key: cord-0857913-68oaxlwj
authors: Tang, Biao; Xia, Fan; Bragazzi, Nicola Luigi; McCarthy, Zachary; Wang, Xia; He, Sha; Sun, Xiaodan; Tang, Sanyi; Xiao, Yanni; Wu, Jianhong
title: Lessons drawn from China and South Korea for managing COVID-19 epidemic: Insights from a comparative modeling study
date: 2021-12-28
journal: ISA Trans
DOI: 10.1016/j.isatra.2021.12.004
sha: a379a8bbe9b295eb31d5da5163d58b089a668805
doc_id: 857913
cord_uid: 68oaxlwj

We conducted a comparative study of the COVID-19 epidemic in three different settings: mainland China, the Guangdong province of China and South Korea, by formulating two disease transmission dynamics models which incorporate epidemic characteristics and setting-specific interventions, and fitting the models to multi-source data to identify initial and effective reproduction numbers and evaluate effectiveness of interventions. We estimated the initial basic reproduction number for South Korea, the Guangdong province and mainland China as 2.6 (95% confidence interval (CI): (2.5, 2.7)), 3.0 (95%CI: (2.6, 3.3)) and 3.8 (95%CI: (3.5,4.2)), respectively, given a serial interval with mean of 5 days with standard deviation of 3 days. We found that the effective reproduction number for the Guangdong province and mainland China has fallen below the threshold 1 since February 8th and 18th respectively, while the effective reproduction number for South Korea remains high until March 2nd Moreover our model-based analysis shows that the COVID-19 epidemics in South Korean is almost under control with the cumulative confirmed cases tending to be stable as of April 14th. Through sensitivity analysis, we show that a coherent and integrated approach with stringent public health interventions is the key to the success of containing the epidemic in China and especially its provinces outside its epicenter. In comparison, we find that the extremely high detection rate is the key factor determining the success in controlling the COVID-19 epidemics in South Korea. The experience of outbreak control in mainland China and South Korea should be a guiding reference for the rest of the world.

Coronaviruses, enveloped viruses characterized by a single-stranded, positive-sense RNA, cause generally mild infections but occasionally lethal communicable disorders leading to the "Severe Acute Respiratory Syndrome" (SARS), the "Middle East Respiratory Syndrome" (MERS), and the current "Coronavirus 2019 Disease" (COVID-19) outbreak [1] [2] [3] [4] [5] that has gradually spread out from the initial epicenter of Wuhan (China) and affected more than 220 countries/territories and international conveyances including the cruise ship Diamond Princess harbored in Yokohama/Japan.

In the absence of effective treatments and vaccines, early adoption of stringent public health measures is crucial in mitigating the scale and burden of an outbreak. Unprecedented restrictive measures, including travel restrictions, contact tracing, quarantine, and lock-down of entire towns/cities adopted by the Chinese authorities have resulted in a significant reduction of the effective reproductive number of COVID-19 [6, 7] . However, these public health interventions have not been considered and/or implemented as effectively in other settings and contexts. Decisionmaking and implementations require, indeed, adaptations and modifications to take into account setting-specific characteristics in terms of community features, local epidemiology and risk assessment, social habits, juridical provisions, organizational coordination, and availability of economic-financial resources. For instance, particularly restrictive measures have been shown not to be effective in certain countries [8] .

Several public health interventions can be implemented to counteract the threat posed by an emerging outbreak [9] with pandemic potential. These interventions can be basically classified into two major categories: the measures in the first category are aimed at protecting the borders and include interventions such as travel restrictions and border entry screening, whereas the measures in the second category have the objective of locally controlling the spreading of the virus and include enhanced epidemiological surveys and surveillance, contact tracing, school closure and other interventions that favor a reduction in the number of social contacts. The effectiveness of intervention measures is variable and, for some, is still under debate. Regarding, for example, extensive travel restrictions, a recent systematic review has shown that this intervention may contribute to delaying but not preventing the transmission and diffusion of a viral outbreak. As such, it is not recommended for implementation, if not within a broader package of public health measures aimed at rapidly containing the outbreak [10] . A similar conclusion can be reached for border entry screening, considered as ineffective or poorly effective per se, and therefore needs to be combined and provided together with other strategies [11] . School closure appears to be potentially effective in containing/reducing viral outbreaks, although further research is warranted to identify the best strategy in terms of timing and length of closure [12] . The measure of quarantine is also particularly controversial, since it raises ethical dilemmas, and political and social concerns [13, 14] , and J o u r n a l P r e -p r o o f Journal Pre-proof quantification of its real impact [13] is difficult due to high uncertainty in its efficacy. However, in the absence of effective medical interventions, for example, during the earlier stage of a pandemic, these measures must be implemented and the success of these measures, despite their disruptive impact on social-economic activities, depends heavily on how these measures are adapted to the specific scenario, in terms not only of clinical and epidemiological variables but also of social aspects, including social habits, juridical provisions, and economic-financial resources.

