Was school closure effective in mitigating coronavirus disease 2019 (COVID-19)? Time series analysis using Bayesian inference

Highlights

• •The effectiveness of school closure to mitigate the epidemic of COVID-19 remains unknown.
• •Time series analyses were conducted using the Bayesian method to evaluate the effectiveness of school closure in Japan.
• •The intervention of school closure did not appear to decrease the incidence of coronavirus infection.

Abstract

Objectives

The Coronavirus disease 2019 (COVID-19) pandemic is causing significant damage to many nations. For mitigating its risk, Japan called on all elementary, junior high, and high schools nationwide to close beginning March 1, 2020. However, its effectiveness in decreasing the disease burden has not been investigated.

Methods

We used daily data of the COVID-19 and coronavirus infection incidence in Japan until March 31, 2020. Time-series analyses were conducted using the Bayesian method. Local linear trend models with interventional effects were constructed for the number of newly reported cases of COVID-19, including asymptomatic infections. We considered that the effects of the intervention started to appear nine days after the school closure.

Results

The intervention of school closure did not appear to decrease the incidence of coronavirus infection. If the effectiveness of school closure began on March 9, the mean coefficient α for the effectiveness of the measure was calculated to be 0.08 (95% confidence interval −0.36 to 0.65), and the actual reported cases were more than predicted, yet with a rather wide confidence interval. Sensitivity analyses using different dates also did not demonstrate the effectiveness of the school closure.

Discussion

School closure carried out in Japan did not show any mitigating effect on the transmission of novel coronavirus infection.

1. Introduction

With the widespread incidence of coronavirus disease 2019 (COVID-19), many countries, including Japan, chose to restrict people's movement. On February 27, 2020, Japan's Prime Minister Shinzo Abe called on all elementary, junior high, and high schools nationwide (from age 6 to 18-years-old) to close until the end of a spring break, through early April for “children's health and safety” (NEWS, 2020). Although it was a request, not an order, most followed the request, with a closure rate of 98.8% among municipal elementary schools and the closure of high schools in 46 out of 47 prefectures (TJTO, 2020). School closures occurred in other nations as well, such as in parts of China, Hong Kong, and Italy (Davidson et al., 2020, Couzin-Frankel, 2020). However, the measures taken in these countries were different from those taken in Japan. For example, Italy closed all universities in addition to other schools, since people in their twenties may readily spread the disease (Palermo, 2020). Most countries elected to have a so-called “lockdown” at the same time, restricting the outings of most people in addition to school children. There is relatively little evidence of school closure for mitigating the spread of COVID-19. Therefore, we conducted a time series analysis with Bayesian statistics to infer the effectiveness of school closure for decreasing the incidence of coronavirus infection in Japan.

2. Methods

We used daily data on the report of COVID-19 and coronavirus infection incidence in Japan, provided by the Ministry of Health and Labor of Japan from inception until March 31, 2020 (https://www.mhlw.go.jp/stf/houdou/houdou_list_202003.html). Time-series analyses were conducted using the Bayesian method. Local linear trend models with interventional effects were constructed for the number of newly reported cases of COVID-19, including asymptomatic infections.

We set the intervention as practically starting on February 29, Saturday, since the Prime Minister called for the closure on the following Monday. With the estimated median incubation period of about five days, and consideration of Japan's policy to test for COVID-19 only in those having symptoms for four days, or two days for the elderly, we considered that the effects of the intervention started to appear nine days after the school closure, i.e., on March 9 (Lauer et al., 2020, Coronavirus, 2020). Predictions until the end of March were made. Because the reopening of schools occurred at different times in each prefecture of Japan, and many reopened fully on the week of writing this manuscript (June 15, 2020), we were unable to evaluate the effectiveness of reopening of schools.

The precise expressions of our model are as follows:

$${\lambda }_{t+1}={\lambda }_t+{\delta }_t+\alpha Z_t+{\epsilon }_t$$

$${\delta }_{t+1}={\delta }_t+{\xi }_t$$

$${\epsilon }_t\sim Normal(0,{\sigma }_{\epsilon })$$

$${\xi }_t\sim Normal(0,{\sigma }_{\xi })$$

$$Y_t\sim Poisson(\exp ({\lambda }_t))$$

The numbers of newly reported patients, Y, are assumed to have a Poisson distribution with the intensity of exp(λ). At each time, λ is mainly determined by the previous state of λ, and the drift component δ. Z is a dichotomous variable that takes 0 before the effect of the intervention is assumed to appear, and 1 afterward. The coefficient α is the expected daily decrease of λ after the intervention is assumed to be effective. Therefore, we considered the intervention would have an effect of suppressing cases if α was negative. Estimations were calculated using data until March 17 for all analyses.

