key: cord-1039430-ubgimbfg
authors: Liu, Ming; Ning, Jing; Du, Yurui; Cao, Jie; Zhang, Ding; Wang, Jiangang; Chen, Mingjun
title: Modelling the evolution trajectory of COVID-19 in Wuhan, China: Experience and suggestions
date: 2020-05-12
journal: Public Health
DOI: 10.1016/j.puhe.2020.05.001
sha: bf5fb56d630223877d99441bbe7a04b34336f0c1
doc_id: 1039430
cord_uid: ubgimbfg

Abstract Objectives In December 2019, a novel coronavirus disease (COVID-19) emerged in Wuhan city, China, which has subsequently led to a global pandemic. At the time of writing, COVID-19 in Wuhan appears to be in the final phase and under control. However, many other countries, especially the US, Italy and Spain, are still in the early phases and dealing with increasing cases every day. Therefore, this article aims to summarise and share the experience of controlling the spread of COVID-19 in Wuhan and provide effective suggestions to enable other countries to save lives. Study Design Data from the National Health Commission of China is used to investigate the evolution trajectory of COVID-19 in Wuhan and discuss the impacts of the intervention strategies. Methods A four-stage modified Susceptible-Exposed-Infectious-Removed (SEIR) model is presented. This model considers many influencing factors, including chunyun (the Spring festival), sealing off the city and constructing the Fang Cang shelter hospitals. In addition, a novel method is proposed to address the abnormal data on 12-13 February as a result of changing diagnostic criteria. Four different scenarios are considered to capture different intervention measures in practice. The exposed population in Wuhan who moved out prior to sealing off the city have also been identified and an analysis on where they had gone was performed using the Baidu migration index. Results The results demonstrate that the four-stage model was effective in forecasting the peak, size and duration of COVID-19. We found that the combined intervention measures are the only effective way to control the spread and not a single one of them can be omitted. We estimate that England will be another epicentre due to its incorrect response at the initial stages of COVID-19. Fortunately, big data technology can help provide early warnings to new areas of the pandemic. Conclusions The four-stage SEIR model was effective in capturing the evolution trajectory of COVID-19. Based on the model analysis, several effective suggestions are proposed to prevent and control the pandemic for countries that are still in the initial phases.

Wholesale market, at the beginning of the COVID-19 outbreak. 3 However, the authorities soon found that these measures were not sufficient to control the spread of the epidemic. The annual period of mass migration for the Spring festival holidays (chunyun) was also fast approaching. To mitigate the spend of COVID-19, the Chinese government implemented unprecedented intervention strategies. The authorities sealed off Wuhan city and several nearby cities on the morning of 23 January 2020 (09:00 am Beijing time). Millions of people were required to stay home until further notice. More than 40,000 medical staff, including doctors and nurses, and countless medical supplies were sent to Hubei province from other provinces/regions of the country. Moreover, the government decided to extend the national holiday, adopt strict measures to limit travel and public gatherings, close all public places of entertainment and implement rigorous temperature monitoring nationwide. 4 Although there were several criticisms declaring that China was overreacting to the outbreak, these measures had a significant impact on mitigating the spread of COVID-19. Moreover, we want to share the experiences and lessons learned from Wuhan and thus provide effective policy suggestions for other countries. Fig.1 illustrates our modified SEIR model. We assume that all people who 'move-in' to Wuhan are susceptible (S in ) 7 . However, we suppose that people who 'move-out' from Wuhan include both the susceptible (S out ) and the exposed (E out ). We further assume that the exposed people are asymptomatic but infectious. 1 Therefore, we have two propagation coefficients between the compartments S and E. We assume all infected individuals seeking treatment are hospitalised based on the availability of space in the hospitals (I h ). We suppose that the hospitalised people are quarantined and cannot infect people outside the hospital again. We also assume that individuals who are not hospitalised (I o ) will remain in the community and spread the disease further. 8 Finally, the removed individuals include two components, the recovered people (R r ) and the death cases (R d ). The detail of our modified SEIR model is shown in the online supplementary file material 9,10,11 . 

All the epidemiological data related to COVID-19 are based on daily reports from the website of the National Health Commission of China. 12 We estimate the transmission rate 0.2225. 4 As the incubation period of COVID-19 has been reported to be between 2 and 14 days, we chose the midpoint of 8 days and thus we have 1/8. Similarly, 1/γ is the average treatment time that has been reported to be 10 days. We suppose that 1/10. The total number of people at the first stage is 14 million; this number declines to 9 million at the third stage. The number of people who move-in and move-out is obtained from the Baidu website 13 . The proportion of infected people who are not hospitalised is dependent upon the number of quarantined beds at time t (number of quarantined beds is reported daily on the website of the Health Commission of Hubei province) 14 . Moreover, we assume that each infected person has contacted 10 susceptible people before he/she is quarantined 15 .

The new confirmed cases on the 12 th and 13 th of February increased significantly 

The predicted data were validated against the actual outbreak data in terms of the number of infected individuals on these days (from 8 December 2019 to 14 March 2020) 8 , which contains 98 time-series data points. After data processing, there is also an approximation of real data for the epidemic in Wuhan. The paired-t-test results in Table 2 prove that our model provides statistically similar results with respect to the outbreak data for the time period. Since all p-values are greater than 0.05, it illustrates that there is no significant difference among the predicted data, the approximate real data and the actual outbreak data. Therefore, our model provides a good-fit for the number of infected individuals in the affected area. 

