Estimating and modelling the transmissibility of Middle East Respiratory Syndrome CoronaVirus during the 2015 outbreak in the Republic of Korea

Background Emerging respiratory infections represent a significant public health threat. Because of their novelty, there are limited measures available to control their early spread. Learning from past outbreaks is important for future preparation. The Middle Eastern Respiratory Syndrome CoronaVirus (MERS‐CoV ) 2015 outbreak in the Republic of Korea (ROK) provides one such opportunity. Objectives We demonstrated through quantitative methodologies how to estimate MERS‐CoV's transmissibility and identified the effective countermeasures that stopped its spread. Methods Using the outbreak data, statistical methods were employed to estimate the basic reproductive number R 0, the average number of secondary cases produced by a typical primary case during its entire infectious period in a fully susceptible population. A transmission dynamics model was also proposed to estimate R 0 and to identify the most effective countermeasures. The consistency between results will provide cross‐validation of the approaches. Results R 0 ranged from 2.5 with 95% confidence interval (CI): [1.7, 3.1] (using the sequential Bayesian method) to 7.2 with 95% CI: [5.3, 9.4] (using the Nowcasting method). Estimates from transmission model were higher but overlapped with these. Personal protection and rapid confirmation of cases were identified as the most important countermeasures. Conclusions Our estimates were in agreement with others from the ROK outbreak, albeit significantly higher than estimates based on other small outbreaks and sporadic cases of MERS‐CoV. The large‐scale outbreak in the ROK was jointly due to the high transmissibility in the healthcare‐associated setting and the Korean culture‐associated contact behaviour. Limiting such behaviour by rapidly identifying and isolating cases and avoiding high‐risk contacts effectively stopped further transmission.


| INTRODUCTION
Quickly measuring transmissibility of an emerging respiratory infectious disease is vital to preparedness of authorities and design of the optimal intervention strategies. The key quantity that characterises the transmissibility is the basic reproductive number (R 0 ), the average number of new infections caused by a single infective individual introduced into a completely susceptible population. 1 It is a threshold parameter: if R 0 <1, the disease dies out without any intervention; otherwise, the disease can persist. To monitor how transmissibility evolves and whether the countermeasures can reduce the transmission along the outbreak course, the effective reproduction number (R t ) is also a useful parameter.
Following the 2003 SARS outbreak, especially the 2009 pandemic flu, effort has been made to rapidly estimate the reproductive number and many statistical methods 2-7 were proposed for this task. Fortunately, these methods have now been made in publicly available software. 8,9 Middle Although limited transmission was reported in these other regions, no sustained onward transmission has been detected outside of the Middle East until 2015. MERS-CoV transmissibility has been estimated to be around the threshold value of 1.0, ranging from 0.4 to 1.5. [10][11][12] These estimates are mainly based on sporadic cases and self-limited clusters. 13 However, the estimation 14 on a large healthcare-associated outbreak in Jeddah and Riyan, the Kingdom of Saudi Arabia (KSA) during spring 2014, with over 300 cases, suggested a higher R 0 ranging from 2.0 to 6.7.
The epidemic in the Republic of Korea (ROK) during 2015 was seeded from a traveller returned from Bahrain after visiting the United Arab Emirates and the KSA, and caused an outbreak of 185 confirmed cases. It has been the largest outbreak outside of the Middle East so far, 15 and much theoretical attention has been attracted to estimate its transmissibility. Hsieh 16 used a phenomenological model to obtain an estimate of R 0 ranging from 7.0 to 19.3. Xia et al. 17 and Kim et al. 18 used transmission dynamics models and obtained R 0 = 4.4 and 5.4, respectively. Reconstructing the transmission tree and considering the heterogeneity in the transmission processes, Nishiura et al. 19 estimated that the reproductive number throughout the whole outbreak has a mean of about 1.0 and a variance of 52.1 (it is worth mentioning that the mean reproductive number throughout the outbreak course is of no help for understanding the transmissibility of the causing pathogens). * These estimates differ from the studies based on previous MERS-CoV outbreaks [10][11][12] and show a quite diverse picture of R 0 for the ROK outbreak. In general, the transmissibility depends not only on the biological properties of a pathogen such as transmission mode and infectivity, but also on the susceptibility and contact patterns of the host populations. 1 The difference in transmissibility among different locations and ethnic populations highlights the importance of its setting dependency. It implies that given the same infectivity of a pathogen, the size and duration of the outbreaks it causes will depend on the contact patterns of the population attributable to their cultureassociated behaviours or geographical-related environment. Different from Westernised culture, Koreans have the tradition to visit relatives and friends in hospitals and can choose the hospitals that they think are the best for their treatment. This culture-associated behaviour along with increased infectivity in hospital environment 10,20 may have facilitated the spread of MERS-CoV in the ROK. 21 Both Xia et al. 17 and Kim et al. 18 used dynamics models to identify the main determinants of transmission in the ROK outbreak.
Both assume that the hospitalised patients can transmit infection to others, which is not true in the ROK outbreak where no infection was caused by confirmed cases as they were all isolated after the confirmation. 21 Further, they both fixed the transition rates so that the stage durations (e.g incubation period and delay from symptom onset to hospitals) were implicitly assumed to be exponential. This is also not true as the observed stage durations are non-exponentially distributed (see Appendix S1). They used the least-square methods to estimate the model parameters, which, in view of a huge amount of uncertainty and heterogeneity in the outbreak, 19 may not be appropriate. To comprehensively understand how these variations affect the estimation of transmissibility, a more general methodology such as Bayesian inference is needed which combined case data and the priors extracted from previous studies or direct estimates from the outbreak data.
In this study, we revisit the estimation of reproductive number of MERS-CoV using statistical methods on the outbreak data released by Korea Centers for Disease Control and Prevention (KCDC) 22 Furthermore, by considering the actual situation of transmission events, we propose a transmission dynamics model to explore how the variation in transition rates affects the decomposition of the key pathways of the spread. The dynamic modelling aims to shed useful insights into the design of effective intervention strategies, which will be critical for controlling emerging respiratory outbreaks in future.

