School of Mathematics and Statistics - Research Publications
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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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ItemPopulation heterogeneity in Plasmodium vivax relapse risk(PUBLIC LIBRARY SCIENCE, 2022-12)A key characteristic of Plasmodium vivax parasites is their ability to adopt a latent liver-stage form called hypnozoites, able to cause relapse of infection months or years after a primary infection. Relapses of infection through hypnozoite activation are a major contributor to blood-stage infections in P vivax endemic regions and are thought to be influenced by factors such as febrile infections which may cause temporary changes in hypnozoite activation leading to 'temporal heterogeneity' in reactivation risk. In addition, immunity and variation in exposure to infection may be longer-term characteristics of individuals that lead to 'population heterogeneity' in hypnozoite activation. We analyze data on risk of P vivax in two previously published data sets from Papua New Guinea and the Thailand-Myanmar border region. Modeling different mechanisms of reactivation risk, we find strong evidence for population heterogeneity, with 30% of patients having almost 70% of all P vivax infections. Model fitting and data analysis indicates that individual variation in relapse risk is a primary source of heterogeneity of P vivax risk of recurrences. Trial Registration: ClinicalTrials.gov NCT01640574, NCT01074905, NCT02143934.
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ItemSpatiotemporal spread of Plasmodium falciparum mutations for resistance to sulfadoxine-pyrimethamine across Africa, 1990-2020(PUBLIC LIBRARY SCIENCE, 2022-08)BACKGROUND: Sulfadoxine-pyrimethamine (SP) is recommended in Africa in several antimalarial preventive regimens including Intermittent Preventive Treatment in pregnant women (IPTp), Intermittent Preventive Treatment in infants (IPTi) and Seasonal Malaria Chemoprevention (SMC). The effectiveness of SP-based preventive treatments are threatened in areas where Plasmodium falciparum resistance to SP is high. The prevalence of mutations in the dihydropteroate synthase gene (pfdhps) can be used to monitor SP effectiveness. IPTi-SP is recommended only in areas where the prevalence of the pfdhps540E mutation is below 50%. It has also been suggested that IPTp-SP does not have a protective effect in areas where the pfdhps581G mutation, exceeds 10%. However, pfdhps mutation prevalence data in Africa are extremely heterogenous and scattered, with data completely missing from many areas. METHODS AND FINDINGS: The WWARN SP Molecular Surveyor database was designed to summarize dihydrofolate reductase (pfdhfr) and pfdhps gene mutation prevalence data. In this paper, pfdhps mutation prevalence data was used to generate continuous spatiotemporal surface maps of the estimated prevalence of the SP resistance markers pfdhps437G, pfdhps540E, and pfdhps581G in Africa from 1990 to 2020 using a geostatistical model, with a Bayesian inference framework to estimate uncertainty. The maps of estimated prevalence show an expansion of the pfdhps437G mutations across the entire continent over the last three decades. The pfdhps540E mutation emerged from limited foci in East Africa to currently exceeding 50% estimated prevalence in most of East and South East Africa. pfdhps540E distribution is expanding at low or moderate prevalence in central Africa and a predicted focus in West Africa. Although the pfdhps581G mutation spread from one focus in East Africa in 2000, to exceeding 10% estimated prevalence in several foci in 2010, the predicted distribution of the marker did not expand in 2020, however our analysis indicated high uncertainty in areas where pfdhps581G is present. Uncertainty was higher in spatial regions where the prevalence of a marker is intermediate or where prevalence is changing over time. CONCLUSIONS: The WWARN SP Molecular Surveyor database and a set of continuous spatiotemporal surface maps were built to provide users with standardized, current information on resistance marker distribution and prevalence estimates. According to the maps, the high prevalence of pfdhps540E mutation was to date restricted to East and South East Africa, which is reassuring for continued use of IPTi and SMC in West Africa, but continuous monitoring is needed as the pfdhps540E distribution is expanding. Several foci where pfdhps581G prevalence exceeded 10% were identified. More data on the pfdhps581G distribution in these areas needs to be collected to guide IPTp-SP recommendations. Prevalence and uncertainty maps can be utilized together to strategically identify sites where increased surveillance can be most informative. This study combines a molecular marker database and predictive modelling to highlight areas of concern, which can be used to support decisions in public health, highlight knowledge gaps in certain regions, and guide future research.
