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Ayoub I, Freeman SA, Saoudi A, Liblau R. Infection, vaccination and narcolepsy type 1: Evidence and potential molecular mechanisms. J Neuroimmunol 2024; 393:578383. [PMID: 39032452 DOI: 10.1016/j.jneuroim.2024.578383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2024] [Revised: 05/13/2024] [Accepted: 05/31/2024] [Indexed: 07/23/2024]
Abstract
NT1 is a rare, chronic and disabling neurological disease causing excessive daytime sleepiness and cataplexy. NT1 is characterized pathologically by an almost complete loss of neurons producing the hypocretin (HCRT)/orexin neuropeptides in the lateral hypothalamus. While the exact etiology of NT1 is still unknown, numerous studies have provided compelling evidence supporting its autoimmune origin. The prevailing hypothetical view on the pathogenesis of NT1 involves an immune-mediated loss of HCRT neurons that can be triggered by Pandemrix® vaccination and/or by infection in genetically susceptible patients, specifically carriers of the HLA-DQB1*06:02 MHC class II allele. The molecular mechanisms by which infection/vaccination can induce autoimmunity in the case of NT1 remain to be elucidated. In this review, evidence regarding the involvement of vaccination and infection and the potential mechanisms by which it could be linked to the pathogenesis of NT1 will be discussed in light of the existing findings in other autoimmune diseases.
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Affiliation(s)
- Ikram Ayoub
- Toulouse Institute for Infectious and Inflammatory Diseases (Infinity), University of Toulouse, CNRS, INSERM, UPS, Toulouse, France.
| | - Sean A Freeman
- Toulouse Institute for Infectious and Inflammatory Diseases (Infinity), University of Toulouse, CNRS, INSERM, UPS, Toulouse, France; Department of Neurology, Toulouse University Hospitals, Toulouse, France
| | - Abdelhadi Saoudi
- Toulouse Institute for Infectious and Inflammatory Diseases (Infinity), University of Toulouse, CNRS, INSERM, UPS, Toulouse, France
| | - Roland Liblau
- Toulouse Institute for Infectious and Inflammatory Diseases (Infinity), University of Toulouse, CNRS, INSERM, UPS, Toulouse, France; Department of Immunology, Toulouse University Hospitals, Toulouse, France
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Liblau RS, Latorre D, Kornum BR, Dauvilliers Y, Mignot EJ. The immunopathogenesis of narcolepsy type 1. Nat Rev Immunol 2024; 24:33-48. [PMID: 37400646 DOI: 10.1038/s41577-023-00902-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/01/2023] [Indexed: 07/05/2023]
Abstract
Narcolepsy type 1 (NT1) is a chronic sleep disorder resulting from the loss of a small population of hypothalamic neurons that produce wake-promoting hypocretin (HCRT; also known as orexin) peptides. An immune-mediated pathology for NT1 has long been suspected given its exceptionally tight association with the MHC class II allele HLA-DQB1*06:02, as well as recent genetic evidence showing associations with polymorphisms of T cell receptor genes and other immune-relevant loci and the increased incidence of NT1 that has been observed after vaccination with the influenza vaccine Pandemrix. The search for both self-antigens and foreign antigens recognized by the pathogenic T cell response in NT1 is ongoing. Increased T cell reactivity against HCRT has been consistently reported in patients with NT1, but data demonstrating a primary role for T cells in neuronal destruction are currently lacking. Animal models are providing clues regarding the roles of autoreactive CD4+ and CD8+ T cells in the disease. Elucidation of the pathogenesis of NT1 will allow for the development of targeted immunotherapies at disease onset and could serve as a model for other immune-mediated neurological diseases.
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Affiliation(s)
- Roland S Liblau
- Toulouse Institute for Infectious and Inflammatory Diseases (Infinity), University of Toulouse, CNRS, INSERM, Toulouse, France.
- Department of Immunology, Toulouse University Hospitals, Toulouse, France.
| | | | - Birgitte R Kornum
- Department of Neuroscience, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Yves Dauvilliers
- National Reference Center for Orphan Diseases, Narcolepsy, Idiopathic Hypersomnia and Kleine-Levin Syndrome, Department of Neurology, Gui-de-Chauliac Hospital, CHU de Montpellier, Montpellier, France
- INSERM Institute for Neurosciences of Montpellier, Montpellier, France
| | - Emmanuel J Mignot
- Stanford University, Center for Narcolepsy, Department of Psychiatry and Behavioral Sciences, Palo Alto, CA, USA.