We set four separate sampling sequences, each consisting of 1000 random samples (including 500 samples discarded for convergence). The estimated numbers of newly reported patients, i.e., E(exp(λ)), were provided with 80% credible intervals (CrI). Sampling convergence was evaluated by Gelman-Rubin statistics and by visually inspecting a trace plot. We used the R software program, version 3.5.1 (R Foundation for Statistical Computing, Vienna, Austria) with the probabilistic programming language Stan (Stan development team) for all Bayesian analyses. Sensitivity analyses were also conducted daily for two days before and up to seven days after March 9 (from March 7 to 16).

This study was exempted from approval by the ethics committee of Kobe University Graduate School of Medicine as the study used only data in the public domain (Table 1 ).

Table 1.

Estimated α (coefficient for intervention effects) using our model with 95% credible intervals. Note: if α is less than zero, the intervention is presumed to be effective in decreasing the number of newly reported cases, and if α is more than zero, the number continues to increase.

Date	Mean	2.50%	50%	97.50%
2020/3/7	−0.0730546	−0.4963609	−0.0654382	0.3024975
2020/3/8	−0.0120034	−0.4408049	−0.0077171	0.4395223
2020/3/9	0.07708999	−0.3620483	0.06212049	0.6504105
2020/3/10	−0.0612241	−0.5434837	−0.0535627	0.3882915
2020/3/11	−0.0666243	−0.5668712	−0.0534936	0.3512293
2020/3/12	−0.0752091	−0.6183997	−0.0548827	0.3680328
2020/3/13	0.01002362	−0.4340389	0.02105906	0.4519322
2020/3/14	−0.0330994	−0.4848221	0.01532164	0.3353767
2020/3/15	0.06710269	−0.3890862	0.06264351	0.5486934
2020/3/16	0.19824602	−0.2410004	0.17405888	0.7859607

3. Results

We found that the intervention of school closure did not appear to decrease the incidence of coronavirus infection. If the effectiveness of school closure began on March 9, the mean α was calculated to be 0.08 (95% confidence interval −0.36 to 0.65), which means the intervention was not effective and the number of newly reported infections continued to increase, although the predicted 80% confidence interval was wide (Fig. 1 ).

Fig. 1.

Local linear trend model showing the number of predicted cases of coronavirus infection in Japan until March 31 (red line for predicted median with the red area for 80% credible intervals). The assumption is that the intervention began on February 29 (solid blue line), and the effectiveness started to appear on March 9, nine days later (blue dotted line). Black and white dots denote actually reported cases. Black dots are data until March 17 and used in our estimation.

Similar results were shown when we conducted sensitivity analyses with different dates of inception of the effectiveness. For example, if the effectiveness of the intervention began on March 7, the mean α was calculated to be −0.07, and newly reported cases after that were calculated to remain relatively stable (Fig. 2 ). However, the actually reported cases by March 31 were more than the predicted median. If the effectiveness appeared far later, on March 16, the calculated mean α was 0.20, and the number of cases was instead predicted to increase (Fig. 3 ). Most of the results of the rest of the sensitivity analyses failed to demonstrate the effectiveness of the school closure measure (see Supplementary file).

Fig. 2.

Local linear trend model showing the number of predicted cases of coronavirus infection in Japan until March 31 (red line for predicted median with the red area for 80%). The assumption is that the intervention began on February 29 (solid blue line), and the effectiveness started to appear on March 7. Black and white dots denote actually reported cases. Black dots are data until March 17 and used in our estimation.

Fig. 3.

Local linear trend model showing the number of predicted cases of coronavirus infection in Japan until March 31 (red line for predicted median with the red area for 80%). The assumption is that the intervention began on February 29 (solid blue line), and the effectiveness started to appear on March 16 (blue dotted line). Black and white dots denote reported cases actually. Black dots are data until March 17 and used in our estimation.

