Does Quarantine of Wuhan Effectively Restrict Early Geographic Spread of Novel Coronavirus Epidemic During Chunyun in China? a Spatial Model Study

Background: Prior to Wuhan quarantine in 2020, chunyun , the largest population mobility on this planet, had begun. We quantify impacts of Wuhan quarantine on COVID-19 spread during chunyun at a nationwide and a local level. Methods: During the period of January 1 to February 9, 2020, a total of 40,278 confirmed COVID-19 cases from 319 municipalities in mainland China were modelled with the cross-coupled meta-population methods using between-city Baidu migration index. Four scenarios of geographic spread of COVID-19 included the presence of both chunyun and quarantine (baseline); quarantine without chunyun (scenario 1); chunyun without quarantine (scenario 2); and the absence of both chunyun and quarantine (scenario 3). Results: Compared with the baseline, scenario 1 resulted in 3.84% less cases by February 9 while scenario 2 and 3 resulted in 20.22% and 32.46% more cases by February 9. Investigation of geographic distribution of cases revealed that chunyun facilitated the COVID-19 spread in most but not all cities, and effectiveness of city quarantine was offset by chunyun . Impacts of quarantine of Wuhan during chunyun on the COVID-19 spread demonstrate geographical heterogeneity. Conclusion: Our result strongly supports the travel restriction as one of the effective emergency responses and highlight the importance of developing area-specific countermeasures.


Introduction
Since early December 2019, an increasing number of atypical pneumonia have been reported in Wuhan 1 , a city with a population of 11 million in the central part of China. In response to this outbreak, the Chinese Center for Disease Control and Prevention (China CDC) conducted an epidemiologic and etiologic investigation on December 31, 2019 2 . It was found that human-to-human transmission occurred since the middle of December 2019 3 , with a novel strain of coronavirus (COVID- 19) isolated and confirmed on 7 January 2020 4 . Along with the increasing number of COVID-19 cases in China, the geographic spread at a meta-population level (e.g. between cities in China, Asia-pacific regions, or northern hemisphere countries) has been reported 5 .
When it appears that human-to-human transmission poses a threat, use of restrictive measures such as isolation of cases and quarantine of contacts becomes apparent options for emergency response 6 . A typical challenge has emerged when chunyun, the largest human migration on the planet, began on Jan 10, 2020 with billions of trips made for family reunions to celebrate the Spring Festival during the national holidays from January 24 to 31 7 . Geographic spread of COVID-19 would have potentially accelerated under this circumstance, and therefore prevention and control of the COVID-19 infiltration into local communities across the nation requires immediate actions to restrict human movements 8 . On January 23 and 24, 2020, the Chinese central government has implemented the metropolis-wide quarantine of Wuhan and several nearby cities 3 . In addition to the quarantine of Wuhan, the central government has announced the extended national holidays and set the back to work date as of February 10, 2020 (except Wuhan) 9 .
In the face of this unprecedented threat and incomplete knowledge of effective 5 countermeasures, it appears appropriate for the authorities to invoke the quarantine of Wuhan as a means to interrupt the geographic spread of COVID-19 and achieve the population health goals 10 . Despite a recent decreasing trend of daily number of confirmed cases 11 , population based evidence is inadequate regarding whether the implementation of quarantine is effective in the context of chunyun. This study aims to evaluate the effectiveness of quarantine for preventing the epidemic, and examine whether the effectiveness varies according to the presence or absence of chunyun and quarantine.

Data sources
Provincial Health Commissions in mainland of China have reported municipal-level incident numbers of COVID-19 suspected, confirmedly infected, recovered, and deceased individuals, respectively on a daily basis since January 2020 12 . We include a total of 319 municipalities having at least one laboratory-confirmed case and ascertained their daily numbers of COVID-19 cases from January 1 to February 9, 2020. These data are publically available and therefore this study was exempted for ethics approval by institutional review boards with respect to data collection, analysis and reporting. The study outcome was the incident laboratory-confirmed COVID-19 pneumonia.
Baidu Migration Index is a free data analytic platform using Baidu web search and Baidu news to present massive behavior data among Baidu users, which has been frequently used to reflect population mobility in China [13][14][15] . We obtained Baidu Migration Index from January 1 to February 9, 2020 to quantify the daily traveler between pair-wise cities. The specific number of travelers from city i to j at day t, , , , is calculated as follows: where , , is the migration index from city i to j at day t, _ ℎ is the number of travelers that left from Wuhan during January 10 to January 19, 2020 (prespecified as 4.10 million 16 ), and ℎ is the sum of traveling index from Wuhan to all other cites at the same period.

