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      The challenges of modeling and forecasting the spread of COVID-19

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          The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remain a challenge. Here, we present and detail three regional-scale models for forecasting and assessing the course of the pandemic. This work is intended to demonstrate the utility of parsimonious models for understanding the pandemic and to provide an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies.

          Abstract

          The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remains a challenge. Here, we detail three regional-scale models for forecasting and assessing the course of the pandemic. This work demonstrates the utility of parsimonious models for early-time data and provides an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies.

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          Most cited references36

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          Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study

          Summary Background Since December, 2019, Wuhan, China, has experienced an outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epidemiological and clinical characteristics of patients with COVID-19 have been reported but risk factors for mortality and a detailed clinical course of illness, including viral shedding, have not been well described. Methods In this retrospective, multicentre cohort study, we included all adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Jinyintan Hospital and Wuhan Pulmonary Hospital (Wuhan, China) who had been discharged or had died by Jan 31, 2020. Demographic, clinical, treatment, and laboratory data, including serial samples for viral RNA detection, were extracted from electronic medical records and compared between survivors and non-survivors. We used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death. Findings 191 patients (135 from Jinyintan Hospital and 56 from Wuhan Pulmonary Hospital) were included in this study, of whom 137 were discharged and 54 died in hospital. 91 (48%) patients had a comorbidity, with hypertension being the most common (58 [30%] patients), followed by diabetes (36 [19%] patients) and coronary heart disease (15 [8%] patients). Multivariable regression showed increasing odds of in-hospital death associated with older age (odds ratio 1·10, 95% CI 1·03–1·17, per year increase; p=0·0043), higher Sequential Organ Failure Assessment (SOFA) score (5·65, 2·61–12·23; p<0·0001), and d-dimer greater than 1 μg/mL (18·42, 2·64–128·55; p=0·0033) on admission. Median duration of viral shedding was 20·0 days (IQR 17·0–24·0) in survivors, but SARS-CoV-2 was detectable until death in non-survivors. The longest observed duration of viral shedding in survivors was 37 days. Interpretation The potential risk factors of older age, high SOFA score, and d-dimer greater than 1 μg/mL could help clinicians to identify patients with poor prognosis at an early stage. Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future. Funding Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences; National Science Grant for Distinguished Young Scholars; National Key Research and Development Program of China; The Beijing Science and Technology Project; and Major Projects of National Science and Technology on New Drug Creation and Development.
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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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              An interactive web-based dashboard to track COVID-19 in real time

              In December, 2019, a local outbreak of pneumonia of initially unknown cause was detected in Wuhan (Hubei, China), and was quickly determined to be caused by a novel coronavirus, 1 namely severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The outbreak has since spread to every province of mainland China as well as 27 other countries and regions, with more than 70 000 confirmed cases as of Feb 17, 2020. 2 In response to this ongoing public health emergency, we developed an online interactive dashboard, hosted by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University, Baltimore, MD, USA, to visualise and track reported cases of coronavirus disease 2019 (COVID-19) in real time. The dashboard, first shared publicly on Jan 22, illustrates the location and number of confirmed COVID-19 cases, deaths, and recoveries for all affected countries. It was developed to provide researchers, public health authorities, and the general public with a user-friendly tool to track the outbreak as it unfolds. All data collected and displayed are made freely available, initially through Google Sheets and now through a GitHub repository, along with the feature layers of the dashboard, which are now included in the Esri Living Atlas. The dashboard reports cases at the province level in China; at the city level in the USA, Australia, and Canada; and at the country level otherwise. During Jan 22–31, all data collection and processing were done manually, and updates were typically done twice a day, morning and night (US Eastern Time). As the outbreak evolved, the manual reporting process became unsustainable; therefore, on Feb 1, we adopted a semi-automated living data stream strategy. Our primary data source is DXY, an online platform run by members of the Chinese medical community, which aggregates local media and government reports to provide cumulative totals of COVID-19 cases in near real time at the province level in China and at the country level otherwise. Every 15 min, the cumulative case counts are updated from DXY for all provinces in China and for other affected countries and regions. For countries and regions outside mainland China (including Hong Kong, Macau, and Taiwan), we found DXY cumulative case counts to frequently lag behind other sources; we therefore manually update these case numbers throughout the day when new cases are identified. To identify new cases, we monitor various Twitter feeds, online news services, and direct communication sent through the dashboard. Before manually updating the dashboard, we confirm the case numbers with regional and local health departments, including the respective centres for disease control and prevention (CDC) of China, Taiwan, and Europe, the Hong Kong Department of Health, the Macau Government, and WHO, as well as city-level and state-level health authorities. For city-level case reports in the USA, Australia, and Canada, which we began reporting on Feb 1, we rely on the US CDC, the government of Canada, the Australian Government Department of Health, and various state or territory health authorities. All manual updates (for countries and regions outside mainland China) are coordinated by a team at Johns Hopkins University. The case data reported on the dashboard aligns with the daily Chinese CDC 3 and WHO situation reports 2 for within and outside of mainland China, respectively (figure ). Furthermore, the dashboard is particularly effective at capturing the timing of the first reported case of COVID-19 in new countries or regions (appendix). With the exception of Australia, Hong Kong, and Italy, the CSSE at Johns Hopkins University has reported newly infected countries ahead of WHO, with Hong Kong and Italy reported within hours of the corresponding WHO situation report. Figure Comparison of COVID-19 case reporting from different sources Daily cumulative case numbers (starting Jan 22, 2020) reported by the Johns Hopkins University Center for Systems Science and Engineering (CSSE), WHO situation reports, and the Chinese Center for Disease Control and Prevention (Chinese CDC) for within (A) and outside (B) mainland China. Given the popularity and impact of the dashboard to date, we plan to continue hosting and managing the tool throughout the entirety of the COVID-19 outbreak and to build out its capabilities to establish a standing tool to monitor and report on future outbreaks. We believe our efforts are crucial to help inform modelling efforts and control measures during the earliest stages of the outbreak.
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                Author and article information