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Marmara V, Marmara D, McMenemy P, Kleczkowski A. Cross-sectional telephone surveys as a tool to study epidemiological factors and monitor seasonal influenza activity in Malta. BMC Public Health 2021; 21:1828. [PMID: 34627201 PMCID: PMC8502089 DOI: 10.1186/s12889-021-11862-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 09/27/2021] [Indexed: 11/29/2022] Open
Abstract
Background Seasonal influenza has major implications for healthcare services as outbreaks often lead to high activity levels in health systems. Being able to predict when such outbreaks occur is vital. Mathematical models have extensively been used to predict epidemics of infectious diseases such as seasonal influenza and to assess effectiveness of control strategies. Availability of comprehensive and reliable datasets used to parametrize these models is limited. In this paper we combine a unique epidemiological dataset collected in Malta through General Practitioners (GPs) with a novel method using cross-sectional surveys to study seasonal influenza dynamics in Malta in 2014–2016, to include social dynamics and self-perception related to seasonal influenza. Methods Two cross-sectional public surveys (n = 406 per survey) were performed by telephone across the Maltese population in 2014–15 and 2015–16 influenza seasons. Survey results were compared with incidence data (diagnosed seasonal influenza cases) collected by GPs in the same period and with Google Trends data for Malta. Information was collected on whether participants recalled their health status in past months, occurrences of influenza symptoms, hospitalisation rates due to seasonal influenza, seeking GP advice, and other medical information. Results We demonstrate that cross-sectional surveys are a reliable alternative data source to medical records. The two surveys gave comparable results, indicating that the level of recollection among the public is high. Based on two seasons of data, the reporting rate in Malta varies between 14 and 22%. The comparison with Google Trends suggests that the online searches peak at about the same time as the maximum extent of the epidemic, but the public interest declines and returns to background level. We also found that the public intensively searched the Internet for influenza-related terms even when number of cases was low. Conclusions Our research shows that a telephone survey is a viable way to gain deeper insight into a population’s self-perception of influenza and its symptoms and to provide another benchmark for medical statistics provided by GPs and Google Trends. The information collected can be used to improve epidemiological modelling of seasonal influenza and other infectious diseases, thus effectively contributing to public health. Supplementary Information The online version contains supplementary material available at 10.1186/s12889-021-11862-x.
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Affiliation(s)
- V Marmara
- Faculty of Economics, Management & Accountancy, University of Malta, Msida, MSD, 2080, Malta
| | - D Marmara
- Faculty of Health Sciences, Mater Dei Hospital, Block A, Level 1, University of Malta, Msida, MSD, 2090, Malta.
| | - P McMenemy
- Department of Mathematics, University of Stirling, Stirling, FK94LA, Scotland, UK
| | - A Kleczkowski
- Department of Mathematics and Statistics, University of Strathclyde, Rm. 1001, 26 Richmond Street, Glasgow, G1 1XH, Scotland
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Karppinen S, Vihola M. Conditional particle filters with diffuse initial distributions. STATISTICS AND COMPUTING 2021; 31:24. [PMID: 33679010 PMCID: PMC7926083 DOI: 10.1007/s11222-020-09975-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 12/04/2020] [Indexed: 06/12/2023]
Abstract
UNLABELLED Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use online adaptations within the methods. In the case of random walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear Gaussian random walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s11222-020-09975-1.