| DATA
The ROK outbreak started from one traveller from the Middle East who was confirmed with the MERS-CoV on 20 May 2015. This outbreak resulted in 186 cases including 38 deaths. Cases were scattered across the country. One case travelled to China, was confirmed and treated there; under the Chinese government's rapid response and control programme, the case did not cause any onward transmission.
Detailed outbreak data are available from KCDC. 22 The information on each confirmed case included symptom-onset date, confirmation * For any outbreak of infectious disease that originated from one index case and self-limited or stopped under control, its overall reproductive number throughout the entire outbreak course has a mean equal to (n − 1)/n for an outbreak of size n. Depending on the structure of the transmission tree, variance in reproductive number can be as small as (n − 1)/n 2 when each case causes one new case and the last one causes none, and as large as (n − 1) 3 /n 2 when the index case cause n − 1 secondary cases. Hence the mean reproductive number throughout the outbreak course is of no help for us to understand the transmissibility of the causing pathogens along the whole course of the outbreak. date, infection place, possible infectors, first and last exposure dates and date of recovery or death.
All the 186 cases had confirmation dates, but only 179 cases had symptom-onset dates with three healthcare workers who tested positive reportedly having no symptoms and another four cases reportedly having symptoms but no symptom-onset dates reported. To use all the 186 cases, we regarded asymptomatic cases as symptomatic, and imputed the symptom-onset dates as following: for each of the seven cases, any date before its confirmation date could be its illness onset date with probabilities given by a gamma distribution obtained from the delays from symptom onset to confirmation of the 179 cases.
Potential exposure windows for 184 cases were recorded. We generated exposure dates by assuming the actual dates were uniformly distributed over the exposure windows for each case. For other two cases that have no recorded exposure windows but have symptomonset dates, any date before the symptom-onset date could be the exposure date with probabilities given by the fitted incubation period distribution.
For 162 cases, the outbreak investigators observed a unique likely infector. As in the KSA nosocomial outbreaks, 23