                Journal
                Proc Natl Acad Sci U S A
                Proc. Natl. Acad. Sci. U.S.A
                pnas
                pnas
                PNAS
                Proceedings of the National Academy of Sciences of the United States of America
                National Academy of Sciences
                0027-8424
                1091-6490
                21 July 2020
                2 July 2020
                2 July 2020
                : 117
                : 29
                : 16732-16738
                Affiliations
                [1] aDepartment of Mathematics, University of California, Los Angeles, CA 90095;
                [2] bDepartment of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095;
                [3] cDepartment of Bioengineering, University of California, Los Angeles, CA 90095;
                [4] dDepartment of Computer Science, Indiana University–Purdue University Indianapolis, Indianapolis, IN 46202;
                [5] eDepartment of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332;
                [6] fDepartment of Political Science, University of Texas at Arlington, Arlington, TX 76019
                Author notes
                1To whom correspondence may be addressed. Email: bertozzi@ 123456ucla.edu .

                This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2018.

                Contributed by Andrea L. Bertozzi, April 15, 2020 (sent for review April 7, 2020; reviewed by Tapio Schneider, Chad Topaz, and Thomas P. Witelski)

                Author contributions: A.L.B., E.F., G.M., and M.B.S. designed research; A.L.B., E.F., G.M., M.B.S., and D.S. performed research; A.L.B., E.F., G.M., and M.B.S. analyzed data; and A.L.B., E.F., G.M., M.B.S., and D.S. wrote the paper.

                Reviewers: T.S., California Institute of Technology; C.T., Williams College; and T.P.W., Duke University.

                Author information
                http://orcid.org/0000-0003-0396-7391
                Article
                202006520
                10.1073/pnas.2006520117
                7382213
                32616574
                e7360f11-87af-4d28-8635-b14d4599dfda
                Copyright © 2020 the Author(s). Published by PNAS.

                This open access article is distributed under Creative Commons Attribution License 4.0 (CC BY).

                History
                Page count
                Pages: 7
                Funding
                Funded by: National Science Foundation (NSF) 100000001
                Award ID: 2027438
                Award Recipient : Andrea L. Bertozzi Award Recipient : George Mohler
                Funded by: National Science Foundation (NSF) 100000001
                Award ID: 1737770
                Award Recipient : Andrea L. Bertozzi Award Recipient : George Mohler
                Funded by: National Science Foundation (NSF) 100000001
                Award ID: 1737585
                Award Recipient : Andrea L. Bertozzi Award Recipient : George Mohler
                Funded by: National Science Foundation (NSF) 100000001
                Award ID: 1737996
                Award Recipient : Andrea L. Bertozzi Award Recipient : George Mohler
                Funded by: Simons Foundation 100000893
                Award ID: 510776
                Award Recipient : Andrea L. Bertozzi
                Categories
                530
                1
                Physical Sciences
                Applied Mathematics
                Inaugural Article
                Custom metadata
                free

                covid-19,pandemic,branching process,compartmental models

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