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Affiliation(s)
- Santeri Karppinen
- Department of Mathematics and Statistics, University of Jyväskylä, 40014 Jyväskylä, Finland
| | - Matti Vihola
- Department of Mathematics and Statistics, University of Jyväskylä, 40014 Jyväskylä, Finland
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Birrell PJ, Wernisch L, Tom BDM, Held L, Roberts GO, Pebody RG, De Angelis D. Efficient Real-Time Monitoring of an Emerging Influenza Pandemic: How Feasible? Ann Appl Stat 2020; 14:74-93. [PMID: 34992706 PMCID: PMC7612182 DOI: 10.1214/19-aoas1278] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
A prompt public health response to a new epidemic relies on the ability to monitor and predict its evolution in real time as data accumulate. The 2009 A/H1N1 outbreak in the UK revealed pandemic data as noisy, contaminated, potentially biased and originating from multiple sources. This seriously challenges the capacity for real-time monitoring. Here, we assess the feasibility of real-time inference based on such data by constructing an analytic tool combining an age-stratified SEIR transmission model with various observation models describing the data generation mechanisms. As batches of data become available, a sequential Monte Carlo (SMC) algorithm is developed to synthesise multiple imperfect data streams, iterate epidemic inferences and assess model adequacy amidst a rapidly evolving epidemic environment, substantially reducing computation time in comparison to standard MCMC, to ensure timely delivery of real-time epidemic assessments. In application to simulated data designed to mimic the 2009 A/H1N1 epidemic, SMC is shown to have additional benefits in terms of assessing predictive performance and coping with parameter nonidentifiability.
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Affiliation(s)
- Paul J. Birrell
- MRC Biostatistics Unit, Cambridge Institute of Public Health, University of Cambridge
| | - Lorenz Wernisch
- MRC Biostatistics Unit, Cambridge Institute of Public Health, University of Cambridge
| | - Brian D. M. Tom
- MRC Biostatistics Unit, Cambridge Institute of Public Health, University of Cambridge
| | - Leonhard Held
- Epidemiology, Biostatistics and Prevention Institute (EBPI), University of Zurich
| | | | | | - Daniela De Angelis
- MRC Biostatistics Unit, Cambridge Institute of Public Health, University of Cambridge
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Guo Z, Xu S, Tong L, Dai B, Liu Y, Xiao D. An artificially simulated outbreak of a respiratory infectious disease. BMC Public Health 2020; 20:135. [PMID: 32000737 PMCID: PMC6993344 DOI: 10.1186/s12889-020-8243-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 01/20/2020] [Indexed: 11/20/2022] Open
Abstract
Background Outbreaks of respiratory infectious diseases often occur in crowded places. To understand the pattern of spread of an outbreak of a respiratory infectious disease and provide a theoretical basis for targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 (ADV 7) in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number (R0), time of isolation of the patients (TOI), interval between onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R0 exceeded 1.5, the median attack rate increased sharply; when R0 = 3, with a delay in the TOI, the attack rate increased gradually and eventually remained stable. When the IOI exceeded 2.3 days, the median attack rate also increased dramatically. When the IR exceeded 0.5, the median attack rate approached zero. The median generation time was 8.26 days, (95% confidence interval [CI]: 7.84–8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and R0, TOI, IOI, and IR were 0.61, 0.17, 0.45, and − 0.27, respectively. Conclusions The random collision model not only simulates how an epidemic spreads with superior precision but also allows greater flexibility in setting the activities of the exposure population and different types of infectious diseases, which is conducive to furthering exploration of the epidemiological characteristics of epidemic outbreaks.
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Affiliation(s)
- Zuiyuan Guo
- Department of Disease Control, Center for Disease Control and Prevention in Northern Theater Command, No. 6, Longshan Road, Shenyang, 110034, China
| | - Shuang Xu
- Department of Disease Control, Center for Disease Control and Prevention in Northern Theater Command, No. 6, Longshan Road, Shenyang, 110034, China
| | - Libo Tong
- Department of Disease Control, Center for Disease Control and Prevention in Northern Theater Command, No. 6, Longshan Road, Shenyang, 110034, China
| | - Botao Dai
- Liaoning Agricultural Development Service Center, Shenyang, China
| | - Yuandong Liu
- Department of Disease Control, Center for Disease Control and Prevention in Northern Theater Command, No. 6, Longshan Road, Shenyang, 110034, China.
| | - Dan Xiao
- China National Clinical Research Center for Neurological Diseases, Beijing Tian Tan Hospital, No. 119, South 4th Ring Road West, Fengtai District, Beijing, China.
