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Model Simulation On the basis of previous study(11), the case data released by Chinese authorities and official media(23,24), the assumptions of the parameters were established and the theoretical dynamics of COVID-19 based on SEIR model was simulated(Figure 4)

Transmission dynamics of the COVID-19 outbreak and effectiveness of government interventions: A data-driven analysis.

JOURNAL OF MEDICAL VIROLOGY, no. 6.0 (2020): 645.0-659.0

Cited by: 21|Views304
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Abstract

Using the parameterized susceptible-exposed-infectious-recovered model, we simulated the spread dynamics of coronavirus disease 2019 (COVID-19) outbreak and impact of different control measures, conducted the sensitivity analysis to identify the key factor, plotted the trend curve of effective reproductive number (R), and performed data f...More

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Introduction
  • An unknown virus was suspected to have emerged into the human population in Wuhan in late December, 2019 through a report of several pneumonia cases by a local hospital[1].Chinese health authorities took actions immediately and had detected a new virus relevant to the outbreak of disease, which was known as novel coronavirus infected pneumonia (NCIP) by 8 January 2020[2] and later be designated as Coronavirus Disease 2019(COVID-19) by the World Health Organization(WHO) [3].The virus was named as the 2019 novel coronavirus (2019nCoV) temporarily on 12 January 2020[1] and officially named as SARS-CoV-2 on 11 February 2020[3]by WHO.

    Coronaviruses, getting their name from the viruses' vague resemblance to monarchical crowns when imaged using an electron microscope,are a large family of viruses that cause disease in mammals and birds.
  • An unknown virus was suspected to have emerged into the human population in Wuhan in late December, 2019 through a report of several pneumonia cases by a local hospital[1].Chinese health authorities took actions immediately and had detected a new virus relevant to the outbreak of disease, which was known as novel coronavirus infected pneumonia (NCIP) by 8 January 2020[2] and later be designated as Coronavirus Disease 2019(COVID-19) by the World Health Organization(WHO) [3].The virus was named as the 2019 novel coronavirus (2019nCoV) temporarily on 12 January 2020[1] and officially named as SARS-CoV-2 on 11 February 2020[3]by WHO.
  • It’s urgent to provide more scientific information for a better understanding of the novel coronavirus and further containment of the outbreak
Highlights
  • An unknown virus was suspected to have emerged into the human population in Wuhan in late December, 2019 through a report of several pneumonia cases by a local hospital[1].Chinese health authorities took actions immediately and had detected a new virus relevant to the outbreak of disease, which was known as novel coronavirus infected pneumonia (NCIP) by 8 January 2020[2] and later be designated as Coronavirus Disease 2019(COVID-19) by the World Health Organization(WHO) [3].The virus was named as the 2019 novel coronavirus (2019nCoV) temporarily on 12 January 2020[1] and officially named as Severe Acute Respiratory Syndrome-CoV-2 on 11 February 2020[3]by World Health Organization.

    Coronaviruses, getting their name from the viruses' vague resemblance to monarchical crowns when imaged using an electron microscope,are a large family of viruses that cause disease in mammals and birds
  • On 30 January 2020, the epidemic of COVID-19 was declared as a Public Health Emergency of International Concern (PHEIC), the highest level in the World Health Organization's emergency response for infectious diseases
  • Coronaviruses can cause illnesses that range from the common cold to much more severe illnesses like Severe Acute Respiratory Syndrome (SARS), Middle East Respiratory Syndrome (MERS) and Coronavirus Disease 2019(COVID-19)[4]
  • Model Simulation On the basis of previous study[11], the case data released by Chinese authorities and official media[23,24], the assumptions of the parameters were established and the theoretical dynamics of COVID-19 based on SEIR model was simulated(Figure 4)
  • The optimization of therapeutic strategy and the development of specific drugs would be of more importance than quarantine and protective procedures as more cases accrue
Methods
  • Mathematical Model One of the mathematical models in epidemic dynamics, known as the "warehouse" model, has been widely applied for a long time since it was forwarded by Kermack and McKendrick in 1927.
  • It includes several basic and improved models such as SIR, SIS, SEIR and so on, among which SEIR is a typical example that takes the incubation period into account[16].
  • The SEIR, an extensively used epidemic model, can reflect the flows of people between four states: susceptible (S), exposed (E), infectious (I), and recovered (R).
Results
  • The Distribution of Confirmed COVID-19 Cases The geographical distributions of existing confirmed cases as of 29 February 2020 in Hubei Province, China and worldwide is shown in Figure 1.
  • The epidemic was spreading rapidly, with 27,700 existing confirmed cases in Wuhan city, 33,565 in Hubei province, 35,566 in China, 40,903 in the whole world.
  • Figure 2 shows the trend of existing confirmed cases home and abroad, which indicates the peak number on 17 February 2020 in China and an obvious rise from 25 February 2020 to 29 February 2020 overseas.
Conclusion
  • The authors' study was mainly a data-driven analysis, with the data coming from epidemiological results of published studies and current case information, programed, simulated and fitted by Python based on the SEIR model.
  • The SEIR model simulation of COVID-19 after data fitting showed the peak existing confirmed cases of 59769 arriving on 15 February 2020.
  • The conclusion was drawn with a good coefficient of determination (R2), which was very close to 1, and the fitting bias was 3.02%, suggesting high precision of the data fitting results.By simulation and data fitting, the model showed the peak existing confirmed cases of 59769 arriving on 15 February 2020, with sufficient goodness of fit.
  • It’s an unprecedented outbreak of coronavirus in the 20th century, which is not exactly the epidemic of a single country, more a public concern of the whole world, more international cooperation are required to combat the novel coronavirus, focusing on both persistent strict domestic interventions and vigilance against exogenous imported cases
Tables
  • Table1: Different government control measures and corresponding k values
Download tables as Excel
Funding
  • This research received no external funding.
Study subjects and analysis
individuals: 1000000
the equations were as follows and the actual incidence was standard incidence. Referring to the design approach of Lipsitch et al[11], our study was modeled in a population (N) of 1,000,000 individuals, consistent with the size of Wuhan city, which was approximately 906,0000 by the end of the year 2019. The model simulation was based on the hypotheses: [1] the whole population was susceptible; [2] unprotected contact between the susceptible and the infected would lead to infection;[3] the susceptible and the infectious were homogenous in the population; [4] the epidemic originated from one single case; [5] no intervention was taken in the early stage of COVID-19 epidemic; [6] the patient would be quarantined in the hospital once confirmed;[7] deterministic dynamic model was employed

