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Accepted Manuscript High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial outbreaks Mathematical modelling in Saudi Arabia and South Korea Sunhwa Choi Eunok Jung Bo Youl Choi Young Joo Hur Moran Ki PII S0195 6701 17 30526 1 DOI 10 1016 j jhin 2017 09 017 Reference YJHIN 5231 To appear in Journal of Hospital Infection Received Date 4 July 2017 Accepted Date 20 September 2017 Please cite this article as Choi S Jung E Choi BY Hur YJ Ki M High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial outbreaks Mathematical modelling in Saudi Arabia and South Korea Journal of Hospital Infection 2017 doi 10 1016 j jhin 2017 09 017 This is a PDF file of an unedited manuscript that has been accepted for publication As a service to our customers we are providing this early version of the manuscript The manuscript will undergo copyediting typesetting and review of the resulting proof before it is published in its final form Please note that during the production process errors may be discovered which could affect the content and all legal disclaimers that apply to the journal pertain M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 1 High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial 1 outbreaks Mathematical modelling in Saudi Arabia and South Korea 2 3 Short title High reproduction numbers of MERS CoV 4 5 Sunhwa Choi 1 Eunok Jung 2 Bo Youl Choi 1 Young Joo Hur 3 Moran Ki4 6 7 1Department of Preventive Medicine Hanyang University Medical College Seoul Korea 8 2Department of Mathematics Konkuk University Seoul Korea 9 3Center for Infectious Disease Control Korea Centre for Disease Control and Prevention Cheongju Korea 10 4Department of Cancer Control and Population Health Graduate School of Cancer Science and Policy 11 National Cancer Centre Goyang Korea 12 13 Corresponding author Moran Ki M D Ph D 14 Department of Cancer Control and Policy Graduate School of Cancer Science and Policy 15 National Cancer Centre 323 Ilsan ro Ilsandong gu Goyang 10408 Korea 16 Tel 82 31 920 2736 Fax 82 50 4069 4908 E mail moranki ncc re kr 17 18 Competing interests None 19 20 21 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 2 Data availability All relevant data are available at http rambaut github io MERS 22 Tools cases2 html 23 24 Funding This work was supported by the National Cancer Centre Grant NCC 1710141 1 25 26 Keywords nosocomial infection basic reproduction number epidemiology Middle East 27 respiratory syndrome coronavirus mathematical modelling South Korea 28 29 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 3 Summary 30 Background Effective countermeasures against emerging infectious diseases require an 31 understanding of transmission rate and basic reproduction number R0 The R0 for severe acute 32 respiratory syndrome SARS is generally considered to be 1 whereas that for Middle East 33 respiratory syndrome MERS is considered to be 1 However this does not explain the large 34 scale outbreaks of MERS that occurred in Kingdom of Saudi Arabia KSA and South Korean 35 hospitals 36 Aim To estimate R0 in nosocomial outbreaks of MERS 37 Methods R0 was estimated using the incidence decay with an exponential adjustment model 38 The KSA and Korean outbreaks were compared using a line listing of MERS cases compiled using 39 publicly available sources Serial intervals to estimate R0 were assumed to be 6 8 days Study 40 parameters R0 and countermeasures d were estimated by fitting a model to the cumulative 41 incidence epidemic curves using Matlab 42 Findings The estimated R0 in Korea was 3 9 in the best fit model with a serial interval of 6 days 43 The first outbreak cluster in a Pyeongtaek hospital had an R0 of 4 04 and the largest outbreak 44 cluster in a Samsung hospital had an R0 of 5 0 Assuming a 6 day serial interval the KSA 45 outbreaks in Jeddah and Riyadh had R0 values of 3 9 and 1 9 respectively 46 Conclusion The R0 for the nosocomial MERS outbreaks in KSA and South Korea was estimated 47 to be in the range of 2 5 which is significantly higher than the previous estimate of 1 48 Therefore more comprehensive countermeasures are needed to address these infections 49 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 4 Introduction 50 The emergence of infectious diseases associated with Middle East respiratory syndrome MERS 51 severe acute respiratory syndrome SARS and Ebola has created unprecedented public health 52 challenges These challenges are complicated by the lack of basic epidemiological data which 53 makes it difficult to predict epidemics Thus it is important to quantify actual outbreaks as 54 novel infectious diseases emerge Disease severity and rate of transmission can be predicted by 55 mathematical models using the basic reproduction number R0 1 For example R0 has been 56 extensively used to assess pathogen transmissibility outbreak severity and epidemiological 57 control 2 4 58 59 In previous studies the R0 for