Transmission of Hand, Foot and Mouth Disease and Its Potential Driving Factors in Hong Kong

Hand-foot-and-mouth disease (HFMD) is a common childhood disease with substantial disease burden in Asia. Mixed results were reported on the associations between HFMD incidence and meteorological factors or school holidays, while limited studies focused on their association on transmissibility. We aimed to measure the transmissibility of HFMD and to examine its potential driving factors in Hong Kong. A likelihood-based procedure was used to estimate time-dependent effective reproduction number (Rt) based on weekly number of HFMD-associated hospitalizations from 2010 to 2014. The associations of between-year effects, depletion of susceptibles, absolute humidity and school holidays with Rt were examined using linear regression. Rt usually started increasing between early spring and summer and peaked in April to May at around 1.1–1.2, followed by a slight rebound in autumn. Depletion of susceptibles and between-years effects explained most of the variances (19 and 13% respectively) in Rt. We found a negative association between depletion of susceptibles and Rt (coefficients ranged from −0.14 to −0.03 for different years), but the estimated effects of absolute humidity and school holidays were insignificant. Overall, HFMD transmission was moderate in Hong Kong and was mainly associated with depletion of susceptibles. Limited impact was suggested from meteorological factors and school holidays.

usually fell outside the main peak of HFMD epidemics. Hong Kong has a humid summer with relatively stable peak absolute humidity in May and August (Fig. 1). The mean absolute humidity was 17.2 g/m 3 and fluctuated from 12.7 to 24.5 g/m 3 during the study periods.
The smoothed effective reproduction number (R t ) for HFMD began to increase above 1 during early January and late March (Fig. 1). Disregarding the exceptionally high R t estimates in early 2014 due to a small number of cases, the smoothed R t peaked at 1.12 to 1.24 in April or May and subsequently declined to below 1 in June or July preceding the peaks of the epidemic curve. The smoothed R t usually remained above 1 for around 4 to 5 months from spring to mid-summer. A rebound of R t occurred between August and October in autumn, then  afterwards fluctuated below 1 for most of the time during winter. In the sensitivity analyses, R t peaked at 1.17 to 1.26 by assuming a mean serial interval of 2 days; while R t peaked at 1.42 to 1.60 when assuming the mean as 7 days. A longer serial interval led to larger uncertainty in the R t estimates and slightly shortened the duration with estimated R t ≥ 1 ( Supplementary Fig. 1). The assumption on case-hospitalization risk (CHR) did not affect the point estimate of R t but will result in narrower 95% confidence intervals for a lower CHR ( Supplementary  Fig. 2).
The regression model fitted with between-year effects, the depletion of susceptibles, absolute humidity and school vacations (Model 4 in Table 1, Fig. 3) explained 35% of the variance in R t during the main epidemic periods. Depletion of susceptibles explained the most (19%) of the variance observed in R t while between-year effects explained 13%. Absolute humidity and school vacations explained 2% and 1% of the variance in R t respectively, though our results suggest absolute humidity does not explain the variance after accounting for autocorrelations ( Table 2). For the sensitivity analysis which accounted for autocorrelations, the total variance in R t explained was 26% (Table 2).
We found a negative association between the depletion of susceptibles and R t of HFMD (coefficients ranging from − 0.14 to − 0.03 among different years) and a marginally insignificant positive association between absolute humidity and the reproduction number (0.11, 95% confidence interval: − 0.01 to 0.22) ( Table 3). A significant positive association was also found between holidays and R t while the association was not significant after adjusting for autocorrelation (Supplementary Table 1). Autocorrelogram and partial autocorrelogram of model residuals suggest unaccounted autocorrelations ( Supplementary Fig. 3); however, results from models with or without adjustment for autocorrelation were very similar ( Table 2 and Supplementary Tables 1 and 2), except that the association between holidays and R t was not significant when accounted for autocorrelation. Sensitivity analyses on the end of HFMD epidemic period showed similar results ( Table 2 and Supplementary Table 2). Results from models stratified by EV71 activity were also similar with our main findings (Supplementary Tables 3 and 4). We also did not find significant associations between other meteorological factors and HFMD transmission, except for temperature in one model accounting for the autocorrelation of R t (results not shown).