Statistical analysis
We used the following cross-coupled meta-population (epidemic) model to consider the geographic spread of COVID-19 between cities across the nation: where , , , and are the numbers of susceptible, exposed, infectious, and recovered individuals, respectively, and is the total population size of city i, is the transmission parameter (we assume it is the same over all cities) at time t, , , is the proportion of individuals moving to city i from city j at time t, is the latent rate, and is the infectious rate. For model fitting convenience, we add another compartment ( ) to the above equations to keep track of cumulative incidence as follows: Fitting was achieved by treating the differential equation (Eq 6) as representing the mean number of cumulative cases per day over China in our study period, and assuming that the observed number of cumulative cases over China were (approximately) Poisson distributed around this mean. Given the model and data, parameter inference was achieved by least 7 square (LS) estimation using L-BFGS-B optimization as implemented in the optim() function in the R statistical language (R Core Team 2020). Uncertainty in the parameter estimates was explored using parametric bootstrap as follows. 1000 simulations from the model (Eq 6 and Poisson noise) were firstly generated using the LS estimates of the parameters. Each simulated dataset was then re-fitted to the model to construct a joint sampling distribution of the parameters, and 95% confidence estimated as the lower 2.5% and upper 97.5% quantiles.
The instantaneous basic reproductive number ( 0 ) was calculated by / . Based on these parameters, we then simulate the probable course of the disease transmission conditioned on the aforementioned three modelling scenarios.

Results
During the period of January 1 to February 9, 2020, a total of 40,278 confirmed COVID-19 cases from 319 municipalities in mainland China were reported (Fig. 1). Fig. 2   In this study, we have also investigated the epidemiological characteristics of COVID-19. We first estimated its instantaneous 0 , and found a decrease from 3.47 to 3.24 on January 26, which is probably due to the observed decrease in population mobility (Fig. 2). In addition, our estimate of latent and infectious period is 6.11 and 3.26 days, respectively, with the former being comparable with existing clinical studies 17,18 and the latter, which has been rarely reported so far. Compared with previously reported basic reproductive number ( 0) which were fixed and ranged from 2.24 to 3.80 3, 18-20 , our estimate is a time varying one and somewhat more reliable as we taken into account a larger sample size as well as population mobility between cities that would potentially affect contact rates between individuals and subsequently the calculation of COVID-19 spread. Notwithstanding the decrease of 0 , there was an increasing trend on February 9 which corresponded to the time when migrants return to study or work. Considering the contribution of chunyun towards geographic spread of COVID-19, this rebound trend of 0 suggest that the epidemic would spread more rapidly. Therefore, more rigorous prevention and control measures need to be strictly implemented in the communities including home quarantines and self-monitoring.
We estimated COVID-19 cases under three scenarios and their respective changes in relation to the baseline number for each city. We found that there was evidently spatial heterogeneity of effects of chunyun and/or quarantine of Wuhan. In principle, chunyun contributed towards the COVID-19 spread in China (Table 1) but not specifically for each locality (Fig. 4a), while quarantine of Wuhan restricted additional spread towards every city (Fig. 4b) across the nation (Table 1). In the absence of both chunyun and quarantine (Fig. 4c), more evident reduction in cases would have occurred to five major urban agglomerations. These urban agglomerations (Fig. 4d) consist of two kinds of city clusters, i.e., well-developed megacities and the other nested in the undeveloped regions of China. There is obvious speculation that these clusters would experience similar outgoing and ingoing travel demands all year round, and therefore the effects of chunyun would be nuance. It is noteworthy that corridor cities near Wuhan (Fig. 4c) did not benefit much from the quarantine as its protective effects were offset by the effects of chunyun. These corridor cities would perhaps become a case reservoir prior to the quarantine of Wuhan. Therefore, these corridor cities should be given a priority for continuing effort in allocation of healthcare resources. Additional strategies should be developed based on area-level characteristics.
Evidence of comparative effectiveness of large-scale quarantine on 11-million populations is rare because the outbreak of contagious disease of this kind is highly unusual and so is to have reliable national data.