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Goudie RJB, Presanis AM, Lunn D, De Angelis D, Wernisch L. Joining and splitting models with Markov melding. BAYESIAN ANALYSIS 2019; 14:81-109. [PMID: 30631389 PMCID: PMC6324725 DOI: 10.1214/18-ba1104] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Analysing multiple evidence sources is often feasible only via a modular approach, with separate submodels specified for smaller components of the available evidence. Here we introduce a generic framework that enables fully Bayesian analysis in this setting. We propose a generic method for forming a suitable joint model when joining submodels, and a convenient computational algorithm for fitting this joint model in stages, rather than as a single, monolithic model. The approach also enables splitting of large joint models into smaller submodels, allowing inference for the original joint model to be conducted via our multi-stage algorithm. We motivate and demonstrate our approach through two examples: joining components of an evidence synthesis of A/H1N1 influenza, and splitting a large ecology model.
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Affiliation(s)
| | - Anne M Presanis
- MRC Biostatistics Unit, University of Cambridge, United Kingdom
| | - David Lunn
- MRC Biostatistics Unit, University of Cambridge, United Kingdom
| | | | - Lorenz Wernisch
- MRC Biostatistics Unit, University of Cambridge, United Kingdom
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Birrell PJ, Pebody RG, Charlett A, Zhang XS, De Angelis D. Real-time modelling of a pandemic influenza outbreak. Health Technol Assess 2018; 21:1-118. [PMID: 29058665 DOI: 10.3310/hta21580] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
BACKGROUND Real-time modelling is an essential component of the public health response to an outbreak of pandemic influenza in the UK. A model for epidemic reconstruction based on realistic epidemic surveillance data has been developed, but this model needs enhancing to provide spatially disaggregated epidemic estimates while ensuring that real-time implementation is feasible. OBJECTIVES To advance state-of-the-art real-time pandemic modelling by (1) developing an existing epidemic model to capture spatial variation in transmission, (2) devising efficient computational algorithms for the provision of timely statistical analysis and (3) incorporating the above into freely available software. METHODS Markov chain Monte Carlo (MCMC) sampling was used to derive Bayesian statistical inference using 2009 pandemic data from two candidate modelling approaches: (1) a parallel-region (PR) approach, splitting the pandemic into non-interacting epidemics occurring in spatially disjoint regions; and (2) a meta-region (MR) approach, treating the country as a single meta-population with long-range contact rates informed by census data on commuting. Model discrimination is performed through posterior mean deviance statistics alongside more practical considerations. In a real-time context, the use of sequential Monte Carlo (SMC) algorithms to carry out real-time analyses is investigated as an alternative to MCMC using simulated data designed to sternly test both algorithms. SMC-derived analyses are compared with 'gold-standard' MCMC-derived inferences in terms of estimation quality and computational burden. RESULTS The PR approach provides a better and more timely fit to the epidemic data. Estimates of pandemic quantities of interest are consistent across approaches and, in the PR approach, across regions (e.g. R0 is consistently estimated to be 1.76-1.80, dropping by 43-50% during an over-summer school holiday). A SMC approach was developed, which required some tailoring to tackle a sudden 'shock' in the data resulting from a pandemic intervention. This semi-automated SMC algorithm outperforms MCMC, in terms of both precision of estimates and their timely provision. Software implementing all findings has been developed and installed within Public Health England (PHE), with key staff trained in its use. LIMITATIONS The PR model lacks the predictive power to forecast the spread of infection in the early stages of a pandemic, whereas the MR model may be limited by its dependence on commuting data to describe transmission routes. As demand for resources increases in a severe pandemic, data from general practices and on hospitalisations may become unreliable or biased. The SMC algorithm developed is semi-automated; therefore, some statistical literacy is required to achieve optimal performance. CONCLUSIONS Following the objectives, this study found that timely, spatially disaggregate, real-time pandemic inference is feasible, and a system that assumes data as per pandemic preparedness plans has been developed for rapid implementation. FUTURE WORK RECOMMENDATIONS Modelling studies investigating the impact of pandemic interventions (e.g. vaccination and school closure); the utility of alternative data sources (e.g. internet searches) to augment traditional surveillance; and the correct handling of test sensitivity and specificity in serological data, propagating this uncertainty into the real-time modelling. TRIAL REGISTRATION Current Controlled Trials ISRCTN40334843. FUNDING This project was funded by the National Institute for Health Research (NIHR) Health Technology programme and will be published in full in Health Technology Assessment; Vol. 21, No. 58. See the NIHR Journals Library website for further project information. Daniela De Angelis was supported by the UK Medical Research Council (Unit Programme Number U105260566) and by PHE. She received funding under the NIHR grant for 10% of her time. The rest of her salary was provided by the MRC and PHE jointly.