MERS has ranged from 0 42 to 0 92 5 8 which suggests that the 60 MERS coronavirus MERS CoV has limited transmissibility However these studies typically 61 considered community acquired MERS infections In this context nosocomial infections can 62 exhibit different reproduction numbers as the transmission routes for community acquired and 63 nosocomial infections often differ 9 Recent studies have also examined large healthcare 64 associated outbreaks of MERS CoV infection in Jeddah and Riyadh within the Kingdom of Saudi 65 Arabia KSA One study reported higher healthcare acquired R0 values than those from 66 community acquired infections when using the incidence decay with exponential adjustment 67 IDEA model which yielded values of 3 5 6 7 in Jeddah and 2 0 2 8 in Riyadh 10 The IDEA 68 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 5 model is simple because it does not consider the population level immune status which makes 69 it especially useful for modelling emerging infectious diseases in resource limited settings 70 The MERS outbreak in South Korea was associated with hospital acquired infections At that 71 time the Korea Centre for Disease Control and Prevention KCDC assumed that the outbreak 72 had an R0 1 Thus the initial countermeasures were not sufficiently aggressive to prevent the 73 spread of MERS CoV infection to other hospitals Therefore we used the IDEA model to 74 evaluate and compare the MERS R0 values from the outbreaks in both the KSA and South Korean 75 hospitals 76 77 78 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 6 Methods 79 Data source 80 The KSA data were obtained using a line listing of MERS CoV cases that was maintained by 81 Andrew Rambaut updated on 19 August 2015 The line listing was created using data from the 82 KSA Ministry of Health and World Health Organization reports WHO 10 Since only 44 of the 83 cases in the KSA listing included the onset date hospitalization dates or reported dates were 84 used instead The Korean data were obtained from the KCDC Among the 186 MERS cases 178 85 had confirmed onset dates The eight cases with unknown dates of onset were assigned dates 86 based on those of laboratory confirmations All cases in the KSA and Korea were confirmed 87 based on laboratory findings Study parameters R0 and countermeasures d were estimated 88 by fitting a model to the cumulative incidence epidemic curves using Matlab software 89 Mathworks Natick MA USA 90 91 The data were narrowed down to only the hospital infection cases Cases with unknown 92 transmissions were considered to be hospital infections if a the patient was in contact with a 93 healthcare worker and or hospitalized patients or b the patient was a healthcare worker Cases 94 were excluded if they could not be verified as hospital infections e g zoonotic transmission 95 family contact or community infection 96 97 98 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 7 Model 99 We used the IDEA model to estimate the R0 as reported previously 11 together with publicly 100 available data The IDEA model is based on the concept that the number of incident cases g1835 in 101 an epidemic generation g1872 that can be counted as 102 g1835 g1872 g1844g2868 g3047 1 When an outbreak occurs epidemic control measures can be implemented which can in turn 103 change the R0 Therefore the relationship between I and R0 with countermeasures g1856 is defined 104 as follows 105 g1835 g1872 g3428 g1844g2868 1 g1856 g3047g3432 g3047 2 The R0 and d parameters are estimated by fitting g1835 from model 2 to the observed cumulative 106 incidence data of MERS using the least squares data fitting method Since the IDEA model is 107 parameterized using epidemic generation time in the present study incidence case counts were 108 aggregated at serial intervals of 6 7 and 8 days 10 109 We considered two large outbreaks in each country studied the outbreaks in Riyadh and 110 Jeddah for the KSA and those in Pyeongtaek St Mary s Hospital and Samsung Seoul Hospital 111 for South Korea The term resnorm is defined as the norm of the residual which is the squared 112 2 norm of the residual it measures the difference between observed data and the fitted value 113 provided by a model However since residuals can be positive or negative a sum of residuals is 114 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 8 not a good measure of overall error in the fit Therefore a better measure of error is the sum of 115 the squared residuals E which is calculated as follows 116 117 E g1832 g1876 g1876datag3036 g1877datag3036 g2870g3036 118 3 119 120 The given input data xdata the observed output data ydata and F x xdata are the 121 functions we wanted to fit where xdata was an epidemic generation ydata was the observed 122 cumulative incidence data and F x xdata was equation 2 123 Since the generation times and the estimated values differ according to serial interval times the 124 resnorm changes accordingly Therefore to compare the resnorm with the serial interval time 125 the relative resnorm was defined as follows 126 E g3007 g3051 g3051datag3284 g2879g3052datag3284 g3118g3052data g3284 g3036 4 127 128 The IDEA model was fitted to the cumulative South Korean MERS CoV case data from the onset 129 date of the first case to the onset date of the last case The outbreak start date was defined as 130 11 May 2015 because that was the symptom onset date for Patient Zero who was the index 131 case and caused the outbreak in the Pyeongtaek hospital MERS patient no 14 caused the 132 outbreak at the Samsung hospital and his symptom onset date was 21 May 2015 The last case 133 of the MERS outbreak in South Korea was observed on 4 July 2015 The KSA MERS outbreak 134 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 9 model was fitted using the cumulative incidence data from 28 March 2014 to 2 June 2014 in 135 Jeddah and from 20 March 2014 to 29 May 2014 in Riyadh 136 137 Ethical Considerations 138 All data used in these analyses were de identified publicly available data obtained from the 139 WHO the KSA Ministry of Health website or KCDC datasets As such these data were deemed 140 to be exempt from institutional review board assessment 141 142 143 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 10 Results 144 The KSA outbreaks were relatively large with 180 cases over the course of 67 days in Jeddah 145 and 142 cases over the course of 71 days in Riyadh The Korean outbreaks involved 186 cases 146 over the course of 55 days including 36 cases over the course of 23 days in the Pyeongtaek 147 hospital and 91 cases over the course of 45 days in the Samsung hospital Most Korean cases 148 180 were hospital acquired with the exception of four cases acquired by household 149 transmission and two cases with unknown modes of transmission In the KSA only two cases 150 involved confirmed zoonotic transmission while a large number of unknown transmissions 151 Jeddah 99 cases Riyadh 69 cases and hospital exposures Jeddah 80 cases Riyadh 70 cases 152 were observed Table I 153 154 The IDEA model was fitted to the daily KSA and Korea MERS CoV case data according to the 155 onset date Figure 1 displays the cumulative MERS CoV case data for the 2014 KSA and the 2015 156 South Korea MERS outbreaks Patient Zero s symptom onset date was 11 May 2015 however 157 he was admitted to the Pyeongtaek hospital on 15 May 2015 Therefore the outbreak was 158 assumed to start on 15 May 2015 via a simulation of the Pyeongtaek hospital outbreak The 159 outbreak start date for the Samsung hospital was determined to be 25 May 2015 following the 160 same logic Figure 1 161 162 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 11 Figure 2 shows the results of the 2014 KSA outbreak Squares circles and asterisks 163 represent data aggregation of the number of cases by serial intervals of 6 7 and 8 days the 164 curves represent model fits for best fit parameters Our estimated R0 values for Jeddah and 165 Riyadh were in the range of 3 95 6 68 and 1 92 2 52 respectively using serial intervals of 6 8 166 days The estimated R0 values for the Korea MERS outbreak were 3 96 4 91 and 5 95 for serial 167 intervals of 6 7 and 8 days respectively Figure 3 Since most cases were related to hospital 168 acquired infections the R0 for each hospital was also considered The outbreak in the Samsung 169 hospital was larger than that in the Pyeongtaek hospital the first Korean outbreak The 170 Pyeongtaek hospital exhibited best fit R0 values of 4 04 4 23 and 4 39 for serial intervals of 6 7 171 and 8 days respectively while the Samsung hospital exhibited greater R0 values of 5 0 6 8 and 172 8 11 for serial intervals of 6 7 and 8 days respectively Figure 3 shows that the IDEA model 173 provided well fitted curves for the cumulative data regarding South Korean MERS symptom 174 onset dates for all cases 175 176 Although the IDEA model seemed to be appropriate the original data never precisely fit the 177 model Therefore the appropriateness of the model was assessed Error was evaluated using 178 the relative resnorm to find the best fit parameters The results indicated that the best fit R0 179 and serial interval values were 4 9 and 7 days for all cases 4 39 and 8 days for the Pyeongtaek 180 hospital and 5 0 and 6 days for the Samsung hospital respectively Countermeasures termed 181 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 12 d increased with each serial interval because the daily effort of countermeasures was 182 aggregated by serial interval 183 184 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 13 Discussion 185 The clusters of MERS CoV cases in KSA healthcare facilities occurred from late March to late 186 May 2014 while the Korean outbreaks occurred from mid May to early July in 2015 These 187 hospital based outbreaks exhibited characteristics different from those of community based 188 outbreaks higher R0 values and case fatality rates 12 13 189 190 The estimated R0 is a basic epidemiological variable that is important for selecting appropriate 191 countermeasure efforts However an emerging infectious disease often has an unknown 192 epidemiology making it difficult to mathematically model Several methods have been 193 proposed to address this issue including the IDEA model The Richards model can also estimate 194 the R0 using the cumulative daily number of cases and the outbreak turning point or the peak 195 g1872g3036 14 In this context Hsieh used the Richards model to estimate the R0 values for the Korean 196 outbreak as 7 0 19 3 Yet the Richards model does not consider any countermeasures 197 implemented during an outbreak therefore it can only be used after an outbreak has peaked 198 199 The present study used the IDEA model to estimate the R0 values from the MERS outbreaks in 200 the KSA and South Korea The IDEA model exhibited a good fit the estimated R0 values for South 201 Korea were 3 9 8 0 and the best fit R0 was 4 9 for a serial interval of 7 days Conversely the R0 202 values for Riyadh and Jeddah were 1 9 2 5 and 3 9 6 9 respectively using serial intervals of 6 203 8 days Majumder et al 10 used the IDEA model and estimated very similar R0 values of 2 0 2 8 204 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 14 for Riyadh and 3 5 6 7 for Jeddah with serial intervals of 6 8 days However the estimated R0 205 values from the present study were much higher than the previously reported values of 1 for 206 MERS the threshold for an epidemic 15 Regardless the Korean government assumed that the 207 outbreak had an R0 value of 1 based on the previous research The initial criterion for 208 quarantine therefore was limited to cases of close contacts which were defined as people 209 who were within 2 metres of a MERS patient for 1 hour 16 These quarantines established 210 using an incorrectly assumed R0 resulted in more MERS patients and greater hospital to 211 hospital transmission 16 212 213 A serial interval is the interval between successive cases of an infectious disease This time 214 period depends on the temporal relationship between the infectiousness of the disease the 215 clinical onset of the source case and the incubation period of the receiving case 17 As MERS 216 becomes infectious with the onset of clinical symptoms the MERS latency period equals the 217 incubation period Therefore the shortest serial interval could be the same as the incubation 218 period and the longest serial interval could be the sum of the incubation period and the 219 maximum duration of infectiousness During the Korean MERS outbreak several super 220 spreading events occurred because the MERS cases were not immediately isolated upon 221 presentation of clinical symptoms 18 Thus these cases contacted susceptible individuals for up 222 to 1 week after the onset of their clinical symptoms However most MERS cases with laboratory 223 confirmation were isolated immediately after clinical symptom onset 19 20 In this study since 224 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 15 the incubation period was 2 14 days median 6 days the serial interval was slightly longer 225 than the incubation period The IDEA model with several serial intervals 4 12 days was used 226 and found that intervals of 6 8 days provided the best fit For the KSA data even though the 227 reported date was used instead of the onset date the R0 was not affected because aggregated 228 data by serial intervals was used in the analysis 229 230 The IDEA model is limited by the fact that the countermeasures term d cannot be compared 231 with the d of another model In this context an increasing d in accordance with increasing serial 232 intervals indicates that the countermeasure efforts are increasing However the size of d cannot 233 be compared between two or more models of different outbreaks Nevertheless the strength of 234 the IDEA model is its simplicity because the R0 value can be estimated using only the cumulative 235 number of cases according to the serial interval 236 237 Conclusions 238 The estimated R0 values from the KSA outbreaks Riyadh and Jeddah ranged from 1 9 to 6 9 239 whereas the estimated values from the South Korean outbreaks ranged from 3 9 to 8 0 Based 240 on these findings it appears that nosocomial MERS CoV outbreaks in the KSA and South Korea 241 had higher R0 values than the previously assumed values of 1 Although community acquired 242 infections are caused by contact nosocomial infections are caused by a combination of contact 243 and aerosol transmission therefore R0 values for hospital infections can be higher than those 244 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 16 for community acquired infections Hence more comprehensive countermeasures are needed 245 to address nosocomial MERS infection and prevent its spread 246 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 17 References 247 1 Chowell G Sattenspiel L Bansal S Vibo