview AvailableHow quickly does a wound heal? Bayesian calibration of a mathematical model of venous leg ulcer healing(OXFORD UNIV PRESS, 2022-12)Chronic wounds, such as venous leg ulcers, are difficult to treat and can reduce the quality of life for patients. Clinical trials have been conducted to identify the most effective venous leg ulcer treatments and the clinical factors that may indicate whether a wound will successfully heal. More recently, mathematical modelling has been used to gain insight into biological factors that may affect treatment success but are difficult to measure clinically, such as the rate of oxygen flow into wounded tissue. In this work, we calibrate an existing mathematical model using a Bayesian approach with clinical data for individual patients to explore which clinical factors may impact the rate of wound healing for individuals. Although the model describes group-level behaviour well, it is not able to capture individual-level responses in all cases. From the individual-level analysis, we propose distributions for coefficients of clinical factors in a linear regression model, but ultimately find that it is difficult to draw conclusions about which factors lead to faster wound healing based on the existing model and data. This work highlights the challenges of using Bayesian methods to calibrate partial differential equation models to individual patient clinical data. However, the methods used in this work may be modified and extended to calibrate spatiotemporal mathematical models to multiple data sets, such as clinical trials with several patients, to extract additional information from the model and answer outstanding biological questions.
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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.
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ItemNo Preview AvailableA model for malaria treatment evaluation in the presence of multiple species(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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ItemNo Preview Available