Modelling the effects of Wuhan’s lockdown during COVID-19, China

Abstract Objective To design a simple model to assess the effectiveness of measures to prevent the spread of coronavirus disease 2019 (COVID-19) to different regions of mainland China. Methods We extracted data on population movements from an internet company data set and the numbers of confirmed cases of COVID-19 from government sources. On 23 January 2020 all travel in and out of the city of Wuhan was prohibited to control the spread of the disease. We modelled two key factors affecting the cumulative number of COVID-19 cases in regions outside Wuhan by 1 March 2020: (i) the total the number of people leaving Wuhan during 20–26 January 2020; and (ii) the number of seed cases from Wuhan before 19 January 2020, represented by the cumulative number of confirmed cases on 29 January 2020. We constructed a regression model to predict the cumulative number of cases in non-Wuhan regions in three assumed epidemic control scenarios. Findings Delaying the start date of control measures by only 3 days would have increased the estimated 30 699 confirmed cases of COVID-19 by 1 March 2020 in regions outside Wuhan by 34.6% (to 41 330 people). Advancing controls by 3 days would reduce infections by 30.8% (to 21 235 people) with basic control measures or 48.6% (to 15 796 people) with strict control measures. Based on standard residual values from the model, we were able to rank regions which were most effective in controlling the epidemic. Conclusion The control measures in Wuhan combined with nationwide traffic restrictions and self-isolation reduced the ongoing spread of COVID-19 across China.


Introduction
Coronavirus disease 2019 , caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), was first identified in December 2019 in Wuhan, the capital city of Hubei province of China. 1 On 30 January 2020 the World Health Organization declared the COVID-19 epidemic a public health emergency of international concern. By 1 March 2020, the overall number of people confirmed with COVID-19 in China had reached 80 174 and a total of 2915 people had died of the disease. 2 Current knowledge about SARS-CoV-2 is that the virus has diverse routes of transmission and there are also now reports of virus transmission from asymptomatic individuals. 3,4 Early estimates of the basic reproductive number (R 0 ) of COVID-19 were 2.2 (95% CI: 1.4 to 3.9), 5 2.68 (95% CI: 2.47 to 2.86), 6 3.6 to 4.0, 7 and 3.77 (range 2.23 to 4.82). 8 A later estimate of R 0 was 6.47 (95% CI: 5.71 to 7.23). 9 These values showed that SARS-CoV-2 is highly contagious and it was projected that without any control measures the infected population would exceed 200 000 in Wuhan by the end of February 2020. 10 Other researchers estimated infected numbers of 191 529 (95% CI: 132 751 to 273 649) by 4 February 2020. 11 In the absence of an effective vaccine, 12 social distancing measures were needed to prevent transmission of the virus. 13,14 The Chinese government therefore implemented a series of large-scale interventions to control the epidemic. The strictest control measures were applied in Wuhan with a complete lockdown of the population. Starting at 10 a.m. on 23 January 2020, Wuhan city officials prohibited all transport in and out of the city of 9 million residents. Within the rest of China, the interventions included nationwide traffic restrictions in the form of increased checkpoints at road junctions to reduce the number of people travelling and self-isolation of the popula-tion at home to reduce outside activities. Hundreds of millions of Chinese residents had to reduce or stop their inter-city travel and intra-city activities due to these measures. 15 Following the interventions in Wuhan, estimates show that the median daily R 0 value of COVID-19 declined from 2.35 on 16 January 2020 to 1.05 by 30 January 2020 16 and the spread of infection to other cities was deferred by 2.91 days (95% confidence interval, CI: 2.54 to 3.29). 15 However, other researchers have suggested that travel restrictions from and to Wuhan city are unlikely to have been effective in halting transmission across China. Despite an estimated 99% reduction in the number of people travelling from Wuhan to other areas (663 713 out of 670 417 people), the number of infected people in non-Wuhan areas may only have been reduced by 24.9% (1016 out of 4083 people) by 4 February 2020. 11 These large-scale public health interventions have caused significant disruption to the economic structure in China and globally. 14,17 Questions remain whether these interventions are necessary or really worked well in China and how to assess the performance of public health authorities in different regions in mainland China in controlling the epidemic.
We present a simple model based on online data on population movements and confirmed numbers of people infected to quantify the consequences of the control measures in Wuhan on the ongoing spread of COVID-19 across mainland China. We also aimed to make a preliminary assessment of the efforts of the public health authorities in 29 provinces and 44 prefecture-level cities during the epidemic.

