The authors have declared that no competing interests exist.
Conceived and designed the experiments: SK MK. Performed the experiments: SK MK. Analyzed the data: SK MK. Contributed reagents/materials/analysis tools: SK MK. Wrote the paper: SK MK.
School closure is considered as an effective measure to prevent pandemic influenza. Although Japan has implemented many class, grade, and whole school closures during the early stage of the pandemic 2009, the effectiveness of such a school closure has not been analysed appropriately. In addition, analysis based on evidence or data from a large population has yet to be performed. We evaluated the preventive effect of school closure against the pandemic (H1N1) 2009 and examined efficient strategies of reactive school closure.
Data included daily reports of reactive school closures and the number of infected students in the pandemic in Oita City, Japan. We used a regression model that incorporated a time delay to analyse the daily data of school closure based on a time continuous susceptible-exposed-infected-removed model of infectious disease spread. The delay was due to the time-lag from transmission to case reporting. We simulated the number of students infected daily with and without school closure and evaluated the effectiveness.
The model with a 3-day delay from transmission to reporting yielded the best fit using
School closure was an effective intervention for mitigating the spread of influenza and should be implemented for more than 4 days. School closure has a remarkable impact on decreasing the number of infected students at the peak, but it does not substantially decrease the total number of infected students.
School closure is one of the important non-pharmaceutical interventions (NPIs) used to mitigate the spread of influenza. An ideal intervention should result in a delay in the peak incidence or a reduction in the number of infected students at the peak and decrease the total number of cases [
There are two types of school closures. First, a proactive closure is implemented to slow down the spread of influenza for the wider community on early onset. Second, a reactive school closure is implemented when many children and staff are infected. Simulation and empirical studies of pandemic influenza have reported that school closure mainly reduced the peak incidence, while only slightly reducing the cumulative infection attack rate [
In Japan, different guidelines were used for the school closures in the early and late phases against the pandemic (H1N1) 2009. Initially, in the early phase when the first case was confirmed, the basic strategy was proactive school closure [
Several studies have reported the effect of reactive school closure during the pandemic (H1N1) 2009 [
The purpose of this study was to estimate the impact of school closure, considering the effect of the time delay as the latent period, by analysing the data of the pandemic (H1N1) 2009 in Oita City, Japan. The data were ideal to accomplish this purpose. First, the data were collected daily so that we could analyse the effect of the latent period in shorter intervals. Second, the proportion of schools surveyed among the total in our data was very high, resulting in data for more than 98% of elementary and junior high school students. Third, because it was a novel influenza and no vaccine was available, vaccine coverage did not influence the data. Therefore, all of the students could be considered susceptible. During the season, 96% of the influenza viruses isolated in Japan were the AH1pdm virus [
Our data included the number of infected students and school closures from August 2009 to March 2010 in Oita City of western Japan. We obtained the data directly from the Oita Prefectural Board of Education and Oita City Board of Education. Every public school was obligated to report the numbers of infected students, including the suspected cases, and the implementation of school closure by class. Every newly infected student and closure was reported daily to the respective board of education. Almost all of the reported students were diagnosed as infected with influenza by physicians using rapid diagnosis tests, and the false negative cases were closely monitored. In our study, the number of students at any level of closure, i.e., class, grade, or whole school, was calculated to precisely estimate the impact of school closure.
Oita City is located west of Kyushu Island and has a population of approximately 450,000 people. It is 400 kilometres from Hyogo and Osaka, where the first case in Japan was confirmed. As Oita City is surrounded by mountains and the sea and separated from other regions geographically, the effect of entry and exit populations was considered minimal. Approximately 96% of students were attending school and living within Oita City [
In addition to simple mechanistic transmission dynamics, we considered AH as one parameter of the epidemic. AH is related to the survival rate of the influenza virus and the significant effect of the epidemic [
We obtained sentinel data to compare the number of cases of infected schoolchildren with other ages of people in Oita City. We were able to determine the weekly number of cases per clinic by age group. In Oita City, 16 outpatient clinics were registered in the influenza sentinel surveillance system. Data were provided by the Oita City Health Care Centre from September 2009 to March 2010. We illustrated the trend of cases of influenza-like illness by age group.
The data that were provided directly from the Oita Prefectural Board of Education and Oita City Board of Education were collected as secondary data sources, and we followed the ethical guidelines for epidemiological research performed in Japan. The data were anonymized and de-identified prior to analysis.
The dataset of the number of infected students used in the analyses was the one transformed by the moving averages method. The raw data showed a weekly pattern. The reported numbers were large on Mondays and very small on school holidays (Saturdays and Sundays). To address weekend bias in the reported data, we calculated a moving average for 7 days; as a result, we obtained smoother data and eliminated the weekly periodicity. However, on Tuesday November 24, 2009, an extraordinarily large number of infected students were reported because of a successive three-day holiday. We could not obtain smooth data for the week by the moving average method only. Therefore, we adjusted the values of the week using the proportions of the previous week. Additionally, a time lag in reporting did not occur because our data were collected only on the days when students were absent.
We analysed data from September 1, 2009 and treated infected students as recovered students before that time because August was summer vacation. The rule of school closure was adopted from September 1, 2009.