Forecasting results due to continuous improvement in the medical environment, the time for clearing the confirmed cases may be further ahead.

To compare the effectiveness of different interventions, four scenarios were created.

The first intervention measure was to seal off the city of Wuhan. All departure routes from Wuhan were closed, including planes, trains, ships and road traffic. People were isolated in their homes, thus reducing exposure to the environment and contact with others. All public places of entertainment, such as restaurants, bars and cinemas, were closed in order to limit public gatherings. The second intervention measure was to provide enough medical resources, including doctors, nurses, drugs, masks, protective clothing, ventilators, and sufficient isolated rooms and beds. The third intervention was the combination of interventions 1 and 2 (i.e. sealing off the city and providing enough medical support, simultaneously). Finally, the fourth scenario was an assumption that the authorities did nothing to control the epidemic. Results are presented in Fig.4 . However, if the Chinese government did not seal off Wuhan city but simply provide enough medical support, the situation would be a little better. It can be seen that the peak time of the epidemic would also be delayed to May and the maximum number of cases would reach approximately 170,000. This finding may be important for some developed countries, such as Germany and Japan, who have abundant medical resources, but they may still pay a heavy price for the epidemic spread.

When these two intervention measures are combined, it can be seen that the scale of the epidemic would be greatly compressed and the peak period is much earlier.

Results show that the maximum number of cases is no more than 40,000 in this combined scenario. In addition, the peak period of the epidemic was in the middle of February. This predicted result is quite consistent with the real situation that was seen in Wuhan. Similarly, we consider that the combined interventions in Wuhan bring great inspiration to South Korea. The COVID-19 epidemic in South Korea also grew rapidly at the beginning; however, after implementing a similar combined measure, the growth trend was well controlled. Finally, if no interventions were implemented, the results show that the peak period of the epidemic would be at the end of April. In such a scenario, millions of people would be infected with COVID-19 and the maximum number of cases could be more than 850,000 in Wuhan. Think about that, no city in any country has such a strong medical capacity to deal with such a serious situation. Due to incorrect responses at the initial stage, unfortunately, we estimate that England will be another epicentre in future weeks. In order to effectively control the spread of the epidemic, it is important to find out where these exposed population who left Wuhan have gone. Baidu Migration Index can help identify the outflow directions of the potential patients through Location

Based Service (LBS) data from millions of mobile phones 13 . Table 3 demonstrates that infected patients from Wuhan travel into other provinces all over the country. In total, 67.43% went to cities in the local Hubei province, the most popular being Xiaogan, Huanggang and Xianning (11.53%, 9.91% and 5.84%, respectively). As Among them, Henan, Hunan and Anhui were the three most popular areas because these provinces are neighboured with Hubei province. Not surprisingly, these provinces were also severely impacted by the COVID-19 epidemic. 

An important parameter in the epidemic model is the basic reproduction number (R0), which is the estimation number of secondary cases caused by an infectious person. This parameter determines the infectivity of the virus at the beginning, when there is an unexpected epidemic outbreak. According to the equation of R0, 17 we assume that 0.65 and further give the range of to be [8, 10] . We use 8

December 2019 as the first day. The test results are shown in Table 4 . We find that R0

is in the range of [2.3, 2.9 ]. Actually, chunyun may result in an increase of R0 value because an infectious person may have more opportunities to contact susceptible people during these days. Overall, the results are consistent with most early reports, which are illustrated in Table 5 . scenarios were investigated to capture different interventions in practice. In addition, the exposed population who moved out of Wuhan before the city was sealed off were analysed and the Baidu migration index was used to identify where they had travelled.

Furthermore, the basic reproduction number of the epidemic was estimated. (3) The general public should reach a consensus that early identification, reporting, isolation, diagnosis and treatment is the best and most effective way to contain the pneumonia caused by COVID-19. It is also an important measure taken by the country to fight the virus. Therefore, the authorities in some countries should change the current medical resources allocation strategy. It is also important to identify and treat patients in the early stages of COVID-19 as much as possible and not let them return home until completely recovered. Obviously, this will lead to a surge in demand for the isolated beds. Fang Cang shelter hospitals were quickly constructed by reforming some large gyms; thus, the imbalance between supply and demand can be alleviated. the epidemic will continuously spread and finally the area that initially did well will be infected again. This is the core reason why China is willing to help other countries to fight COVID-19 as soon as it has recovered from the same epidemic.

None sought

This work was supported by National Natural Science Foundation of China 

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A four-stage modified SEIR model to caputure the evolution trajectory of the COVID-19 in Wuhan

The model consideres many influencing factors, including chunyun, sealing off the city and constructing shelter hospitals

A novel method to address the abnormal data on Feb 12-13 due to the changing of diagnostic criteria

Analysis of the move-out exposed population from Wuhan to identified where they had gone using Baidu migration index

Several effective suggestions proposed for countries to prevent and control the epidemic

None declared