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Affiliation(s)
- Paul J Birrell
- Medical Research Council Biostatistics Unit, Cambridge Institute of Public Health, University of Cambridge, Cambridge, UK
| | | | - André Charlett
- National Infections Service, Public Health England, London, UK
| | - Xu-Sheng Zhang
- National Infections Service, Public Health England, London, UK
| | - Daniela De Angelis
- Medical Research Council Biostatistics Unit, Cambridge Institute of Public Health, University of Cambridge, Cambridge, UK.,National Infections Service, Public Health England, London, UK
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Corbella A, Zhang XS, Birrell PJ, Boddington N, Pebody RG, Presanis AM, De Angelis D. Exploiting routinely collected severe case data to monitor and predict influenza outbreaks. BMC Public Health 2018; 18:790. [PMID: 29940907 PMCID: PMC6020250 DOI: 10.1186/s12889-018-5671-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Accepted: 06/04/2018] [Indexed: 12/03/2022] Open
Abstract
Background Influenza remains a significant burden on health systems. Effective responses rely on the timely understanding of the magnitude and the evolution of an outbreak. For monitoring purposes, data on severe cases of influenza in England are reported weekly to Public Health England. These data are both readily available and have the potential to provide valuable information to estimate and predict the key transmission features of seasonal and pandemic influenza. Methods We propose an epidemic model that links the underlying unobserved influenza transmission process to data on severe influenza cases. Within a Bayesian framework, we infer retrospectively the parameters of the epidemic model for each seasonal outbreak from 2012 to 2015, including: the effective reproduction number; the initial susceptibility; the probability of admission to intensive care given infection; and the effect of school closure on transmission. The model is also implemented in real time to assess whether early forecasting of the number of admissions to intensive care is possible. Results Our model of admissions data allows reconstruction of the underlying transmission dynamics revealing: increased transmission during the season 2013/14 and a noticeable effect of the Christmas school holiday on disease spread during seasons 2012/13 and 2014/15. When information on the initial immunity of the population is available, forecasts of the number of admissions to intensive care can be substantially improved. Conclusion Readily available severe case data can be effectively used to estimate epidemiological characteristics and to predict the evolution of an epidemic, crucially allowing real-time monitoring of the transmission and severity of the outbreak. Electronic supplementary material The online version of this article (10.1186/s12889-018-5671-7) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Alice Corbella
- Medical Research Council, Biostatistics Unit - University of Cambridge, School of Clinical Medicine, Cambridge, UK.
| | - Xu-Sheng Zhang
- Centre for Infectious Disease Surveillance and Control, Public Health England, London, UK
| | - Paul J Birrell
- Medical Research Council, Biostatistics Unit - University of Cambridge, School of Clinical Medicine, Cambridge, UK
| | - Nicki Boddington
- Centre for Infectious Disease Surveillance and Control, Public Health England, London, UK
| | - Richard G Pebody
- Centre for Infectious Disease Surveillance and Control, Public Health England, London, UK
| | - Anne M Presanis
- Centre for Infectious Disease Surveillance and Control, Public Health England, London, UK
| | - Daniela De Angelis
- Medical Research Council, Biostatistics Unit - University of Cambridge, School of Clinical Medicine, Cambridge, UK.,Centre for Infectious Disease Surveillance and Control, Public Health England, London, UK
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Abstract
In recent years, the role of epidemic models in informing public health policies has progressively grown. Models have become increasingly realistic and more complex, requiring the use of multiple data sources to estimate all quantities of interest. This review summarises the different types of stochastic epidemic models that use evidence synthesis and highlights current challenges.
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Affiliation(s)
- Paul J. Birrell
- Paul Birrell is a Senior Investigator Statistician at the MRC Biostatistics Unit, University of Cambridge, School of Clinical Medicine, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge CB2 0SR, United Kingdom
| | - Daniela De Angelis
- Daniela De Angelis is a Programme Leader at the MRC Biostatistics Unit, University of Cambridge, School of Clinical Medicine, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge CB2 0SR, United Kingdom
| | - Anne M. Presanis
- Anne Presanis is a Senior Investigator Statistician at the MRC Biostatistics Unit, University of Cambridge, School of Clinical Medicine, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge CB2 0SR, United Kingdom
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