We used a regression model based on the time continuous susceptible-exposed-infected-removed (SEIR) model. For simplicity, we ignored death and a change in school by students, because the interval of analysis was so short that such effects might not significantly influence the results. In addition, although children contact their friends during school closure [
We denoted the delay due to the latency period of infection by
Then,
Diagram of the relationship between the day of infection, the day of becoming infectious, and the day a case is reported, in the case of
In data analyses, we used a generalized discrete SEIR model to estimate the number of infected students and added AH as a parameter related to the spread of infection. In our generalized model, newly infected students are given by the following.
Using common logarithms of the values, if the observed value was 0, we replaced it with 0.5.
We were able to determine
Students isolated by school closure should not be exposed to the risk of infection. Therefore, susceptible students were divided into subjects in opened schools,
Simulation for the number of infected students under school closure is given by Eq (
We were able to determine the
We used
The graph of the numbers of infected students shows two notable peaks using a moving average (
From September 2009 to March 2010, (A) a comparison of infected raw values of students and the moving average for 7-day values, (B) comparison of the number of absent students under school closure and students reported as a case, and (C) comparison of absolute humidity (AH) and the number of students reported as a case. The grey dashed line indicates AH of 11 g/m3. The number of absent students under school closure, number of students reported as a case, and AH are shown as a moving average for 7 days.
During the first peak, the number of absent students corresponded to the number of infected students, and during the second peak, the number of absent students were not as large as the number of infected students. AH and the number of infected students by time are shown in
In
Data were collected from 16 randomly chosen hospitals in Oita City and provided by Oita City Health Care Centre. The general age distribution in Japanese schools is 4–6 years for kindergarten, 7–12 years for elementary school, 13–15 years for junior high school, and 16–18 years for high school students.
The results of regression analysis with different time delay based on the Eq (
Delay | Predicting infected students | Susceptible students under school closure | ||||
---|---|---|---|---|---|---|
Partial regression coefficients | Partial regression coefficients | |||||
-4.461 | -0.016 | 0.994 ( |
0.855 | 0.979 | 0.738 ( |
|
-4.477 | -0.013 | 0.989 ( |
0.763 | 1.015 | 0.774 ( |
|
-4.490 | -0.011 | 0.985 ( |
0.677 | 1.049 | 0.764 ( |
|
-4.502 | -0.009 | 0.979 ( |
0.497 | 1.124 | 0.698 ( |
|
-4.518 | -0.007 | 0.971 ( |
0.319 | 1.198 | 0.659 ( |
The meaning of partial regression coefficients in predicting infected students are shown in Eq (
†
Simulation curves of the number of infected students and the cumulative number of infected students for
From September 2009 to March 2010, (A) the number of newly infected students and (B) cumulative number of infected students. The parameters we used for each
We calculated the correlation coefficient to determine
From September 2009 to March 2010, (A) the number of newly infected students and (B) cumulative number of infected students.
Newly infected students | Cumulative number of infected students | |||
---|---|---|---|---|
Delay | ||||
0.741 | <0.001 | 0.983 | <0.001 | |
0.922 | <0.001 | 0.994 | <0.001 | |
0.964 | <0.001 | 0.999 | <0.001 | |
0.913 | <0.001 | 0.992 | <0.001 | |
0.817 | <0.001 | 0.980 | <0.001 |
In this study, we discuss the evaluation of our model, the meaning of the time delay, and the impact of school closure as demonstrated by simulation.
Our model can provide a useful basis for simulating the observed outbreak and evaluating possible preventive measures for mitigating the spread of influenza. We evaluated the effect of school closure by analysing daily reports of school closure and the number of cases in every public school in Oita City during pandemic (H1N1) 2009 using a regression model involving time delay, the influence of school closure, and AH. The delay was between infection and becoming infectious (
In the observed curve, the number of infected students had two notable peaks, whereas in our simulation, the two peaks were faint (Figs
Other studies have reported multiple peaks in one season. In Iki City, Nagasaki, Japan, an epidemiological study reported two outbreaks among schoolchildren in pandemic (H1N1) 2009 [
We designed the regression model from the SEIR model by incorporating a time delay (
In Japan, the optimal duration of reactive class closure has been investigated in several studies. Sugiura et al. reported that the minimum effective number of days for a class to be closed was 5 days. They did not refer to the timing [
We simulated the daily number of infected students and counted the cumulative number of infected students with and without school closure. School closure decreased the number of infected students at the peak by as much as 24% and the number of cumulative infected students by only 8.0% (
We have to note that the epidemic became prolonged in our simulation. If a delay in the peak and a reduction in the cumulative number of infected students must be achieved, a different type of school closure strategy should be adopted. The Hyogo and Osaka prefectures implemented significant school closures proactively during pandemic (H1N1) 2009. The prefecture-wide school closure strategy may have an effect from the viewpoint of a delay in the peak [
Our study has several limitations. First, we only analysed the spread of influenza within schools disregarding interaction between students and people within the community. Students under school closure may have contact within families and community [
We evaluated the impact of school closure by analysing daily reports of school closure and the number of cases in every public school in Oita City in pandemic (H1N1) 2009 using a regression model involving a time delay. School closure was an effective intervention for mitigating the spread of influenza. Our model included the delay between infection and becoming infectious. The best fitting delay was 3 days. This result suggests that school closure should be implemented for more than 4 days. School closure has a remarkable effect in decreasing the number of infected students at the peak, but it is less effective in decreasing the total number of infected students.
We thank the Oita Prefectural Board of Education and Oita City Board of Education for their help with this study.