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      Mathematical models for devising the optimal SARS-CoV-2 strategy for eradication in China, South Korea, and Italy

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          Abstract

          Background

          Coronavirus disease 2019 (COVID-19), which is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), spreads rapidly and has attracted worldwide attention.

          Methods

          To improve the forecast accuracy and investigate the spread of SARS-CoV-2, we constructed four mathematical models to numerically estimate the spread of SARS-CoV-2 and the efficacy of eradication strategies.

          Results

          Using the Susceptible-Exposed-Infected-Removed (SEIR) model, and including measures such as city closures and extended leave policies implemented by the Chinese government that effectively reduced the β value, we estimated that the β value and basic transmission number, R 0 , of SARS-CoV-2 was 0.476/6.66 in Wuhan, 0.359/5.03 in Korea, and 0.400/5.60 in Italy. Considering medicine and vaccines, an advanced model demonstrated that the emergence of vaccines would greatly slow the spread of the virus. Our model predicted that 100,000 people would become infected assuming that the isolation rate α in Wuhan was 0.30. If quarantine measures were taken from March 10, 2020, and the quarantine rate of α was also 0.3, then the final number of infected people was predicted to be 11,426 in South Korea and 147,142 in Italy.

          Conclusions

          Our mathematical models indicate that SARS-CoV-2 eradication depends on systematic planning, effective hospital isolation, and SARS-CoV-2 vaccination, and some measures including city closures and leave policies should be implemented to ensure SARS-CoV-2 eradication.

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          Most cited references13

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          A novel coronavirus outbreak of global health concern

