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      Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020

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          Abstract

          The initial cluster of severe pneumonia cases that triggered the COVID-19 epidemic was identified in Wuhan, China in December 2019. While early cases of the disease were linked to a wet market, human-to-human transmission has driven the rapid spread of the virus throughout China. The Chinese government has implemented containment strategies of city-wide lockdowns, screening at airports and train stations, and isolation of suspected patients; however, the cumulative case count keeps growing every day. The ongoing outbreak presents a challenge for modelers, as limited data are available on the early growth trajectory, and the epidemiological characteristics of the novel coronavirus are yet to be fully elucidated.

          We use phenomenological models that have been validated during previous outbreaks to generate and assess short-term forecasts of the cumulative number of confirmed reported cases in Hubei province, the epicenter of the epidemic, and for the overall trajectory in China, excluding the province of Hubei. We collect daily reported cumulative confirmed cases for the 2019-nCoV outbreak for each Chinese province from the National Health Commission of China. Here, we provide 5, 10, and 15 day forecasts for five consecutive days, February 5th through February 9th, with quantified uncertainty based on a generalized logistic growth model, the Richards growth model, and a sub-epidemic wave model.

          Our most recent forecasts reported here, based on data up until February 9, 2020, largely agree across the three models presented and suggest an average range of 7409–7496 additional confirmed cases in Hubei and 1128–1929 additional cases in other provinces within the next five days. Models also predict an average total cumulative case count between 37,415 and 38,028 in Hubei and 11,588–13,499 in other provinces by February 24, 2020.

          Mean estimates and uncertainty bounds for both Hubei and other provinces have remained relatively stable in the last three reporting dates (February 7th – 9th). We also observe that each of the models predicts that the epidemic has reached saturation in both Hubei and other provinces. Our findings suggest that the containment strategies implemented in China are successfully reducing transmission and that the epidemic growth has slowed in recent days.

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          Most cited references11

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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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              Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts

              Mathematical models provide a quantitative framework with which scientists can assess hypotheses on the potential underlying mechanisms that explain patterns in observed data at different spatial and temporal scales, generate estimates of key kinetic parameters, assess the impact of interventions, optimize the impact of control strategies, and generate forecasts. We review and illustrate a simple data assimilation framework for calibrating mathematical models based on ordinary differential equation models using time series data describing the temporal progression of case counts relating, for instance, to population growth or infectious disease transmission dynamics. In contrast to Bayesian estimation approaches that always raise the question of how to set priors for the parameters, this frequentist approach relies on modeling the error structure in the data. We discuss issues related to parameter identifiability, uncertainty quantification and propagation as well as model performance and forecasts along examples based on phenomenological and mechanistic models parameterized using simulated and real datasets.
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                Author and article information

                Contributors
                Journal
                Infect Dis Model
                Infect Dis Model
                Infectious Disease Modelling
                KeAi Publishing
                2468-2152
                2468-0427
                14 February 2020
                2020
                14 February 2020
                : 5
                : 256-263
                Affiliations
                [a ]Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, GA, USA
                [b ]Department of Mathematics, Center for Computational Science, Tulane University, New Orleans, LA, USA
                [c ]Infectious Disease Prevention and Control Branch, Public Health Agency of Canada, Ottawa, Canada
                Author notes
                []Corresponding author. gchowell@ 123456gsu.edu
                Article
                S2468-0427(20)30005-1
                10.1016/j.idm.2020.02.002
                7033348
                32110742
                dc8bd160-c9af-4e9a-95e8-59bd971bb951
                © 2020 The Authors

                This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

                History
                : 10 February 2020
                : 11 February 2020
                : 12 February 2020
                Categories
                Special issue on Modelling and Forecasting the 2019 Novel Coronavirus (2019-nCoV) Transmission; Edited by Prof. Carlos Castillo-Chavez, Prof. Gerardo Chowell-Puente, Prof. Ping Yan, Prof. Jianhong Wu

                covid-19,coronavirus,china,real-time forecasts,phenomenological models

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