Data sources
The Chinese Transport Commission does not release detailed data on population movements between cities. We therefore used data from Baidu Migration (Baidu Inc., Beijing, China), a largescale data set based on an application that tracks the movements of mobile phone users and publishes the data in real time. 18 We extracted data on interand intra-city population movements from 1 January 2020 to 29 February 2020 in mainland China, including data for the same period in 2019 from 12 January to 12 March (based on the lunar calendar). The Baidu platform represents the inter-city travel population of each city by the immigration and emigration indices. The intensity of intra-city population movements in each city is the ratio of the number of people travelling within a city to the number of residents in the city.
To determine the number of people represented by the migration index per unit, we used data on population movements during the 2019 Spring Festival travel rush in China (over 40 days from 21 January 2019 to 1 March 2019). We extracted the actual number of people entering and leaving Beijing and Shanghai cities, and the number of people leaving Foshan, Nanjing, Qingdao, Shenzhen and Wuhan cities from the official website of the local municipal transport commissions. [19][20][21][22][23][24][25] We constructed a simple regression equation with a constant term of 0, with the y coordinates representing the number of travellers and x coordinates representing the Baidu migration index. We estimated that each unit of the Baidu migration index was about equivalent to 56 137 travellers (Fig. 1 Data sources: we obtained the migration index from the Baidu Migration website 18 and the number of travellers from the websites of the municipal transportation commissions. [19][20][21][22][23][24][25] Notes: The annual 40-day Spring Festival travel rush dates were 21 January to 1 March 2019. The municipal commissions of transport in Beijing and Shanghai released the numbers of people leaving and entering the cities, but other cities only released the number of people leaving. The migration index is the ratio of the number of people travelling within a city to the number of residents in the city. We obtained data on the number of people with confirmed (clinically defined) COVID-19 in each province and prefecture-level city from the National Health Commission of China and its affiliates. 2 We used the cumulative number of confirmed cases of COVID-19 on 1 March 2020 as the final values, because after that there were few locally confirmed cases in China except in Wuhan. In addition, on 5 February 2020 the Chinese National Health Committee issued its protocol for the diagnosis and treatment of pneumonia with novel coronavirus infections (5th trial version), 26 and counted clinically diagnosed cases as confirmed cases in Hubei province. More than 10 000 additional confirmed cases were therefore added to the total in Hubei province on 12 January 2020.