Discussion
HFMD epidemics in Hong Kong occurred at least once per year and larger epidemics occurred every 2 to 3 years, similar to the pattern in other subtropical and tropical regions such as Macau, Taiwan, Singapore and Vietnam [24][25][26] . The main spring-summer peak usually started around March and peaked in June or July, while a milder autumn peak occurred after the start of a new school year in September. Smaller winter epidemics, which sometimes occurred in other subtropical regions, were also observed in 2012 and 2014 in Hong Kong 1,2,27,28 .
The estimated R t usually exceeded 1 by March each year, corresponding to the exponential growth phase of the HFMD epidemic. R t peaked in around April to May, suggesting that HFMD transmission was most intense well before summer. R t dropped below 1 in June or July and rebounded to above 1 around September, probably driven by a new cohort of susceptible children entering kindergartens and the increase in contact rates among children in the new school year. However, further confirmatory study is needed to demonstrate the difference in transmission between the entry versus higher grades in kindergartens. R t usually fluctuated below the threshold of 1in winter although mild HFMD activity can be observed in some years, indicating a generally low HFMD transmission during winter.
The estimated annual peak values of R t ranged from 1.14 to 1.24 in the study period, indicating a relatively moderate HFMD transmissibility in Hong Kong. A transmission study in mainland China using a susceptible-infected-recovered model estimated a slightly higher R t , ranging from 1.4 to 1.6 across different geographical regions 22 . In our study, the yearly intercepts log(R 0 S 0 j ), which is the logarithm of the product between R 0 and the fraction of susceptibles at the beginning of each year, were estimated to range from − 0.19 to 0.07 between 2008 and 2014, translating to an R 0 ranging from 1.7 to 2.2 assuming 50% susceptibility at the start of the epidemic 4,29,30 . Two studies using similar statistical methods estimated that the R 0 of HFMD ranged from 2.5 to 5.5 for the causative enterovirus serotypes CA16, CA6 and EV71 in Hong Kong and Singapore 20,21 . The estimates appear to be higher than that in our study, as the studies focused on institutional outbreaks rather than at the community level. In addition, R 0 was highly sensitive to the assumed incubation period (R 0 reduced by up to 50% for incubation period of 3 days instead of 5 days 20 ) and the incubation period was assumed to be 5 days in the two studies, which is towards the upper end of the commonly quoted incubation period 31,32 .
Our results indicate that 35% of the variance in weekly R t for HMFD can be explained by between-year effects, the depletion of susceptibles, absolute humidity and school holidays ( Table 1). The order for potential driving factors of HFMD in our main results remained the same as that in the sensitivity analysis (explaining 22-49% of the variance in R t ), indicating that the relative importance of the above factors were not affected by the definition of the epidemic period 23 . The depletion of susceptibles appears to be the most important driving factor of HFMD transmission, while absolute humidity and school holiday seem to have limited effects on HFMD transmission.   Between-year effects also explained a noticeable portion (13%) of the variation in HFMD transmission in Hong Kong. One possible reason was the alternating predominant serotype with different basic transmissibility and associated immunity in the community 5,20,21 . For example, 71% of the HFMD outbreaks in 2013 were associated with the subtype CA6, but only less than 30% for other years in our study period 5 . In the following year, only around 10% of the outbreaks were associated with the subtype CA6, with a similar proportion as other subtypes CA4, CA10 and EV71 5 . The remaining unexplained variance in R 0 may be partly due to factors such as the different control measures in the kindergartens and schools which were difficult to measure. The unexplained variance may also due to stochasticity and individual-level factors.
