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      A spatial model of COVID-19 transmission in England and Wales: early spread, peak timing and the impact of seasonality


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          An outbreak of a novel coronavirus was first reported in China on 31 December 2019. As of 9 February 2020, cases have been reported in 25 countries, including probable human-to-human transmission in England. We adapted an existing national-scale metapopulation model to capture the spread of COVID-19 in England and Wales. We used 2011 census data to inform population sizes and movements, together with parameter estimates from the outbreak in China. We predict that the epidemic will peak 126 to 147 days (approx. 4 months) after the start of person-to-person transmission in the absence of controls. Assuming biological parameters remain unchanged and transmission persists from February, we expect the peak to occur in June. Starting location and model stochasticity have a minimal impact on peak timing. However, realistic parameter uncertainty leads to peak time estimates ranging from 78 to 241 days following sustained transmission. Seasonal changes in transmission rate can substantially impact the timing and size of the epidemic. We provide initial estimates of the epidemic potential of COVID-19. These results can be refined with more precise parameters. Seasonal changes in transmission could shift the timing of the peak into winter, with important implications for healthcare capacity planning.

          This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK.

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          Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia

          Abstract Background The initial cases of novel coronavirus (2019-nCoV)–infected pneumonia (NCIP) occurred in Wuhan, Hubei Province, China, in December 2019 and January 2020. We analyzed data on the first 425 confirmed cases in Wuhan to determine the epidemiologic characteristics of NCIP. Methods We collected information on demographic characteristics, exposure history, and illness timelines of laboratory-confirmed cases of NCIP that had been reported by January 22, 2020. We described characteristics of the cases and estimated the key epidemiologic time-delay distributions. In the early period of exponential growth, we estimated the epidemic doubling time and the basic reproductive number. Results Among the first 425 patients with confirmed NCIP, the median age was 59 years and 56% were male. The majority of cases (55%) with onset before January 1, 2020, were linked to the Huanan Seafood Wholesale Market, as compared with 8.6% of the subsequent cases. The mean incubation period was 5.2 days (95% confidence interval [CI], 4.1 to 7.0), with the 95th percentile of the distribution at 12.5 days. In its early stages, the epidemic doubled in size every 7.4 days. With a mean serial interval of 7.5 days (95% CI, 5.3 to 19), the basic reproductive number was estimated to be 2.2 (95% CI, 1.4 to 3.9). Conclusions On the basis of this information, there is evidence that human-to-human transmission has occurred among close contacts since the middle of December 2019. Considerable efforts to reduce transmission will be required to control outbreaks if similar dynamics apply elsewhere. Measures to prevent or reduce transmission should be implemented in populations at risk. (Funded by the Ministry of Science and Technology of China and others.)
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            Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study

            Summary Background Since Dec 31, 2019, the Chinese city of Wuhan has reported an outbreak of atypical pneumonia caused by the 2019 novel coronavirus (2019-nCoV). Cases have been exported to other Chinese cities, as well as internationally, threatening to trigger a global outbreak. Here, we provide an estimate of the size of the epidemic in Wuhan on the basis of the number of cases exported from Wuhan to cities outside mainland China and forecast the extent of the domestic and global public health risks of epidemics, accounting for social and non-pharmaceutical prevention interventions. Methods We used data from Dec 31, 2019, to Jan 28, 2020, on the number of cases exported from Wuhan internationally (known days of symptom onset from Dec 25, 2019, to Jan 19, 2020) to infer the number of infections in Wuhan from Dec 1, 2019, to Jan 25, 2020. Cases exported domestically were then estimated. We forecasted the national and global spread of 2019-nCoV, accounting for the effect of the metropolitan-wide quarantine of Wuhan and surrounding cities, which began Jan 23–24, 2020. We used data on monthly flight bookings from the Official Aviation Guide and data on human mobility across more than 300 prefecture-level cities in mainland China from the Tencent database. Data on confirmed cases were obtained from the reports published by the Chinese Center for Disease Control and Prevention. Serial interval estimates were based on previous studies of severe acute respiratory syndrome coronavirus (SARS-CoV). A susceptible-exposed-infectious-recovered metapopulation model was used to simulate the epidemics across all major cities in China. The basic reproductive number was estimated using Markov Chain Monte Carlo methods and presented using the resulting posterior mean and 95% credibile interval (CrI). Findings In our baseline scenario, we estimated that the basic reproductive number for 2019-nCoV was 2·68 (95% CrI 2·47–2·86) and that 75 815 individuals (95% CrI 37 304–130 330) have been infected in Wuhan as of Jan 25, 2020. The epidemic doubling time was 6·4 days (95% CrI 5·8–7·1). We estimated that in the baseline scenario, Chongqing, Beijing, Shanghai, Guangzhou, and Shenzhen had imported 461 (95% CrI 227–805), 113 (57–193), 98 (49–168), 111 (56–191), and 80 (40–139) infections from Wuhan, respectively. If the transmissibility of 2019-nCoV were similar everywhere domestically and over time, we inferred that epidemics are already growing exponentially in multiple major cities of China with a lag time behind the Wuhan outbreak of about 1–2 weeks. Interpretation Given that 2019-nCoV is no longer contained within Wuhan, other major Chinese cities are probably sustaining localised outbreaks. Large cities overseas with close transport links to China could also become outbreak epicentres, unless substantial public health interventions at both the population and personal levels are implemented immediately. Independent self-sustaining outbreaks in major cities globally could become inevitable because of substantial exportation of presymptomatic cases and in the absence of large-scale public health interventions. Preparedness plans and mitigation interventions should be readied for quick deployment globally. Funding Health and Medical Research Fund (Hong Kong, China).
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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.

                Author and article information

                Philos Trans R Soc Lond B Biol Sci
                Philos Trans R Soc Lond B Biol Sci
                Philosophical Transactions of the Royal Society B: Biological Sciences
                The Royal Society
                July 19, 2021
                May 31, 2021
                May 31, 2021
                : 376
                : 1829 , Theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’ compiled and edited by Ellen Brooks-Pollock, Leon Danon, Thibaut Jombart and Lorenzo Pellis
                : 20200272
                [ 1 ]Department of Engineering Mathematics, Population Health Sciences, University of Bristol, Bristol BS8 1QU, , UK
                [ 2 ]Bristol Veterinary School, Population Health Sciences, University of Bristol, Bristol BS8 1QU, , UK
                [ 3 ]NIHR Health Protection Research Unit (HPRU) in Behavioural Science and Evaluation, Population Health Sciences, University of Bristol, Bristol BS8 1QU, , UK
                [ 4 ]Mathematics Institute, and School of Life Sciences, University of Warwick, , Coventry CV4 7AL, UK
                Author notes

                One contribution of 21 to a theme issue ‘ Modelling that shaped the early COVID-19 pandemic response in the UK’.

                Author information
                © 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.

                : April 17, 2021
                Funded by: Engineering and Physical Sciences Research Council, http://dx.doi.org/10.13039/501100000266;
                Award ID: EP/V051555/1
                Funded by: Medical Research Council, http://dx.doi.org/10.13039/501100000265;
                Award ID: MC_PC_19067
                Funded by: UK Research and Innovation, http://dx.doi.org/10.13039/100014013;
                Award ID: MR/V038613/1
                Research Articles
                Custom metadata
                July 19, 2021

                Philosophy of science
                modelling,human movement,spatial,seasonality
                Philosophy of science
                modelling, human movement, spatial, seasonality


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