How differentiation and combination of these interventions within a coherent and systematic package of public health measures contribute to different outbreak outcomes is an urgent global health issue that must be addressed in order to ensure that lessons from countries that have early experienced COVID-19 outbreak can be learned by other countries in their preparedness and management of a likely pandemic.

Several mathematical models have been devised to predict the epidemiologic trend of the COVID-19 outbreak, including stochastic/mathematical (integer derivative [15, 16] or fractional-order [17] [18] [19] ) models, mass-action, (spatial) structured metapopulation, agent-based networked, and other compartmentalized models [20] , among others. According to a systematic survey of the literature, synthesizing 242 studies, 46.1% of studies used compartmental models, 31.8% statistical models (growth models and time series), 6.7%, 4.7%, 3.3%, 2.3% and 1.3% Artificial Intelligence-, Bayesian approach-, hybrid, network-and individual agent-based models, respectively [21] .

In the present paper, we conducted a comparative study of the COVID-19 epidemic in three different settings: mainland China, the Guangdong province of China and South Korea.

In South Korea, the first COVID-19 case (a 36-year-old Chinese woman, with a recent travel history to Wuhan) was reported on January 8 th 2020. A severe cluster of cases emerged in the city of Daegu, where on February 23 rd 2020 a 61 years old woman spread the virus to hundreds of worshippers at Shincheonji Church of Jesus. On March 5 th 2020, a further cluster of cases occurred at a nursing home in Gyeongsan, which has been declared a "special care zone" in an effort to contain the viral outbreak. As of March 8 th 2020, South Korea has reported 7,313 cases, with 130 total recovered cases and 50 deaths, with no sign that the epidemic was slowing down. As of June 8 th 2021, a number of 164,028 total cases have been reported, with 2,034 deaths and 151,923 total recovered cases.

There were 1,275 newly daily confirmed cases.

In comparison, intensive social contacts and massive mobility associated with the Chinese Traditional Spring Festival, combined with an initial delay in responding to the outbreak, resulted in exponential growth of infections in the (then) epicenter (Wuhan) and large case importations to other Chinese cities. On January 23 rd 2020, the Chinese government decisively implemented a systematic package of measures in the epicenter, including the lock-down/quarantine of Wuhan city In contrast to South Korea, there was a relatively large ratio of imported cases in Guangdong province, particularly, in Shenzhen (a megacity in Guangdong province) more than 70 percent of the confirmed cases are imported [22] . The present paper is the fully peer-reviewed and final edited version of a draft initially submitted to the pre-print server of the World Health Organization, as mandated by the institution itself for rapid dissemination of COVID-19 related research during the pandemic to facilitate and assist quick implementation of public health policies in a data-driven and evidence-based way [1, 2] .

We obtained data of the confirmed COVID-19 cases, the cumulative number of quarantined individuals, cumulative death cases in mainland China from the "National Health Commission" of Figure 1 (A-C). In addition, we obtained the data of the cumulative confirmed cases, cumulative cured cases and daily cases under medical observation for the Guangdong province ( Figure 1 (E)) of China. We also obtained the data of cumulative confirmed cases and cumulative tested cases for South Korea from the Korea Centers for Disease Control and Prevention (KCDC) [24, 25] , as shown in Figures 1(D) , and (F). The data were released and analyzed anonymously. Note that the first confirmed case was reported on January 23 rd 2020 for South Korea, and also on January 23 rd 2020 mainland China started the lock-down of Wuhan city, the epicenter, and implemented other interventions. Note that the data for reported cases, either confirmed or quarantined, or under medical observation or tested, was used in China or South Korea since January 23 rd 2020.