Our results showed an insignificant positive association between absolute humidity and R t . Together with the low R 2 explained, the absolute humidity may have limited effect on the transmission of HFMD in Hong Kong. We did not identify any other important driving meteorological factors (e.g. rainfall and sunshine) on HFMD transmission, with an exception for temperature under the model adjusting for autocorrelations (data not shown). A number of studies have reported a positive association between HFMD incidence and meteorological factors such as temperature and relative humidity, although some of the studies were conducted in temperate regions [6][7][8][9][10][11][12][13] . Once an epidemic takes off, the number of new cases will continue increasing even when R t decreases but stays above 1. This feature somehow makes our results less comparable with previous findings which mostly focused on incidence. Another possible reason for the inconsistency is that Hong Kong is a subtropical city with relatively high temperature (median 27.0 °C, IQR 21.7-28.7 °C) and relative humidity (median 83.1%, IQR 79.4-86.4%) in most of the main epidemic periods and transmission of HFMD may be most efficient at a temperature of 23.9 °C and higher relative humidity 22 . Our model is therefore underpowered to detect the full impact of the meteorological factors due to the small number of days when the transmission is not active in Hong Kong. More evidence on the underlying biological mechanism of HFMD transmission is needed to improve the understanding of the potential effect of meteorological factors.
Summer or spring school breaks with duration longer than one month were reported to be associated with lower HFMD transmission 22 . Our results however did not suggest that school holidays substantially reduced the transmission of HFMD in Hong Kong. This may be partially explained by the fact that Hong Kong has relatively short school holidays except for the summer holidays. In many cases, R t has already been decreasing well before the summer holiday (Fig. 2). Besides, previous findings showed that household plays an important role in HFMD transmission, where the transmission risk among siblings could reach 84% 33 . Public playground, which younger children would go for during school holidays, was reported as a risk factor of HFMD transmission 18,19 . We did not attempt to examine the potential effect of reactive school closure due to HFMD outbreaks, during which the social activities of the children may have a very different pattern from those in holidays. There were large HFMD outbreaks in 2010 in Hong Kong which led to some school closures and had significantly raised the awareness and preparedness in the schooling setting in the subsequent years. Considering the high social cost and enhanced preventive measures already in place at schools, the additional effect of school closure to reduce HFMD transmission may be limited. Furthermore, even if the EV71 vaccine would be available in Hong Kong in the future, it may have limited effect on HFMD transmission at the population, as the EV71 serotype was responsible for less than 20% of the HFMD outbreaks in Hong Kong 5 . However, EV71 is disproportionately responsible for the most severe HFMD infections 1 .
This study focused on the transmissibility of HFMD which has more direct implications on the control measures, while incidence depends on the combined effect of transmissibility and time to symptom appearance. Our study has several limitations. First, our estimations were based on hospitalized HFMD cases and may not reflect trend of population incidence reliably if the CHR changed substantially within a short period. Second, R t could be overestimated if there were substantial imported cases or differences in transmissibility among serotypes. Third, we adopted the dates of summer vacations from the Education Bureau, but some kindergartens started schools earlier in August. This may partly explain the rebound of R t slightly earlier than the start of the school year in September for most schools. Finally, we could not establish causation between HFMD transmission and various potential driving factors. However, the lack of association between meteorological variables and HFMD transmissibility may indicate limited effectiveness in weather-based strategies, especially for places such as Hong Kong with strengthened hygiene measures in schools. Weekly and daily population were estimated by linear interpolation assuming the growing rate of population were uniform during each halfyear interval. Daily counts of HFMD cases (n s ) were derived from the weekly data as follows: we first calculated the weekly HFMD-associated hospitalizations rate I t by dividing the weekly number by the interpolated weekly population. The cumulative incidence of HFMD-associated hospitalizations (C t ) in each week t was then calculated. We used cubic spline interpolation to obtain the cumulative daily incidence (C s ), and took the daily difference of C s to derive daily incidence (I s ). The case-hospitalization risk (CHR), which is defined as the risk of hospitalization among all HFMD cases, was assumed to be constant at 1.3%, based on a previous study in Hong Kong 2 . Finally, n s was derived using daily incidence, case-hospitalization risk and daily population.