| Modelling the transmissibility
To describe the ROK outbreak, we propose a transmission dynamics model by ignoring complexes such as age and geographical heterogeneity in transmission rate. MERS-CoV is zoonotic and can transmit via direct contact or large virus-laden droplets. It can pass from animals to humans and from humans to humans. 12 Because of no zoonotic infection in the ROK outbreak, we only consider the human-to-human transmission. Although all transmissions occurred within hospitals, the affected hospitals were distributed across the ROK 21,22 so we assume the ROK population of size N=51 413 925 in mid-2015 24 are involved in the outbreak. On 4th May, all the people are assumed to be susceptible (S) except the index case who carried the virus but was not ill until 11th May. Contacts with cases will first become infected (E) and become infectious (I) after the latent period. In this study, we assume that latent period is equal to incubation. It has been noted elsewhere that asymptomatic MERS-CoV infections are not rare 23,25 ; however, only three asymptomatic infections were detected among 16,752 close contacts during the ROK outbreak. 26 As these asymptomatic cases do not cause further infections, we assume that all infected people are symptomatic and admitted to hospitals and then being confirmed (C). It is worth mentioning that during the ROK outbreak, all transmissions occurred in hospitals. That is, the people who got infected (except the index case) are patients in hospitals due to other diseases or healthcare workers or visitors who visited friends and relatives there. Once confirmed, the cases would be put under security and isolation in designated facilities. The ROK outbreak data show that no infection was caused by confirmed cases so we assume confirmed infections do not contribute to the transmission process. 17,18 Confirmed cases either recover or die. The ROK population is therefore decomposed into four compartments: S-E-I-C and transmission dynamics is approximated by The timeline of intervention measures along with the exposure dates of cases. Here, exposure dates of cases are assumed to be uniformly distributed over the recorded potential exposure windows. The index case is exclusive with his exposure window from 29 April to 2 May 2015 The definitions and priors of parameters are listed in Table 1. We as- The basic reproductive number before intervention at day t 1 is, and after the intervention, it becomes Here, E() stands for the mean of the distribution. To test model sensitivity to variation in people's responses, we also consider the simplified situation by ignoring the differences in people's response and assuming a same diagnosis rate (i.e a constant delay from symptom onset to confirmation) over the whole outbreak.
Here, it is worth discussing the target population of transmission dynamics of MERS-CoV infection in the ROK. All cases in the outbreak, including healthcare workers, patients and visitors, were linked to healthcare settings 19,27 ; it is thus appropriate to assume that the transmission only acts on the people in the healthcare facilities as did in Lee et al. 28 However, it should be noticed that the people in the ROK can freely visit any hospitals they want and relatives and friends have the tradition to visit the patients in hospitals. 21 This may indicate that the infection can actually spread on a wide and large population.
Technically, as the frequency-dependent contact rate in equation (1) was assumed, whether using N = 51 413 925 or N = 10 000 as, 28 provided N≫186, this will not affect the estimation of model parameters.

| Inference model
To reflect the huge dispersion in the daily number of cases, the nega- Assuming that the observed incidence x i (1), x i (2),…, x i (T i ) are conditionally independent, the total likelihood given parameters Θ is where the starting points of the three series are t E = 3, t I = 1, t C = 10, respectively, and their end points are T E = 48, T I = 53, T C = 55.
(As the exposure date of the index case is earlier than 11th May, only 185 cases are used for the exposure date series.) The priors f(Θ) for parameters are extracted from the literature or direct estimation from the ROK outbreak data (see Table 1). Employing Bayesian framework through the combination of the priors f(Θ) and the likelihood L(Θ,η;x), the posterior distribution can be obtained by Markov chain Monte Carlo simulations (MCMC). From these samples, we obtain means and their 95% confidence intervals (CIs) for parameters. 29 The DIC that was used to compare the performance of model variants is defined 30 as The most parsimonious model variant is the one that has the smallest DIC.

