Assessment of the prevention and control effects on the outbreak of COVID-19 in Hunan, China: Based on a SEIAR Dynamic Model

Background: A new infectious disease, Coronavirus disease 2019 (COVID-19) has been first reported during December 2019 in Wuhan, China, cases have been exported to other cities and abroad rapidly. Hunan is the neighboring province of Wuhan, a series of preventive and control measures were taken to control the outbreak of COVID-19. It is critical to assess these measures on the epidemic progression for the benefit of global expectation. Method: A Susceptible-exposed-infections/asymptomatic-removed (SEIAR) model was established to evaluate the effect of preventive measures. Berkeley Madonna 8.3.18 was employed for the model simulation and prediction, and the curve-fitting problem was solved by Runge-Kutta fourth-order method. Results: In this study, we found that R t was 2.71 from January 21 to 27 and reduced to 0.21 after January 27, 2020. If measures have not been fully launched, patients in Hunan would reach the maximum (8.96 million) on March 25, 2020, and end in about 208 days; when measures have been fully launched, patients in Hunan would just reach the maximum (699) on February 9, 2020, and end in about 56 days, which was very closed to the actual situation. Conclusion: The outbreak of COVID-19 in Hunan, China has been well controlled under current measures, full implementation of measures could reduce the peak value, short the time to peak and duration of the outbreak effectively, which could provide a reference for controlling of COVID-19 for other countries.


BACKGROUND
A new infectious disease named Coronavirus disease 2019 (COVID-19), caused by Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been first reported in Wuhan, China during December 2019 [1]. On January 23, 2020, Wuhan had been sealed off from outside, and the highest level of public health response to emergencies has been implemented in China. On January 31, the World Health Organization (WHO) announced that this outbreak of COVID-19 has become a public health emergency of international concern (PHEIC) [2]. As of April 14, 2020 Beijing time, there were just 2004 patients left and the outbreak of COVID-19 in China was gradually under control.
But SARS-CoV-2 has spread rapidly over the world, 1917225 confirmed cases and 123401 deaths of COVID-19 have been reported in the world, including America (N=613886), Spain (N=174060), Italy (N=162488) and so on [3], which has caused a global pandemic.
Hunan is the neighboring province of Wuhan, China ( Figure 1). Coinciding with Spring Festival travel rush, the period of mass migration in China, many people from Wuhan traveled to Hunan before the lockdown [4,5]. The first case of COVID-19 in Hunan was diagnosed on January 21, 2020, and the total number of COVID-19 in Hunan was 1018, ranking the 5th in provinces of China [3]. After the outbreak, a series of preventive and control measures like rigorous temperature monitoring, closing public 4 spaces and entertainment, extending the national holiday, limiting travel and public gatherings, detection and treatment of patients, screening of close contacts, personal protection, publicity and education and so on were taken to control the spread of COVID-19. On February 29, 2020, there were no new cases in the outbreak in Hunan, and on March 14, 2020, there were no existing cases in Hunan anymore. The epidemic situation in Hunan has been well controlled, but we have never quantitatively evaluated the effectiveness of these measures, which is thus critical to assess the effects of these measures on the epidemic progression for the benefit of global expectation.
In this study, a Susceptible-exposed-infections/asymptomatic-removed (SEIAR) dynamic model was developed to estimate the transmissibility of SARS-CoV-2 and evaluate the effectiveness of prevention and control measures, to provide a reference for controlling the spread of COVID-19 for other countries.

Data source
The reported case of COVID-19 in Hunan was collected from the Health Commission and the Center for Disease Control and Prevention of Hunan [6]. Migration data was collected from Baidu map insight--migration big data [7]. The epidemic curve from January 21 to March 14, 2020 was collected for our study, the simulation time step was one day. 5 After the outbreak, a series of unprecedented nationwide measures in Hunan were taken to control the spread of COVID-19 [6]. a) Active monitoring: Temperature monitoring points have been set up in airports, railway stations, passenger stations, wharves, high-speed entrances and exits, shopping malls, supermarkets, hotels, hospitals, residential areas and so on, people with abnormal temperature would be isolated and observed immediately. For the migratory person, especially those who just came from Wuhan or other cities of Hubei province, doctors would observe them for 14 days and measure their temperature twice a day to find out whether they have fever, cough, chest distress or other symptoms that relevant to this disease, once relevant symptoms has been found, they would be sent to medical institutions for isolation and treatment.

