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      SEIR modeling of the COVID-19 and its dynamics

      research-article
      , ,
      Nonlinear Dynamics
      Springer Netherlands
      COVID-19, Coronavirus, SEIR model, Nonlinear dynamics, Control

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          Abstract

          In this paper, a SEIR epidemic model for the COVID-19 is built according to some general control strategies, such as hospital, quarantine and external input. Based on the data of Hubei province, the particle swarm optimization (PSO) algorithm is applied to estimate the parameters of the system. We found that the parameters of the proposed SEIR model are different for different scenarios. Then, the model is employed to show the evolution of the epidemic in Hubei province, which shows that it can be used to forecast COVID-19 epidemic situation. Moreover, by introducing the seasonality and stochastic infection the parameters, nonlinear dynamics including chaos are found in the system. Finally, we discussed the control strategies of the COVID-19 based on the structure and parameters of the proposed model.

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          Most cited references23

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          A Novel Coronavirus from Patients with Pneumonia in China, 2019

          Summary In December 2019, a cluster of patients with pneumonia of unknown cause was linked to a seafood wholesale market in Wuhan, China. A previously unknown betacoronavirus was discovered through the use of unbiased sequencing in samples from patients with pneumonia. Human airway epithelial cells were used to isolate a novel coronavirus, named 2019-nCoV, which formed a clade within the subgenus sarbecovirus, Orthocoronavirinae subfamily. Different from both MERS-CoV and SARS-CoV, 2019-nCoV is the seventh member of the family of coronaviruses that infect humans. Enhanced surveillance and further investigation are ongoing. (Funded by the National Key Research and Development Program of China and the National Major Project for Control and Prevention of Infectious Disease in China.)
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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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              Emerging coronaviruses: Genome structure, replication, and pathogenesis

              Abstract The recent emergence of a novel coronavirus (2019‐nCoV), which is causing an outbreak of unusual viral pneumonia in patients in Wuhan, a central city in China, is another warning of the risk of CoVs posed to public health. In this minireview, we provide a brief introduction of the general features of CoVs and describe diseases caused by different CoVs in humans and animals. This review will help understand the biology and potential risk of CoVs that exist in richness in wildlife such as bats.
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                Author and article information

                Contributors
                pyx244896301@163.com
                Journal
                Nonlinear Dyn
                Nonlinear Dyn
                Nonlinear Dynamics
                Springer Netherlands (Dordrecht )
                0924-090X
                1573-269X
                18 June 2020
                : 1-14
                Affiliations
                GRID grid.216417.7, ISNI 0000 0001 0379 7164, School of Physics and Electronics, , Central South University, ; Changsha, 410083 China
                Author information
                http://orcid.org/0000-0002-6360-9038
                Article
                5743
                10.1007/s11071-020-05743-y
                7301771
                32836803
                24f22ed6-0136-46d2-9fcf-72fb1592f193
                © Springer Nature B.V. 2020

                This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.

                History
                : 25 April 2020
                : 4 June 2020
                Funding
                Funded by: Natural Science Foundation of China
                Award ID: No. 61901530
                Award ID: No. 11747150
                Award Recipient :
                Funded by: China Postdoctoral Science Foundation
                Award ID: No. 2019M652791
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/501100012152, National Postdoctoral Program for Innovative Talents;
                Award ID: No. BX20180386
                Award Recipient :
                Categories
                Original Paper

                covid-19,coronavirus,seir model,nonlinear dynamics,control
                covid-19, coronavirus, seir model, nonlinear dynamics, control

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