Model design
Our model needed to consider factors affecting the final cumulative numbers of confirmed cases in areas outside Wuhan. We analysed data from 44 regions in mainland China, which accepted travellers from Wuhan city, including 15 prefecture-level cities in Hubei province and 29 other provinces in mainland China (Tibet was excluded since only one confirmed case was reported). The data are available in Supplementary Data 1 in the data repository for this article. 27 We noticed that the number of confirmed cases of COVID-19 in cities within Hubei province and in other provinces outside Hubei were closer in the early period of the epidemic (Supplementary Data 2 in the data repository). 27 For example, the cumulative number of confirmed cases by the end of 26 January 2020 in Chongqing municipality and Xiaogan city (Hubei province) were 110 and 100, respectively. However, the cumulative number of confirmed cases in Chongqing and Xiaogan by the end of 27 February were 576 and 3517, respectively. We surmise that this was partly because Xiaogan city had received more cases of infection from Wuhan than from Chongqing after the risk of human-to-human transmission of COVID-19 was confirmed and announced on 20 January 2020. This surmise was confirmed by Fig. 2 (see also Supplementary Data 3 in the data repository). 27 The proportion of travel- Notes: Actual scenario was the intervention in Wuhan city. Basic control was few people leaving Wuhan; strict controls was nobody allowed to leave Wuhan. I n refers to the actual total number of people travelling out of Wuhan on the nth day of January 2020. lers from Wuhan city to other cities in Hubei province compared to the total travellers from Wuhan increased rapidly from 70% (288 000 of 414 000 people) before 19 January 2020 to 74% (390 000 of 526 000 people) on 20 January 2020, and over 77% (28 000 of 37 000 people) after 26 January 2020.
We therefore concluded that the first key factor (x 1 ) affecting the final cumulative number of confirmed cases in cities outside Wuhan on 1 March 2020 was the sum of people travelling out of Wuhan during 20-26 January 2020 (there were few population movements after 27 January 2020 because of the control measures). These people had a higher probability of being infected but  lower transmission ability because of the epidemic control measures. The second key factor was the sum of the number of infected people travelling from Wuhan city to other areas before 19 January 2020. According to later reports, there is a mean 10-day delay between infection and detection of infection, comprising a mean incubation period of about 5 days and a mean delay of 5 days from symptom onset to detection of a case. 5,7,8 So the second key factor (x 2 ) can be represented by the cumulative number of confirmed cases at the end of 29 January 2020. These seed cases had higher transmission ability because no protection measures were yet in place for susceptible people.
We constructed a binary regression model based on these two key factors and used a standardized regression coefficient (COEFF) to evaluate the importance of the independent variables x 1 and x 2 : where y is the number of cumulative confirmed cases by 1 March 2020, x 1 is the sum number of people leaving Wuhan during 20 -26 January 2020, x 2 is the number of cumulative confirmed cases by 29 January 2020, where y is the dependent variable, x j is the jth independent variable, b j is the regression coefficient of x j . S xj is the standard deviation of x j and the S y is the standard deviation of y.

Evaluation of interventions in Wuhan
To evaluate the effect of the lockdown in Wuhan, we assumed that the number of cumulative confirmed cases by 29 January 2020 (x 2 ) was fixed, and we revised the sum of travellers from the city during 20-26 January 2020 (x 1 ) up or down according to the strength of interventions applied. The baseline intervention was lockdown on 23 January 2020. We defined two levels of travel control measures: basic (few people leaving Wuhan) and strict (nobody allowed to leave Wuhan). We then modelled three alterative scenarios: (i) lockdown starting 3 days earlier (on 20 January) with basic controls; (ii) lockdown starting 3 days earlier (on 20 January) with strict controls; and (iii) lockdown starting 3 days later (on 26 January) with basic controls ( Table 1).
The final cumulative number of confirmed cases for the three alterative scenarios are predicted by the binary regression model (Equation 1). As shown in Table 1

Assessment of regional interventions
We used the predicted final cumulative confirmed cases by this model to assess regional efforts to control the spread of COVID-19. When the predicted value is greater than the true value, it indicates that the region has a better prevention and control effect; when it is lower than the true value it means that the prevention and control effect is poor. We calculated the standard residual (SR) for each region as the quantitative evaluation index for this comparison as follows: (2) where y i is the true final cumulative number of confirmed cases in region i, ŷ i is the predicted number of confirmed cases in region i, S e is the standard devia-tion of the residuals. Based on the value of the standard residual, we classified regions arbitrarily by five grades of effectiveness of interventions (excellent: SR < −1.0; good: SR −1.0 to −0.5; neutral: SR −0.5 to 0.5; poor: SR 0.5 to 1.0; very poor: SR > 1.0).
We constructed all the regression models using the regress function of MATLAB software, version R2016a (MathWorks, Natick, United States of America).

Movements of residents
More than 9 million residents were isolated in Wuhan city after the epidemic control measures started on 23 January 2020. According to data from Baidu Migration, only 1.   27 In response to the government's call to reduce travel, the mean intensity of intra-city population movements for 316 cities in mainland China was only 2.61 per day during 24 January 2020 to 15 February 2020 according to data from Baidu Migration. Population activity was greatly reduced compared with the same period in 2019 (4.53 per day) and the first 23 days of January 2020 (5.25 per day), respectively ( Fig. 5; Supplementary Data 3 in the data repository). 27