Models and statistical analysis SEIAR model
A SEIAR model was established to evaluate the effect of prevention and control measures in Hunan. According to the disease status, people were divided into five departments, susceptible people(S), exposed people (E), symptomatic infected people (I), asymptomatic infected people (A) and removed people(R). [8,9]. The model was 7 developed based on the following facts or assumptions: 1) S was assumed to have an equal infectious rate (β) with I, the ratio of infectious rate of A to I was  ; 2) E would turn to I or A after a certain exposed period (1/ω), the latency coefficient (ω) meant the rate each E turn to I or A per unit day; 3) 1/γ was the infectious period of I or A, γ meant the removal rate, the number of I and A turn to R per unit time was (γ1A+γ2I); 4) The deaths of COVID-19 were ignored because it was very low in Hunan [8,9].
dS/dt, dE/dt, dI/dt, dA/dt and dR/dt indicated the number of individuals (n) at time t in the corresponding departments, respectively, the model equations were as follows: (1)

Parameter estimation
There were five initial values and six parameters in the model, which were listed in Table 1. b) According to Baidu migration big data in China, there were about 250 thousand people traveled from Wuhan to Hunan one week before the lockdown [7], and the incidence rate of COVID-19 in Wuhan at that time was about 0.1% [11,12], it was estimated that exposed people entered Hunan at that time was E0=250 c) The mean incubation period (1/) was 5.2 days (95% CI: 4.1 -7.0) [13], =1/5.2.
As of February 12, 2020, 972 symptomatic infectious people and 121 asymptomatic infectious people were reported in Hunan, so the proportion of asymptomatic infectious rate of people in the model was P=121/(972+121)=11.1%. e) Once symptomatic infected individuals were diagnosed, they would be isolated, and the average time from onset to diagnosis was 3 days in Hunan, so, the removal rate of I was γ2=1/3; While those asymptomatic infected individuals would not be easily found and isolated, the recovery day of A was 14 days [14], so the removal rate of A was γ1=1/14.

Simulation methods
Data from the outbreak of COVID-19 in Hunan was fitted to a SEIAR model curve

Evaluation about the effectiveness of prevention and control measures
Based on the implementation degree of the prevention and control measures in Hunan, we divided the time into two periods. The first period was from January 21 to 27, 2020, when these measures have not been fully launched; the second period was from January 28 to March 14, 2020, during which these measures have been fully launched.
a) The effects on Rt 9 The regeneration number (Rt) meant the expected number of secondary infections which result from introducing a single infected individual into an otherwise susceptible population at the time t [15]. Calculate Rt in these two periods to evaluate the prevention and control effect in Hunan. If Rt > 1, the outbreak would continue, if Rt < 1, the outbreak would go to end, the more reduction of Rt, the better the control effect. Rt was calculated by the following formula [13]: b) The effects on peaks and epidemic duration Two prediction models based on different parameters obtained by model fitting in different periods were established, the peaks and epidemic duration in two models were compared to explore whether the full implementation of prevention and control measures has an impact on the peak value, peak time and duration of the epidemic.

Epidemiological features of the outbreak of COVID-19 in Hunan
The first case of COVID-19 in Hunan was diagnosed on January 21, 2020, the  10 and spaces among patients in Hunan was shown in Figure 3.

The effects of measures on Rt
The results of curve fitting of the data in Hunan and SEIAR model showed that the simulated result agreed well with the reported data when

The effects of measures on peaks and epidemic duration
The prediction results showed that if prevention and control measures have not been fully launched, the total number of patients in Hunan would reach the maximum The forecast results were shown in Figure 5.

DISCUSSION
It is important to decrease Rt to control the transmission of virus [14][15][16][17][18]. Due to different time and places, Rt obtained by different researchers were ranged from1.10 to 11 6.47 in China [14][15][16][17][18]. The number of patients is changing rapidly, the measures taken in different time and places are not all the same, which make it necessary to adjust the model and parameters in respect of different situations in different regions. In this study, we found that Rt was 2.71 from January 21 to 27 in Hunan, which was similar to R0 in the early stage of Wuhan [14,16,18], and reduced to 0.21 rapidly after January 27, 2020, In addition, we also found that the proportion of asymptomatic infected people of COVID-19 was low in Hunan (P=11.1%), but the infection rate were just little lower than symptomatic infected people (  =0.83 to 0.84). In the follow-up work, we should pay more attention to asymptomatic infected people and carry out effective methods to find out them, especially from the focus groups, such as employees and students returning to enterprises or schools from Wuhan or abroad, close contacts of confirmed patients, medical workers and so on to reduce the impact of asymptomatic infection on the re-outbreak of COVID-19.
The actual situation was changeable and complex, differences remained between the simulation and actual data, which is the limitation of our study. Besides, the number of imported COVID-19 cases in China is increasing with the rapid growth of cases abroad, which may have some impact on the development of the epidemic of COVID-19 in China, the model and parameters need further adjustment according to the actual situation.

CONCLUSIONS
The outbreak of COVID-19 in Hunan, China has been well controlled by current measures, full implementation of measures could reduce the peak value, short the time to peak and duration of the outbreak effectively, which could provide a reference for controlling of COVID-19 for other countries.  Table 1 List of parameters and initial values of each categorie in model