          In December, 2019, Wuhan, Hubei province, China, became the centre of an outbreak of pneumonia of unknown cause, which raised intense attention not only within China but internationally. Chinese health authorities did an immediate investigation to characterise and control the disease, including isolation of people suspected to have the disease, close monitoring of contacts, epidemiological and clinical data collection from patients, and development of diagnostic and treatment procedures. By Jan 7, 2020, Chinese scientists had isolated a novel coronavirus (CoV) from patients in Wuhan. The genetic sequence of the 2019 novel coronavirus (2019-nCoV) enabled the rapid development of point-of-care real-time RT-PCR diagnostic tests specific for 2019-nCoV (based on full genome sequence data on the Global Initiative on Sharing All Influenza Data [GISAID] platform). Cases of 2019-nCoV are no longer limited to Wuhan. Nine exported cases of 2019-nCoV infection have been reported in Thailand, Japan, Korea, the USA, Vietnam, and Singapore to date, and further dissemination through air travel is likely.1, 2, 3, 4, 5 As of Jan 23, 2020, confirmed cases were consecutively reported in 32 provinces, municipalities, and special administrative regions in China, including Hong Kong, Macau, and Taiwan. 3 These cases detected outside Wuhan, together with the detection of infection in at least one household cluster—reported by Jasper Fuk-Woo Chan and colleagues 6 in The Lancet—and the recently documented infections in health-care workers caring for patients with 2019-nCoV indicate human-to-human transmission and thus the risk of much wider spread of the disease. As of Jan 23, 2020, a total of 835 cases with laboratory-confirmed 2019-nCoV infection have been detected in China, of whom 25 have died and 93% remain in hospital (figure ). 3 Figure Timeline of early stages of 2019-nCoV outbreak 2019-nCoV=2019 novel coronavirus. In The Lancet, Chaolin Huang and colleagues 7 report clinical features of the first 41 patients admitted to the designated hospital in Wuhan who were confirmed to be infected with 2019-nCoV by Jan 2, 2020. The study findings provide first-hand data about severity of the emerging 2019-nCoV infection. Symptoms resulting from 2019-nCoV infection at the prodromal phase, including fever, dry cough, and malaise, are non-specific. Unlike human coronavirus infections, upper respiratory symptoms are notably infrequent. Intestinal presentations observed with SARS also appear to be uncommon, although two of six cases reported by Chan and colleagues had diarrhoea. 6 Common laboratory findings on admission to hospital include lymphopenia and bilateral ground-glass opacity or consolidation in chest CT scans. These clinical presentations confounded early detection of infected cases, especially against a background of ongoing influenza and circulation of other respiratory viruses. Exposure history to the Huanan Seafood Wholesale market served as an important clue at the early stage, yet its value has decreased as more secondary and tertiary cases have appeared. Of the 41 patients in this cohort, 22 (55%) developed severe dyspnoea and 13 (32%) required admission to an intensive care unit, and six died. 7 Hence, the case-fatality proportion in this cohort is approximately 14·6%, and the overall case fatality proportion appears to be closer to 3% (table ). However, both of these estimates should be treated with great caution because not all patients have concluded their illness (ie, recovered or died) and the true number of infections and full disease spectrum are unknown. Importantly, in emerging viral infection outbreaks the case-fatality ratio is often overestimated in the early stages because case detection is highly biased towards the more severe cases. As further data on the spectrum of mild or asymptomatic infection becomes available, one case of which was documented by Chan and colleagues, 6 the case-fatality ratio is likely to decrease. Nevertheless, the 1918 influenza pandemic is estimated to have had a case-fatality ratio of less than 5% 13 but had an enormous impact due to widespread transmission, so there is no room for complacency. Table Characteristics of patients who have been infected with 2019-nCoV, MERS-CoV, and SARS-CoV7, 8, 10, 11, 12 2019-nCoV * MERS-CoV SARS-CoV Demographic Date December, 2019 June, 2012 November, 2002 Location of first detection Wuhan, China Jeddah, Saudi Arabia Guangdong, China Age, years (range) 49 (21–76) 56 (14–94) 39·9 (1–91) Male:female sex ratio 2·7:1 3·3:1 1:1·25 Confirmed cases 835† 2494 8096 Mortality 25† (2·9%) 858 (37%) 744 (10%) Health-care workers 16‡ 9·8% 23·1% Symptoms Fever 40 (98%) 98% 99–100% Dry cough 31 (76%) 47% 29–75% Dyspnoea 22 (55%) 72% 40–42% Diarrhoea 1 (3%) 26% 20–25% Sore throat 0 21% 13–25% Ventilatory support 9·8% 80% 14–20% Data are n, age (range), or n (%) unless otherwise stated. 2019-nCoV=2019 novel coronavirus. MERS-CoV=Middle East respiratory syndrome coronavirus. SARS-CoV=severe acute respiratory syndrome coronavirus. * Demographics and symptoms for 2019-nCoV infection are based on data from the first 41 patients reported by Chaolin Huang and colleagues (admitted before Jan 2, 2020). 8 Case numbers and mortalities are updated up to Jan 21, 2020) as disclosed by the Chinese Health Commission. † Data as of Jan 23, 2020. ‡ Data as of Jan 21, 2020. 9 As an RNA virus, 2019-nCoV still has the inherent feature of a high mutation rate, although like other coronaviruses the mutation rate might be somewhat lower than other RNA viruses because of its genome-encoded exonuclease. This aspect provides the possibility for this newly introduced zoonotic viral pathogen to adapt to become more efficiently transmitted from person to person and possibly become more virulent. Two previous coronavirus outbreaks had been reported in the 21st century. The clinical features of 2019-nCoV, in comparison with SARS-CoV and Middle East respiratory syndrome (MERS)-CoV, are summarised in the table. The ongoing 2019-nCoV outbreak has undoubtedly caused the memories of the SARS-CoV outbreak starting 17 years ago to resurface in many people. In November, 2002, clusters of pneumonia of unknown cause were reported in Guangdong province, China, now known as the SARS-CoV outbreak. The number of cases of SARS increased substantially in the next year in China and later spread globally, 14 infecting at least 8096 people and causing 774 deaths. 12 The international spread of SARS-CoV in 2003 was attributed to its strong transmission ability under specific circumstances and the insufficient preparedness and implementation of infection control practices. Chinese public health and scientific capabilities have been greatly transformed since 2003. An efficient system is ready for monitoring and responding to infectious disease outbreaks and the 2019-nCoV pneumonia has been quickly added to the Notifiable Communicable Disease List and given the highest priority by Chinese health authorities. The increasing number of cases and widening geographical spread of the disease raise grave concerns about the future trajectory of the outbreak, especially with the Chinese Lunar New Year quickly approaching. Under normal circumstances, an estimated 3 billion trips would be made in the Spring Festival travel rush this year, with 15 million trips happening in Wuhan. The virus might further spread to other places during this festival period and cause epidemics, especially if it has acquired the ability to efficiently transmit from person to person. Consequently, the 2019-nCoV outbreak has led to implementation of extraordinary public health measures to reduce further spread of the virus within China and elsewhere. Although WHO has not recommended any international travelling restrictions so far, 15 the local government in Wuhan announced on Jan 23, 2020, the suspension of public transportation, with closure of airports, railway stations, and highways in the city, to prevent further disease transmission. 16 Further efforts in travel restriction might follow. Active surveillance for new cases and close monitoring of their contacts are being implemented. To improve detection efficiency, front-line clinics, apart from local centres for disease control and prevention, should be armed with validated point-of-care diagnostic kits. Rapid information disclosure is a top priority for disease control and prevention. A daily press release system has been established in China to ensure effective and efficient disclosure of epidemic information. Education campaigns should be launched to promote precautions for travellers, including frequent hand-washing, cough etiquette, and use of personal protection equipment (eg, masks) when visiting public places. Also, the general public should be motivated to report fever and other risk factors for coronavirus infection, including travel history to affected area and close contacts with confirmed or suspected cases. Considering that substantial numbers of patients with SARS and MERS were infected in health-care settings, precautions need to be taken to prevent nosocomial spread of the virus. Unfortunately, 16 health-care workers, some of whom were working in the same ward, have been confirmed to be infected with 2019-nCoV to date, although the routes of transmission and the possible role of so-called super-spreaders remain to be clarified. 9 Epidemiological studies need to be done to assess risk factors for infection in health-care personnel and quantify potential subclinical or asymptomatic infections. Notably, the transmission of SARS-CoV was eventually halted by public health measures including elimination of nosocomial infections. We need to be wary of the current outbreak turning into a sustained epidemic or even a pandemic. The availability of the virus' genetic sequence and initial data on the epidemiology and clinical consequences of the 2019-nCoV infections are only the first steps to understanding the threat posed by this pathogen. Many important questions remain unanswered, including its origin, extent, and duration of transmission in humans, ability to infect other animal hosts, and the spectrum and pathogenesis of human infections. Characterising viral isolates from successive generations of human infections will be key to updating diagnostics and assessing viral evolution. Beyond supportive care, 17 no specific coronavirus antivirals or vaccines of proven efficacy in humans exist, although clinical trials of both are ongoing for MERS-CoV and one controlled trial of ritonavir-boosted lopinavir monotherapy has been launched for 2019-nCoV (ChiCTR2000029308). Future animal model and clinical studies should focus on assessing the effectiveness and safety of promising antiviral drugs, monoclonal and polyclonal neutralising antibody products, and therapeutics directed against immunopathologic host responses. We have to be aware of the challenge and concerns brought by 2019-nCoV to our community. Every effort should be given to understand and control the disease, and the time to act is now. This online publication has been corrected. The corrected version first appeared at thelancet.com on January 29, 2020
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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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              Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)