| Estimating the transmissibility
Some packages coded in R-computing language are available for estimating the transmissibility once the incidence time series data and serial interval (SI), which is defined as the difference in symptomonset dates of infectee-infector pairs, are known. The six approaches used are listed in Table 2 and briefly described below. For these methods, we assume the SI distribution of mean = 12.62 days and SD = 4.29 days, which is directly estimated from the data ( Figure A3 in Appendix S1) and close to the previous estimate by Cowling et al. 31 Exponential growth rate method 3 estimates R 0 by formula

| Model selection of transmission dynamics
The model comparison (Table 3) shows that the model variants with the breaking point in contact rate and diagnosis response to infection  Figure 4B EG, exponential growth rate method; ML, maximum-likelihood method; SB, sequential Bayesian method; TD, time-dependent transmission tree method using tree reconstruction method. 2 The four methods are coded in package "R0." 8 GT: generation time, time gap in infected times between an infectee and its infector which is usually approximated by serial interval-the gap in symptom onset between an infectee and its infector.
at 28 May 2015 are the best. Figure 2 Tables C2 and C3 in Appendix S3). These estimates are compatible with the previous studies. [16][17][18] Although all [16][17][18] used cumulative data while we use daily incidence data, the similar estimates were obtained. This implies the limited influence of using different data set on the results. These estimates show that R 0 of MERS-CoV in the ROK is far beyond the threshold level.

| Statistical estimation of transmissibility
The three estimation methods (exponential growth rate, maximum likelihood and sequential Bayesian) show estimates of R 0 ( Estimates of R t from transmission trees reconstructed are shown in Figure 4. The two methods 2,7 show different patterns in R t along the outbreak course: the relative smooth changes for the former ( Figure 4A) and erratic evolution for the latter ( Figure 4B).
The huge variance in Figure 4B indicates the cluster transmissions.
For example, three cases have symptom onset on 21st May; the estimate of R t on the day has mean of 28 but a wide 95% CI ranging from 0 to 85. The large variation in R t can also be seen on 20th May and 5th June. The difference between the two methods is because Hens et al. 7 further include the information of infector-infectee pair contacts. Nonetheless, the overall average decline patterns of R t in Figure 4 appear similar to those shown in Figure 3. With the fully reconstructed transmission tree, we can easily estimate generationbased reproductive number R g . From the sample transmission tree listed in Figure 4, we found R g reduced quickly, from initially R g = 28

| Interventions
The transmission dynamics model considers the actual observation that the infected people can transmit infection to others only during the period from symptom onset to confirmation. Correlation analysis (Table 4) shows that the rapid diagnosis through shortening delay from symptom onset to confirmation and self-protection are the main contributing factors to transmissibility. With countermeasures from 28th May, which reflect in both the self-protection coefficient (w = 9%) and shortened delay from symptom onset to confirmation (from D 0 = 9.3 days to D 1 = 4.1 days; cf., 33

| DISCUSSION
The characterisations based on the previous small outbreaks and sporadic cases suggest that MERS-CoV is severe but not very contagious. [10][11][12] The ROK outbreak caused 185 new cases and lasted about 2 months (Figures 1 and 4C). All 186 cases were put into special care and 38 died in the end. In this study, we applied different statistical estimation methods. [7][8][9] The estimates from these methods are roughly in agreement with each other and these estimates suggest It is well known that the overall transmissibility of MERS-CoV in community is very low. 35 Most introductions are not followed by human-to-human transmission or with only limited transmission. 36 Occasionally due to a range of factors such as long delay from symptom onset to isolation, long stay in hospitals and visiting more healthcare facilities, 37 more extensive outbreaks can happen such as the spring 2014 outbreak in the KSA. 14 Naturally if you measure R 0 in one of these larger outbreaks, it will be bigger-it might be difficult to tell Our dynamics model is simplified in many aspects, such as ignoring the age variation in transmissibility and superspreaders. 27,28,31 Although transmission was only taken place in hospitals, our model   Lee et al. 28