Our baseline model is the classical deterministic susceptible-exposed-infectious-removed (SEIR) epidemic model refined by incorporating contact tracing-quarantine-test-isolation strategies ( Figure   2 ). We stratify the population into susceptible ( ), exposed ( ), symptomatic/asymptomatic infected ( / ), hospitalized ( ) and recovered ( ) compartments, and we further stratify the population to include quarantined susceptible ( ), and quarantined suspected individuals ( ). These stratifications were used in our previous studies [6, 7, 26 ] and agreement of model predictions with real data provides a validation of the model structure reflecting the interventions implemented in Wuhan and in mainland China. Here, we add an additional quarantined suspected compartment, which consists of exposed infectious individuals resulting from contact tracing and individuals with common fever. These individuals with common fever but quarantined as COVID-19 suspected contributed to the difficulty of implementing an effective quarantine process due to the size of this compartment. In what follows, exposure, transmission and infection compartments are always used for modeling the COVID-19.

In our model formulation, the transmission probability is denoted by β and the contact rate is denoted by c. By enforcing contact tracing, a proportion, , of individuals exposed is quarantined, and can either move to the compartment or with rate of (or (1 -) )), depending on whether they are effectively infected or not [27, 28] , while the other proportion, 1q, consists of individuals exposed to the virus who are missed from contact tracing and move to the exposed compartment at rate of βc(1 − q)once effectively infected or stay in compartment otherwise.

Note that contact tracing is not triggered by asymptomatic infected individuals, who can infect susceptible individuals. We use constant m to denote the transition rate from the susceptible compartment to the (COVID-19) suspected compartment due to fever and/or illness-like symptoms. 

where is the total population which is the sum of the populations of all the compartments.

Keeping the time-dependent parameters in model (C1) as constants and using the next generation matrix method introduced in the studies [29, 30] , we can calculate the basic reproduction number of model (C1) as follows:

here, 0 = (0), 0 = (0) , and 0 / 0 = 1 . Then, substituting all the time-dependent parameters/variables into the formula of the basic reproduction number, we can obtain the effective reproduction number of model (C1), which is given by:

As the total population is very large, we can assume that ( )/ ( ) ≈ 1 , thus the effective reproduction number is reduced to

In epidemiology, the basic reproduction number (R0), used to measure the transmission potential of a disease, is the average number of secondary infections produced by a typical case of an infection in a population where everyone is susceptible. Once the intervention implemented results effective, the effective transmission potential is measured by the effective reproductive number that can be time-dependent as intervention measures vary over time. If falls below 1 and remains below 1, there will be a decline in the number of cases.

The prevention and control interventions were gradually improved in mainland China, and there are several key time points when mitigation measures were gradually strengthened: 1) On January 23 rd Wuhan was locked down, and most parts of China shortly adopted a similar strategy; 2) On January 26 th , the government announced to extend the Chinese Traditional New Year Festival holiday so self-isolation/protection was maximized; 3) On February 7th the Chinese government created the partnership between each one of the 16 provinces to its sister-city in the epicenter, the Hubei province, to reinforce the health care workers and equipment in the sister-city in Hubei; 4) On February 12th the Hubei province started to include the clinically diagnosed cases into the confirmed cases to enhance its quarantine/isolation measure; 5) On February 14th , Wuhan refined its management protocol of residential quarters; 6) On February 16th, the National Health Commission of the People's Republic of China revised its New Coronavirus Pneumonia Prevention and Control Plan to further clarify and enhance the public health interventions in four key areas: Quarantine high-risk individuals as much as possible, Test suspected individuals as much as possible； Treat patients as best as possible；and Receive and cure all the patients.