              Estimation of the prevalence and contagiousness of undocumented novel coronavirus (SARS-CoV2) infections is critical for understanding the overall prevalence and pandemic potential of this disease. Here we use observations of reported infection within China, in conjunction with mobility data, a networked dynamic metapopulation model and Bayesian inference, to infer critical epidemiological characteristics associated with SARS-CoV2, including the fraction of undocumented infections and their contagiousness. We estimate 86% of all infections were undocumented (95% CI: [82%–90%]) prior to 23 January 2020 travel restrictions. Per person, the transmission rate of undocumented infections was 55% of documented infections ([46%–62%]), yet, due to their greater numbers, undocumented infections were the infection source for 79% of documented cases. These findings explain the rapid geographic spread of SARS-CoV2 and indicate containment of this virus will be particularly challenging.
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                Author and article information

                Contributors
                js951227@163.com
                liqiuyuexzh@126.com
                cqli@sibs.ac.cn
                sfphbzv@qq.com
                2215746263@qq.com
                wangtao69@sina.com
                kaikaixinxin@sjtu.edu.cn
                christopher.corpe@kcl.ac.uk
                18801119270@163.com
                13791795950@163.com
                wjincityu@yahoo.com
                Journal
                J Transl Med
                J Transl Med
                Journal of Translational Medicine
                BioMed Central (London )
                1479-5876
                5 September 2020
                5 September 2020
                2020
                : 18
                : 345
                Affiliations
                [1 ]GRID grid.8547.e, ISNI 0000 0001 0125 2443, Shanghai Public Health Clinical Center, , Fudan University, ; 2901 Caolang Road, Jinshan District, Shanghai, 201508 People’s Republic of China
                [2 ]Wuhan Academy of Social Science, Wuhan, Hubei China
                [3 ]GRID grid.16821.3c, ISNI 0000 0004 0368 8293, State Key Laboratory for Oncogenes and Bio-ID Center, School of Biomedical Engineering, , Shanghai Jiao Tong University, ; Shanghai, China
                [4 ]GRID grid.13097.3c, ISNI 0000 0001 2322 6764, King’s College London, Nutritional Science Department, ; 150 Stamford Street, Waterloo, SE19NH London, UK
                Author information
                http://orcid.org/0000-0002-0062-2489
                Article
                2513
                10.1186/s12967-020-02513-7
                7474336
                ccef3cc5-6924-43d5-9f30-3bc3371fb97a
                © The Author(s) 2020

                Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

                History
                : 11 April 2020
                : 27 August 2020
                Funding
                Funded by: National Special Research Program of China for Important Infectious Diseases
                Award ID: 2018ZX10302103-003
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/501100001809, National Natural Science Foundation of China;
                Award ID: 81672383
                Award Recipient :
                Categories
                Research
                Custom metadata
                © The Author(s) 2020

                Medicine
                covid-19,sars-cov-2,mathematical models,hospital isolation
                Medicine
                covid-19, sars-cov-2, mathematical models, hospital isolation

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