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      Calibrating COVID-19 susceptible-exposed-infected-removed models with time-varying effective contact rates

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          Abstract

          We describe the population-based susceptible-exposed-infected-removed (SEIR) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g. to the daily number of confirmed new cases, as the history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data to produce a robust methodology for calibration of a wide class of models of this type.

          This article is part of the theme issue ‘Data science approaches to infectious disease surveillance’.

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          Most cited references22

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          brms: An R Package for Bayesian Multilevel Models Using Stan

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            Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models

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              Early dynamics of transmission and control of COVID-19: a mathematical modelling study

              Summary Background An outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to 95 333 confirmed cases as of March 5, 2020. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe SARS-CoV-2 transmission with four datasets from within and outside Wuhan, we estimated how transmission in Wuhan varied between December, 2019, and February, 2020. We used these estimates to assess the potential for sustained human-to-human transmission to occur in locations outside Wuhan if cases were introduced. Methods We combined a stochastic transmission model with data on cases of coronavirus disease 2019 (COVID-19) in Wuhan and international cases that originated in Wuhan to estimate how transmission had varied over time during January, 2020, and February, 2020. Based on these estimates, we then calculated the probability that newly introduced cases might generate outbreaks in other areas. To estimate the early dynamics of transmission in Wuhan, we fitted a stochastic transmission dynamic model to multiple publicly available datasets on cases in Wuhan and internationally exported cases from Wuhan. The four datasets we fitted to were: daily number of new internationally exported cases (or lack thereof), by date of onset, as of Jan 26, 2020; daily number of new cases in Wuhan with no market exposure, by date of onset, between Dec 1, 2019, and Jan 1, 2020; daily number of new cases in China, by date of onset, between Dec 29, 2019, and Jan 23, 2020; and proportion of infected passengers on evacuation flights between Jan 29, 2020, and Feb 4, 2020. We used an additional two datasets for comparison with model outputs: daily number of new exported cases from Wuhan (or lack thereof) in countries with high connectivity to Wuhan (ie, top 20 most at-risk countries), by date of confirmation, as of Feb 10, 2020; and data on new confirmed cases reported in Wuhan between Jan 16, 2020, and Feb 11, 2020. Findings We estimated that the median daily reproduction number (R t) in Wuhan declined from 2·35 (95% CI 1·15–4·77) 1 week before travel restrictions were introduced on Jan 23, 2020, to 1·05 (0·41–2·39) 1 week after. Based on our estimates of R t, assuming SARS-like variation, we calculated that in locations with similar transmission potential to Wuhan in early January, once there are at least four independently introduced cases, there is a more than 50% chance the infection will establish within that population. Interpretation Our results show that COVID-19 transmission probably declined in Wuhan during late January, 2020, coinciding with the introduction of travel control measures. As more cases arrive in international locations with similar transmission potential to Wuhan before these control measures, it is likely many chains of transmission will fail to establish initially, but might lead to new outbreaks eventually. Funding Wellcome Trust, Health Data Research UK, Bill & Melinda Gates Foundation, and National Institute for Health Research.
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                Author and article information

                Contributors
                Journal
                Philos Trans A Math Phys Eng Sci
                Philos Trans A Math Phys Eng Sci
                RSTA
                roypta
                Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
                The Royal Society
                1364-503X
                1471-2962
                January 10, 2022
                November 22, 2021
                November 22, 2021
                : 380
                : 2214 , Theme issue ‘Data science approaches to infectious disease surveillance’ compiled and edited by Qingpeng Zhang
                : 20210120
                Affiliations
                [ 1 ] MACSI, Department of Mathematics and Statistics, University of Limerick, , Limerick, V94 T9PX, Ireland
                [ 2 ] School of Mathematics and Statistics, University College Dublin, , Dublin, D04 V1W8, Ireland
                [ 3 ] Insight Centre for Data Analytics, , Ireland
                [ 4 ] Confirm Centre for Smart Manufacturing, , Ireland
                [ 5 ] Irish Epidemiological Modelling Advisory Group (IEMAG), , Ireland
                Author notes

                One contribution of 14 to a theme issue ‘ Data science approaches to infectious disease surveillance’.

                Electronic supplementary material is available online at https://doi.org/10.6084/m9.figshare.c.5674233.

                Author information
                http://orcid.org/0000-0003-3410-2817
                http://orcid.org/0000-0002-4754-3614
                Article
                rsta20210120
                10.1098/rsta.2021.0120
                8607149
                34802273
                c9480c75-e3fe-48bf-a39f-5ebe77db9ba6
                © 2021 The Authors.

                Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

                History
                : June 04, 2021
                : July 26, 2021
                Funding
                Funded by: Science Foundation Ireland, http://dx.doi.org/10.13039/501100001602;
                Award ID: SFI/12/RC/2275_P2
                Award ID: SFI/12/RC/2289_P2
                Award ID: SFI/16/IA/4470
                Award ID: SFI/16/RC/3835
                Award ID: SFI/16/RC/3918
                Categories
                1008
                119
                Articles
                Research Articles
                Custom metadata
                January 10, 2022

                epidemic modelling,differential equations,calibration,generalized additive model,thin-plate splines

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