Corresponding to the package of gradually improved prevention and control interventions carried out by the governments, the parameters related to the interventions should be time-varying, i.e., functions of time . More in detail, as effect of the implementation of lockdown and limiting the population movement since January 23rd, the contact rate should be a decreasing function of time ; because of the enhanced close contact tracing and quarantine, the quarantine rate should be an increasing function of time ; since the improve testing capacity, the diagnosis rate should be an increasing function of time , correspondingly, the diagnosis period decreases over time. Here, we assume that all of the three rates are changing exponentially at the initial stage, then gradually slow down their speed and approach to a maximum/limit rate. Based on the above assumptions, the time-dependent contact rate ( ), quarantined rate ( ), and detection rate ( ) can be defined as follows:

where 0 denotes the initial contact rate (on January 23rd 2020) with (0) = 0 , denotes the minimal contact rate with the intervention being implemented. Constant 0 is the initial quarantined rate of exposed individuals with (0) = 0 , is the maximum quarantined rate with > 0 . Similarly, constant δ I0 is the initial diagnosis rate, is the fastest diagnose rate with > 0 .

For the Guangdong province, the recovery rate has been improved over the time, and this is reflected 

When carrying out the parameter estimations, we first informed several parameters in model (C1) and model (K1) with fixed values retrieved from the scholarly literature. These include the transition rate of exposed individuals to the infected class , the rate at which the quarantined uninfected contacts were released into the wider community , and the recovery rate of the asymptomatic infections , as shown in Table 1 . In addition, the initial values of suspected population, quarantined infected population, quarantined susceptible population, and recovered population are obtained from official statistical reports, epidemiological surveys and databases mentioned in the data section (Table 1) . We used the least square (LS) method with a priori interval for each parameter to fit the proposed models to the data, where the objective function is the residual sum of squares between the real data and the predicted number by solving model (C1)/model (K1). The built-in function "ODE45" in Matlab is used to solve the ODE systems while the "fmincon" function is used to search for the optimal solutions of the objective functions. We generated 1,000 time series of the cumulative cases, death cases and tested cases following a Poisson distribution with mean given by the real data, and fitted the models to each set. Consequently, we obtained the estimated mean values of the parameters, as listed in Table 1 .

We employed the method developed by White and Pagano [31] to estimate the basic reproduction 

By using the number of daily newly reported cases from January 10 th to January 23 rd 2020, we estimate 0 for mainland China, and using the newly reported cases from January 19 th to January 31 st 2020 we estimate 0 for the Guangdong province. Also, we estimate 0 for South Korea based on the number of daily newly reported cases from January 23 rd to March 2 nd 2020.

All the estimates are given in Table 2 . In particular, given the serial interval with mean of 5 and standard deviation of 3, 0 for mainland China, the Guangdong Province and South Korea is estimated to be 3.8 (95%CI: (3.5, 4.2)), 3.0 (95%CI: (2.6, 3.3)) and 2.6 (95%CI: (2.5, 2.7)), respectively. In particular, the initial COVID-19 reproduction rate in South Korea was smaller than that in the Guangdong Province.

In order to investigate the variation of 0 with respect to the serial interval, we carry out a sensitivity analysis by changing the mean of the serial interval from 4 to 8 days, the standard deviation (Std) from 3 to 5. The sensitivity analysis is reported in Table 2 , and we notice that 0 increases when the mean of the serial interval increases, and we remark that serial interval examined by recent studies is shorter than that earlier estimation [33] [34] [35] . It also follows from Table 2 that increasing Std of the serial interval only slightly decreases the estimated 0 for a given mean of the serial interval.

We also estimate the effective reproduction numbers for the considered regions, using the number of daily newly reported cases from the date the first case was reported until March 2 nd 2020 ( Figure 3 ). It shows that the effective reproduction number in mainland China and in its Guandong province has fallen below the threshold 1 since February 18 th and February 7 th , while the effective reproduction number of South Korea remains very high, indicating that there is still room for improving the interventions in South Korea.

