Stochastic and spatio-temporal analysis of the Middle East Respiratory Syndrome outbreak in South Korea, 2015

Lee, Hyunsun

The demographical distribution of each generation over the 17 hospitals in Fig. 2 as well as in Table 1 is depicted in Fig. 10 . One may expect a strong association between the size (bed counts) of the hospital and the number of MERS cases. However, we found the association to be very weak with a coefficient of determination close to zero for this particular outbreak. This explains the importance of quarantine regardless of hospital size. Our interest lies in the spatio-temporal proximity of occurrence between two patients where one patient infected MERS to the other, i.e. the two connected vertices in Fig. 7 . For this purpose, we use the geographical distance and the difference of the confirmation dates (serial interval) between these paired patients. The distance is measured by the haversine formula between two hospitals in latitude and longitude in Table 1 . While this Euclidean distance may not give the exact travel distance in a metropolis such as Seoul in South Korea, we assume that it is sufficient to characterize the geometrical distances between hospitals or the travel distances of patients. The distributions of the distance and the serial interval between all connected vertices in Fig. 7 are depicted in Fig. 11 . As we observe in the graph on the left in Fig. 11 , there are three major distances, approximately 0 km, 53 km and 81 km, that are well associated with the major distances in Fig. 10 , characterizing inter-hospital or intra-hospital transmission. Most of the patients in Gen 1 are located at Hospital K1 in Fig. 10 , where the index case in Gen 0 was also confirmed, contributing the highest probability at the distance of 0 km in the left graph of Fig. 11 . The major hospitals in Gen 2 are S2, K1-K3 and D1-D2. Considering the three prominent distances in the graph on the left in Fig. 11 , we infer that the disease was transmitted intensely between S2 and K1-K3 (about 53 km apart), and between K1-K3 and D1-D2 (about 81 km apart), rather than transmitted directly between S2 and D1-D2 (about 133 km apart), unless otherwise intra-hospital (0 km apart) transmission in Gen 2. Lastly, the major hospitals in Gen 3 are located mostly within 25 km from each other in Seoul, and the total number of patients in Gen 3 is not as high as those in other generations. The mean serial time interval is 9.8057 days with a 95% confidence interval of (9.1975, 10.414) in the graph on the right in Fig. 11 . Fig. 12 demonstrates the spatio-temporal autocorrelation results of the MERS outbreak in South Korea, based on Equation (6). The first row in Fig. 12 is the profile of Coðs; tÞ over the entire transmission period in the three-dimensional presentation in Fig. 9 . The function hðzÞ ¼ G 1 ðzÞ À z on the left and the probability of ultimate extinction in terms of days on the right. the left and the corresponding contour plots in st -plane in the right. The second to the fourth rows in Fig. 12 are the autocorrelations for Gens 1, 2 and 3, respectively. The autocorrelation over the full domain has a few distinct spikes at certain sand t-lags. The peaks in the spatial and temporal lag domain explains that there are a few hospitals mainly involved in the transmission, that characterizes a typical pattern of inter-and intra-hospital transmission. These patterns of the autocorrelation in spatial and temporal directions can be closely associated with Fig. 11 . The transmissions in Gen 1 were mainly intrahospital as there is very little spatial distribut