Conclusions
Scientific RepoRts | 6:27500 | DOI: 10.1038/srep27500 We obtained the daily mean temperature (°C) and daily relative humidity (%) between 2010 and 2014 from the Hong Kong Observatory 36 . Absolute humidity was shown to have a more direct effect on the activity of several viruses and hence was used in our main analysis [37][38][39] . We calculated absolute humidity (g/m 3 ), using Bolton's conversion formula based on mean temperature and relative humidity 40 . Weekly absolute humidity was calculated as the arithmetic mean of daily absolute humidity in the corresponding week.
School vacations considered in the study include the Christmas, New Year, Chinese Lunar New Year, Easter and school summer holidays, which usually last for at least one week for most kindergartens and schools in Hong Kong. The period of school vacations was determined according to the guideline of school calendar issued by the Education Bureau 41 . The summer holiday was defined as from mid-July to the end of August, while the other holidays were defined as the week(s) when most of the general holiday days fell.
Effective reproduction number. We adopted the likelihood-based approach proposed by Wallinga et al. and Cauchemez et al. to estimate the daily reproduction number (R s ) 42,43 accounting for right censoring, which is outlined below. We first calculated the relative probability (p ks ) that cases with illness onset on day k were infected by cases showing symptoms on day s, based on an assumed serial interval distribution w(·). We then obtained X s , the number of secondary case infected by cases on day s, by assuming a binomial distribution Bin(n s , p ks ) and observable infected cases governed by w(·). R s was calculated by dividing X s with n s . The weekly R t was calculated as the geometric mean of the estimated daily R s . We assumed a negligible number of imported cases in the study period. The serial interval of HFMD was assumed to follow a Weibull distribution with mean 3.7 days and standard deviation 2.6 days 33 . Sensitivity analyses were conducted assuming serial intervals with mean 2 days and 7 days respectively and a CHR of 0.6% and 2.8%. To capture the overall trend of HFMD transmissibility in Hong Kong, we also estimated the smoothed R t based on spline smoothed average weekly incidence with the lowest generalized cross-validation (GCV) score 44 .

Potential factors of HFMD transmissibility.
To further examine the potential factors that influence HFMD transmission, we used the linear regression approach as proposed by te Beest et al. 23 . Weekly R t was used as proxy of HFMD transmission. R t was assumed to be proportional to the basic reproduction number R 0 , scaled by the between-year effects, depletion of susceptibles and effects of absolute humidity (AH) and school vacations (V). Based on the above assumption, the linear regression model can be expressed as 23 : where R tj is the effective reproduction number in week t of year j; β oj denotes the between-year intercepts, which represents different susceptibility in the beginning of each year j; C tj is the weekly cumulative incidence of HFMD up to week t-1. The coefficients β j , β AH and β V represent the effect of the yearly depletion of susceptibles, absolute humidity and school vacations. To assess the potential impact of autocorrelation, we conducted a sensitivity analysis by fitting models accounting for autocorrelations in R t .
The analysis was restricted to the main wave of HFMD epidemics, defined as the period from the beginning of exponential growth phase through the last week of August for each year. The exponential growth phase was defined as the period when the estimated daily number of HFMD increased steadily and the growth rate (Δ n s ) continuously increased for no less than two months at the beginning of an epidemic. This allowed for the different start time of HFMD epidemic in each year (Fig. 2) and controlled for the new cohort of students admitted to the kindergartens in September each year. We also carried out sensitivity analyses by defining the end of HFMD epidemic period in July, September or October. Other meteorological factors such as temperature, relative humidity and air pressure were also tested. We also carried out a sensitivity analysis by stratifying the years of EV71 activity to account for the potential impacts of changing predominant serotypes.
All analyses were conducted in R version 3.1.1 (R Foundation for Statistical Computing, Vienna, Austria). We provided detailed statistical methods in the web appendix.