By simultaneously fitting the model (C1) to the multiple source data on the cumulative number of reported cases, deaths, quarantined and suspected cases in mainland China, we obtain estimations for unknown parameters and initial conditions, listed in Table 1 . The best fitting result is shown as black curves in Figure 4 with the estimated baseline exponential decreasing rate ( 1 = 10 ) in the contact rate function. We then conduct a sensitivity analysis of the cumulative reported, death, quarantined, suspected cases, and the infected (asymptomatic/symptomatic) individuals by shrinking the exponential index 1 , representing the weakening of the control interventions relevant to the contact rate. As shown in Figure 6 , the numbers of cumulative reported, death, quarantined, suspected cases, and the peak value of the infected all increase significantly. In particular, with 1 = 0 corresponding to no reduction of the contact rate from the initial period, the number of cumulative confirmed cases increases by more than six times as of April 1 st (~600,000 cases) and the peak value of the infected will increase by more than 3 times, in comparison with the actual situation under the strong control measures implemented by the Chinese government.

We also conduct a sensitivity analysis regarding the detection rate ( ), by decreasing the value of 3 . We obtain a similar conclusion that the cumulative confirmed cases would reach the number of 350,000 cases as of April 1 st with a constant detection rate (no improvement of detection), shown in Table 1 . The best fitting result is shown as black curves in Figure 7 . Comparing the estimated values of the detection rate in China and South Korea, we find an important difference that the diagnosis rate in South Korea (a constant value of 0.651) is much higher than that in China, being even higher than the maximal diagnosis rate in China. This is in line with the real control interventions adopted by the Korean government, that is to say, the government has actively coordinated the production of testing kits of COVID-19, consequently, the testing kits have been always available, even during the peak period of the epidemic. Apparently, as shown in Figure   7 (A-B), the COVID-19 epidemics in Korea will be almost under control as of April 14 th with the confirmed cases tending to be stable. In order to test whether the extremely high detection rate is the key factor determining the success in controlling the COVID-19 in South Korea, we plotted the cumulative confirmed cases and the infectious population ( ) by decreasing the detection rate by 70%, 50% and 30%, respectively, as shown in Figure Further, by simultaneously fitting the model (C1) to the multiple source data on the cumulative number of reported cases, recovery and suspected cases of Guangdong province, we parameterize the model and obtain the estimations for the unknown parameters and initial conditions, listed in Table 1 . The best fitting result is shown as green curves in Figure 8 . Similarly, we consider the In Guangdong, the province with the largest population in China, most cases at the initial phase of the COVID-19 outbreak are imported, and immediately after the lockdown of Wuhan on January 23 rd 2020, the province implemented a systematic approach towards prevention and control, with gradual enhancement, leading to the effective control of otherwise potentially catastrophic outcomes.

In comparison with South Korea, Guangdong has more inhabitants and a less developed economy.

Also, from our model-free estimation, the basic reproduction number in South Korea is less than that computed for the Guangdong province. Therefore, the COVID-19 epidemic potential in South

Korea was initially weaker than that in Guangdong. (1) the initial and maximum quarantine rates in Guangdong were much higher than those in the entire country China, while the initial and minimum contact rates were lower than those in the country, contributing to the observed better control effect in the province than the national average. We note that future works may aim to address items of major public health concern such as: based on how a given regional epidemic situation is evolving, inform the decision-making for switching of intervention tactics and control measures. For instance, at which point does a country/territory make the decision to switch from tactics based on strict contact tracing to those based on travel restriction and mass quarantine? While contact tracing may be effective in controlling an outbreak with few initial cases, strong response efforts, and low pathogen transmissibility, this effectiveness may fade as cases accumulate [36] . In other words, the effectiveness of control measures may be dependent on the time and epidemic state at which they are implemented; therefore, switching tactics based on the local epidemic evolution may be optimal for regional and hence global control.

Through the parametrization and simulation of disease transmission models with intervention mechanisms and informed with multiple data sources, regional demographics, and regional intervention features, our work provides a foundational framework for the intervention evaluation and intervention scenario analysis. This study highlights the opportunity for evaluation of control measures and the learning from select regions to inform the future decision-making for the preparedness, real-time management as well as risk assessment of COVID-19.

It should be mentioned that several studies have provided evidence of pre-symptomatic transmission of COVID-19 [36, 37] . As reported in the study conducted by Subramanian et al. [38] , ignoring presymptomatic transmission may lead to the underestimation of the basic reproduction number. Not accounting for the infectivity of the exposed class is a limitation of our model, which warrants future studies.

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