Understanding and Modeling the Super-spreading Events of the Middle East Respiratory Syndrome Outbreak in Korea

which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Editorial Super-spreading events (SSE) have been reported for many infectious disease outbreaks such as measles [1], tuberculosis [2], Ebola [3], and severe acute respiratory syndrome (SARS) [4-6]. The SARS outbreaks in Singapore, Hong Kong, and China in 2003 particularly made the importance of SSE evident in understanding transmission dynamics, predicting models, and containing outbreaks. However, the criteria of SSE and their effects on outbreak control measures are still unclear. Though there is an arbitrary definition for SSE [5, 6], there is no consistent and generally accepted definition yet [7]. Lloyd-Smith et al. introduced ν, the individual reproductive number, which is the expected number of secondary cases transmitted by a particular primary case, to explain a SSE with epidemiological modeling and successfully show that SSE are not exceptional events, but are " normal features of disease spread " as observed from the right-hand tail of a distribution of ν [7]. In a traditional epidemic model, the variation of ν is ignored and ν = R 0 for all cases, yielding Z ~ Poisson (R 0), where Z is the number of secondary infections caused by each case and R 0 is the basic reproductive number. Lloyd-Smith et al. generated a general model, Z ~ negative binomial (R 0 , k), where ν is gamma distributed with the mean R 0 and dispersion parameter, k. The lesser the value of k is, the greater is the heterogeneity of ν. After fitting these models to the SARS outbreaks in Singapore and Beijing, they found that the negative binomial model was unequivocally favored over other models. For example, k in the SARS outbreak in Singapore was estimated as 0.16 with the negative binomial model, which meant that ν was highly over-dispersed; results showed that a majority of SARS cases (73%) were barely infectious (ν < 1), but a small proportion (6%) were highly infectious (ν > 8) [7]. According to their findings, an infectious disease with a large individual variation of infectiousness (ν) shows " infrequent but explosive epidemics " after the introduction of a single case. They also defined a super-spreader as any infected individual who infects more than the 99 th percentile of the Poisson (R) distribution, where R is the effective reproductive number of a disease. SSE also played a crucial role in …