4. Discussion

Our analysis did not demonstrate the effectiveness of school closures that occurred in Japan, in mitigating the risk of coronavirus infection in the nation. Although the effectiveness could have occurred in some scenarios of sensitivity analyses, most scenarios in our sensitivity analyses also did not demonstrate its effectiveness.

The effectiveness of school closure has been studied for other infections such as influenza; these studies have suggested that school closure may be useful in reducing or delaying the epidemic peak. However, there was significant heterogeneity in the data, and generalization of the findings remains difficult. Reopening of schools sometimes reversed the effects, and the optimal timing and duration of school closure, as well as the target age range and the ideal scale of closure, remain unknown (Jackson et al., 2013, Bin Nafisah et al., 2018, Viner et al., 2020). School children are liable to suffer from influenza every year, and the rationale for school closure to mitigate its epidemic appears sound. Decreasing influenza in children by vaccination could even decrease the disease burden among the elderly (Reichert et al., 2001). However, children are not a significant population that suffers from COVID-19, and young children less than 20-years-old comprised only about 2% of all infected cases, according to a large-scale epidemiological study in China (Novel Coronavirus Pneumonia Emergency Response Epidemiology Team, 2020). A study using mathematical models suggested that school closure, including universities, is indeed effective in mitigating the impact of the COVID-19 outbreak, but only when combined with other measures (Dong et al., 2020). While it is theoretically possible that school closure affecting children could reduce transmission among them and potentially to other generations, its impact is likely to be much less than the one conducted for influenza. Therefore, our findings that school closure in Japan did not demonstrate its effectiveness in mitigating the transmission of coronavirus infection are not surprising.

An epidemiological study on COVID-19 in children identified 2143 pediatric patients in China and found that infants may be vulnerable to coronavirus infection. The proportion of severe and critical cases among those less than 1-year-old was 10.6%, followed by 7.3% in those aged 1–5 years (Ferguson et al., 2020). However, the school closure done in Japan was only for those aged 6–18, and those vulnerable were not likely to be protected by the measure. A cluster of outbreaks was found in Kyoto, Japan, among college students (More Coronavirus, 2020), but again college/university students were not included in the school closure in Japan. When school closure is to be implemented to prevent the spread of COVID-19, those who are vulnerable to the disease and those who are likely to spread it should also be included.

Our study has several limitations. First, our local linear trend model might not be an appropriate model for the current epidemic of COVID-19 in Japan. One might argue that the school closure could have prevented rather stochastic clusters or outbreaks among school children, which could have not happened thanks to the measure. However, suppose we accept such a theory of stochasticity in justifying the school closure. In that case, we will continue the measure until the coronavirus pandemic comes to an end, since we will never know when to discontinue the measure while fearing unpredictable stochastic outbreaks. Second, the estimated α value using data by the time of intervention effectiveness might not be accurately predicting the α value afterward, i.e., the α value after March 18. Third, our estimations resulted in rather wide confidence intervals, and the results should be interpreted cautiously. Fourth, school closures in other forms might be useful in mitigating the epidemic, such as ones including infants and small children, or university students. Fifth, school closures combined with other measures such as traffic limitations or even city lockdown might be useful. Therefore, we are not claiming that school closures overall are ineffective in mitigating the COVID-19 epidemic in a nation. However, we would like to suggest that the school closure carried out in Japan in March did not demonstrate meaningful effectiveness in controlling the COVID-19 epidemic. Further studies will be necessary to investigate the effectiveness of school closures in other forms in different settings.

Conflict of interest

All authors do not have any conflicts of interest to declare.

Funding

This study is self-funded.

Ethical approval

This study was exempted from approval by the ethics committee of Kobe University Graduate School of Medicine as the study used only data in the public domain without having conflicts with individual patient safety, confidentiality, or others.

Authors’ contributions

Conceptualization was made by K.I., A.D.; methodology was developed by K.I., A.D., and C.M.; statistical analyses were mainly conducted by C.M.; study validation was given by K.I.; writing – the original draft was prepared by K.I.; writing – review and editing were done by all authors. All authors have read and agreed to the published version of the manuscript.

Appendix A. Supplementary data

The following are the supplementary data to this article: