key: cord-1054092-lcpk5se4
authors: Fang, Yaqing; Nie, Yiting; Penny, Marshare
title: Transmission dynamics of the COVID‐19 outbreak and effectiveness of government interventions: A data‐driven analysis
date: 2020-03-16
journal: J Med Virol
DOI: 10.1002/jmv.25750
sha: 9d7c26085fbd542bbbd265b777d7de34b672a489
doc_id: 1054092
cord_uid: lcpk5se4

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 fitting after the simulation. By simulation and data fitting, the model showed the peak existing confirmed cases of 59 769 arriving on 15 February 2020, with the coefficient of determination close to 1 and the fitting bias 3.02%, suggesting high precision of the data‐fitting results. More rigorous government control policies were associated with a slower increase in the infected population. Isolation and protective procedures would be less effective as more cases accrue, so the optimization of the treatment plan and the development of specific drugs would be of more importance. There was an upward trend of R in the beginning, followed by a downward trend, a temporary rebound, and another continuous decline. The feature of high infectiousness for severe acute respiratory syndrome coronavirus 2(SARS‐CoV‐2) led to an upward trend, and government measures contributed to the temporary rebound and declines. The declines of R could be exploited as strong evidence for the effectiveness of the interventions. Evidence from the four‐phase stringent measures showed that it was significant to ensure early detection, early isolation, early treatment, adequate medical supplies, patients’ being admitted to designated hospitals, and comprehensive therapeutic strategy. Collaborative efforts are required to combat the novel coronavirus, focusing on both persistent strict domestic interventions and vigilance against exogenous imported cases.

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 (nCoV) infected pneumonia by 8 January 2020 2 and later be designated as COVID-19 by WHO. 3 The virus was named as the 2019-nCoV temporarily on 12 January 2020 1 and officially named as severe acute respiratory syndrome coronavirus 2 (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. Coronaviruses can cause illnesses that range from the common cold to much more severe illnesses like SARS, Middle East respiratory syndrome, and COVID-19. 2 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 now-closed market being a common factor in infections encouraged the belief that the infection may be linked with certain animals. The species that harbored the SARS-CoV-2 was probably bat, containing 96% identical at the whole-genome level. 4 The COVID-19 may include signs of fever, cough, shortness of breath and general breathing difficulties, organ failures or even death, posing a severe threat to the whole society. The WHO declared the coronavirus outbreak a global health emergency on 30 January 2020. 5 The global epidemic seemed to be spreading at an alarming rate, causing 79 824 accumulative laboratory-confirmed infections with 2870 deaths as of 29 February 2020 in China 6 and 6009 outside China, 7 so it deserved priority attention and intensive research. Chinese health authorities stated that it was likely to transmit from person to person even before any actual signs appeared, which made it especially difficult to prevent and control. 8 However, Chinese government have attached extremely great importance and taken a range of prompt public health measures in response to the epidemic, starting by the strict exit screening measures in Wuhan on 23 January and followed by extensive medical support in Wuhan, individual going out under protective equipment (masks), school postponement, cancellation of mass gatherings, spontaneous isolated population, and so on.

Meanwhile, researchers all around the world have been scrambling to ascertain how the virus spreads and find out the effective ways to put this outbreak quickly under control. Compared to the R 0 of H1N1 (1.25) 9 and that of SARS (2.2-3.6), 10 R 0 , the basic reproductive number, is defined as the expected number of additional cases that one case will generate, on average without external intervention. R 0 value is usually applied to reflect the potential and severity of infectious diseases. The larger R 0 is, the stronger the transmission power will be. If R 0 is less than 1, it means that the disease will gradually die out. 14 Despite all of the results of the nCoV, the epidemic kept in a constant state of change, especially after the rigorous measures have been taken by Chinese government, so it calls for more comprehensive research such as updated R 0 estimates, more appropriate index under the circumstances of intervention such as effective reproductive number (R), methodological improvements, and effect evaluation of control measures to reflect the dynamic and progress of it. In this study, we provided the latest distributions of COVID-19 in Wuhan, China, and the whole world.

Besides, we adopted the model of susceptible-exposed-infectiousrecovered (SEIR) to estimate the dynamics and the potential spread based on the current data of cases, to calculate the R 0 and R under different scenarios of the epidemic, and to draw preliminary conclusions about the effectiveness of government measures.

The data of COVID-19 in the study were mainly obtained from National Health Commission of the People's Republic of China, Chinese Center for Disease Control and Prevention, WHO, and various websites of Chinese government agencies, official media, as well as some previous studies as of 29 February 2020.

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. 15 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).

In this study, equations for the population change of each warehouse were established as follows 15 

Sensitivity analysis is one of the commonly used methods to analyze uncertainty in the assessment. The sensitivity factors which had an important influence on the results were identified one by one from a number of uncertainty factors, and their influence degree and sensitivity degree on the overall results were analyzed and measured. The parameter whose slight variation could lead to a large change in the result was regarded as a sensitivity factor; otherwise, a nonsensitivity factor. 16 To explore the various influences of different parameters on the amount of infected people, sensitivity analysis was conducted.

The equation of sensitivity coefficient (E) was as follows 

The basic reproductive number R 0 determines the potential of an epidemic, the extent of transmission in the absence of control measures, and the ability of control measures to decrease spread. In contrast to R 0 , the effective reproductive number R measures the number of secondary cases generated by an infectious case once an epidemic is underway. The calculation formula of R 0 17 based on the SEIR model was

where T g denoted the generation period, approximate to serial interval;

and ρ denoted the ratio of incubation period to generation time.

We took the value of each parameter reasonably according to the above formula

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 FANG ET AL.

where the data of confirmed cases and suspected cases were from 19 In this study, the value of T g (mean 8.4 days) was assumed to be the same as Lipsitch findings 10 and the value for ρ (0.61) was derived from the average ρ of the result of Chan et al. 20 

Data fitting is the process of fitting models to data and analyzing the accuracy of the curve, 21 (Table S1 ). 

On the basis of the previous study, 10 It could be clearly seen that the greater the government control policy, the smaller the k value, the slower the S value reduction slope of the susceptible population, and the lower the I value distribution peak of the infected population. 

The R values in Figure 8 were calculated on the basis of case information available from 20 January to 29 February 2020. To show a more intuitive and clear picture of R, Figure 9 was drawn to visualize the trend of R values overtime, which indicated that there was an upward trend of R from 20 January to 30 January, a downward trend from 31 January to 11 February, a short rebound on 12 February and another continuous decline from 13 to 29 February. Time-series analysis was adopted to verify the decline statistically and the result by Dickey-Fuller Test was shown in Figure 10 , which proved to be nonstationary data (P > .05, and the data were decomposed into time series, as shown in Figure 11 , whose result (No. 01 trend of Figure 11 ) was consistent with that of .9809627046850399. 2 When data fitting was introduced, the SEIR model simulation of COVID-19 was presented in Figure 16 , with the peak existing confirmed cases of 59 769 arriving on 15 February 2020, close to the actual number of 58 016 on 17 February 2020. 25 The fitting bias was 3.02%, less than 5%.

This study was mainly a data-driven analysis, with the data coming fever or dyspnea, nutrition support treatment, and so on. [28] [29] [30] There was no specific antiviral strategies available, though Remdesivir, a promising drug that has been proved to be effective in fighting against Ebola virus, has been in the step of clinical trial in China. 27 Introduction of specific drug would be of great benefit to the containment of the outbreak.

It should be noted that estimation of R 0 during the pre-epidemic stage could be plagued by data uncertainty and variability, 31 so we introduced the effective reproductive number (R), whose equation (Table S2) century, which is not exactly the epidemic of a single country, more a public concern of the whole world; therefore, more international cooperation are required to combat the nCoV, focusing on both persistent strict domestic interventions and vigilance against exogenous imported cases.

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

The authors declare that there are no conflict of interests.

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