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ItemCOVID-19 morbidity in Afghanistan: a nationwide, population-based seroepidemiological study.(BMJ, 2022-07-27)OBJECTIVE: The primary objectives were to determine the magnitude of COVID-19 infections in the general population and age-specific cumulative incidence, as determined by seropositivity and clinical symptoms of COVID-19, and to determine the magnitude of asymptomatic or subclinical infections. DESIGN, SETTING AND PARTICIPANTS: We describe a population-based, cross-sectional, age-stratified seroepidemiological study conducted throughout Afghanistan during June/July 2020. Participants were interviewed to complete a questionnaire, and rapid diagnostic tests were used to test for SARS-CoV-2 antibodies. This national study was conducted in eight regions of Afghanistan plus Kabul province, considered a separate region. The total sample size was 9514, and the number of participants required in each region was estimated proportionally to the population size of each region. For each region, 31-44 enumeration areas (EAs) were randomly selected, and a total of 360 clusters and 16 households per EA were selected using random sampling. To adjust the seroprevalence for test sensitivity and specificity, and seroreversion, Bernoulli's model methodology was used to infer the population exposure in Afghanistan. OUTCOME MEASURES: The main outcome was to determine the prevalence of current or past COVID-19 infection. RESULTS: The survey revealed that, to July 2020, around 10 million people in Afghanistan (31.5% of the population) had either current or previous COVID-19 infection. By age group, COVID-19 seroprevalence was reported to be 35.1% and 25.3% among participants aged ≥18 and 5-17 years, respectively. This implies that most of the population remained at risk of infection. However, a large proportion of the population had been infected in some localities, for example, Kabul province, where more than half of the population had been infected with COVID-19. CONCLUSION: As most of the population remained at risk of infection at the time of the study, any lifting of public health and social measures needed to be considered gradually.
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ItemA Multiscale Mathematical Model of Plasmodium Vivax Transmission(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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ItemPush or Pull? Cell Proliferation and Migration During Wound Healing(Frontiers Media SA, 2022-04-29)Wound healing of the skin is a complex process that is still not well-understood. Wound management is expensive for both individuals and the health system overall, and can reduce quality of life for patients. Given these significant socio-economic impacts, wound healing has long been a focus of scientific research. Recentin vivomouse studies have identified two key regions in wounded skin tissue: A non-proliferative leading edge that actively migrates into wounded space, and a proliferative hub in which cells have enhanced mitotic properties. This work uses mathematical and computational modelling to investigate the effect of changing the mechanical characteristics of cells in these two key regions. In this paper we explore what characteristics are sufficient for wound healing, particularly focusing on cell proliferation, since wounds are not able to repair successfully without sufficient levels of cell division. By considering contact inhibited proliferation, where small cells are unable to divide, we find that a quiescent region develops if the proliferative hub is able to grow over time, essentially limiting the number of cells that are able to divide. In contrast, if the size of the proliferative hub is kept below some threshold, then contact inhibition has a less significant role in wound repair. This work builds upon existing cell-based computational studies of wound healing and could be modified to investigate different stages of wound healing, impaired healing and wound treatments.
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ItemDetection and identification of cis-regulatory elements using change-point and classification algorithms.(BioMed Central, 2022-01-25)BACKGROUND: Transcriptional regulation is primarily mediated by the binding of factors to non-coding regions in DNA. Identification of these binding regions enhances understanding of tissue formation and potentially facilitates the development of gene therapies. However, successful identification of binding regions is made difficult by the lack of a universal biological code for their characterisation. RESULTS: We extend an alignment-based method, changept, and identify clusters of biological significance, through ontology and de novo motif analysis. Further, we apply a Bayesian method to estimate and combine binary classifiers on the clusters we identify to produce a better performing composite. CONCLUSIONS: The analysis we describe provides a computational method for identification of conserved binding sites in the human genome and facilitates an alternative interrogation of combinations of existing data sets with alignment data.