Modelling spread of COVID-19
We constructed the following simple regression model to explain the final cumulative number of confirmed cases (y) in regions other than Wuhan: where x 1 is the sum of the number of people travelling out of Wuhan during 20-26 January 2020 and x 2 is the cumulative number of confirmed cases by 29 January 2020 for 15 prefecture-level cities in Hubei province and 29 other provincial regions (Supplementary Data 1 in the data repository). 27 The standard regression coefficients calculated from Equation 1 of x 1 and x 2 were 0.657 and 0.380 respectively, indicating that x 1 is more important than x 2 for determining the final cumulative number of confirmed cases. The true and fitted values of the cumulative confirmed cases by 1 March 2020 in the 44 non-Wuhan regions are shown in Fig. 6.
Based on the interpretative model (Equation 3), we predicted the final cumulative confirmed cases of the 44 non-Wuhan regions for the three modelled intervention plans. The results are shown in Supplementary Data 1 in the data respository. 27 Even starting lockdown with only 3-days delay, the estimated total cumulative number of confirmed cases of COVID-19 by 1 March 2020 in non-Wuhan regions was 41 330, an increase of 34.6% compared with the actual numbers (30 699 cases). In contrast, even with lockdown starting 3 days earlier we estimated 21 235 and 15 796 people infected under basic and strict controls, respectively: 30.8% and 48.6% reductions, respectively, compared with the actual intervention.

Predicted cumulative confirmed cases
When predicting confirmed cases of COVID-19 in Wuhan, x 1 is the number of residents in the city. There were around 9 480 000 residents in Wuhan around 26 January 2020 according to a press release from the Wuhan government. The cumulative number of confirmed cases of COVID-19 (x 2 ) were 2261 by 29 January 2020. Based on Equation 3, we therefore predicted that at least 56 572 people in Wuhan were infected (70.3535 + (0.0054 × 9 480 000) + (2.3484 × 2261)).

Effectiveness of regional interventions
The true and predicted final cumulative numbers of confirmed cases of COVID-19 in 29 provincial regions and 44 prefecture-level cities outside Hubei based on the interpretative model are listed in Table 2 and Table 3. More details of the data are available in Supplementary Data 1 in the data repository. 27 Based on the values of the standard residual, we graded Guizhou, Henan and Hunan provinces as having an excellent level of effectiveness against the spread of COVID-19 (SR: −2.06, −1.85 and −1.13, respectively), whereas Heilongji-  Table 3).

Discussion
We   and, so far, our estimate is closer than other estimates to the official report of 50 333 confirmed cases. 29 Many of the virus transmission control measures taken by China went beyond the requirements of the International Health Regulations for responding to emergencies, 30 setting new benchmarks for epidemic prevention in other countries. We found that the lockdown in Wuhan combined with nationwide traffic restrictions and self-isolation measures reduced the ongoing spread of COVID-19 across mainland China. As shown in Fig. 7, data from Baidu Migration showed that the number of newly diagnosed cases of COVID-19 just in Wuhan city far exceeded the total number of cases in non-Wuhan regions of mainland China because of the early lack of attention to the epidemic.
Our method enabled us to assess the efforts of public health authorities in different regions of mainland China during the early stage of the epidemic. We found that the authorities of Guizhou, Henan and Hunan provinces did the best job of prevention and control of the epidemic, whereas Heilongjiang, Guangdong, Shandong, Sichuan and Jiangxi provinces performed relatively poorly compared with other provinces. The four cities of Huanggang, Xianning, Enshi and Jingmen performed well and Ezhou, Suizhou, Xiaogan and Yichang cities performed relatively poorly.
Our model was able to assess the impact of the lockdown in Wuhan city on the epidemic in mainland China, and it confirmed that preventing the movement of people in and out of an area was an important measure to contain the epidemic. However, the Baidu Migration index does not fully accurately represent the real number of migration, so there may be errors in model estimation, and our model is not applicable to other regions and countries to assess the ongoing efforts of public health authorities in controlling disease transmission.
As of May 2020, the epidemic of SARS-CoV-2 was still growing rapidly worldwide. We believe that the international community can learn from the strict interventions applied in Wuhan and the experience from China. ■