admitted patients with pneumonia who had been working in Wuhan: 4
Coronaviruses can cause illnesses that range from the common cold to much more severe illnesses like Severe Acute Respiratory Syndrome (SARS), Middle East Respiratory Syndrome (MERS) and Coronavirus Disease 2019(COVID-19)[4]. The outbreak of COVID-19 originated from the four admitted patients with pneumonia who had been working in Wuhan Huanan Seafood Wholesale Market, doing business in live poultry, aquatic products, and some wild animals. The nowclosed market being a common factor in infections encouraged the belief that the infection may be linked with certain animals

individuals: 1000000
The incidence in the original model was bilinear, because the model assumed that the frequency of exposure U was directly proportional to the total population N in the environment, however the actual exposure frequency of patients was limited, that was to say, if the exposure frequency was a constant K, then the equations were as follows and the actual incidence was standard incidence. Referring to the design approach of Lipsitch et al[11], our study was modeled in a population (N) of 1,000,000 individuals, consistent with the size of Wuhan city, which was approximately 906,0000 by the end of the year 2019. The model simulation was based on the hypotheses: [1] the whole population was susceptible; [2] unprotected contact between the susceptible and the infected would lead to infection;[3] the susceptible and the infectious were homogenous in the population; [4] the epidemic originated from one single case; [5] no intervention was taken in the early stage of COVID-19 epidemic; [6] the patient would be quarantined in the hospital once confirmed;[7] deterministic dynamic model was employed

confirmed cases: 41
where Y(t) was the number of infections with symptoms by time t. We assumed the number of confirmed cases was i, the number of suspected cases was s, and the ratio of suspected cases to confirmed cases was k, then where the data of confirmed cases and suspected cases were from national health commission, the value of k was calculated to be 0.695(41/59) according to the result of Huang C et al[19],which showed 41 confirmed cases out of the 59 suspected cases. T[1] was the date of the first confirmed case of the novel coronavirus infection, which was 8 December 2019[20]

existing confirmed cases: 27700
The Distribution of Confirmed COVID-19 Cases The geographical distributions of existing confirmed cases as of 29 February 2020 in Hubei Province, China and worldwide is shown in Figure 1. The epidemic was spreading rapidly, with 27,700 existing confirmed cases in Wuhan city, 33,565 in Hubei province, 35,566 in China, 40,903 in the whole world(supplemental table 1). Figure 2 shows the trend of existing confirmed cases home and abroad, which indicates the peak number on 17 February 2020 in China and an obvious rise from 25 February 2020 to 29 February 2020 overseas

cases: 2391
The rebound was caused by inducing clinical diagnosis in the 4th phase of government measures. The number of new confirmed cases in Hubei province on 12 February was 14840(of which 13332 were clinically diagnosed), which was an extraordinary large increase compared to an average of 2391 cases from 1 February to 11 February (supplemental table 2). That accounted for the temporary rebound of R

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Author
Yaqing Fang
Yaqing Fang
Yiting Nie
Yiting Nie
Marshare Penny
Marshare Penny
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