It has been long known [1]-[3] that children play an important role in the community spread of infectious disease, in particular of influenza. The many contacts children have with one another at school increase their risk of being infected by several droplet-transmitted pathogens, and make schools an important source of transmission to households, from where the disease can spread further. For instance, during the 2009 H1N1 pandemic, a correlation was observed [4] between the opening dates of schools and the onset of widespread transmission of H1N1 in the US. Similarly, the timing of school terms, with the corresponding changes in contact patterns, has been shown to explain the evolution of the H1N1 epidemic in the UK [5].

School closure is thus regarded as a viable mitigation strategy for epidemics [6],[7], especially in the case of novel pandemics for which pharmaceutical interventions, such as vaccines, are not readily available and delaying disease spread is a priority. The impact of school closure on the spread of infectious disease has been studied using historical data [8]-[13], comparison of contact patterns during week days, weekends and holiday periods [5],[14],[15], and agent-based models at different scales [9],[16]-[19]. School closure, however, comes with a steep socio-economic cost, as parents need to take care of their children and might be forced to take time off work. This can even have a detrimental impact on the availability of public health staff. Such harmful side effects have led some to question the effective benefit of school closure [20],[21] and have prompted research on the design and evaluation of non-pharmaceutical low-cost mitigation strategies.

In this context, the availability of data on contacts between school children is a crucial asset on two accounts. First, even limited information on mixing patterns within and between classes or grades can suggest more refined strategies than whole-school closure. Second, high-resolution contact data allow the development of individual-based computational models of disease spread that can be used to test and compare different mitigation strategies. Because of this, over the last few years a great deal of effort has been devoted to gathering data on human contact patterns in various environments [22], using methods that include diaries and surveys [14],[23]-[31], and more recently wearable sensors that detect close-range proximity [32],[33] and face-to-face contacts [34]-[39].

In this study we use a high-resolution contact network measured by using wearable sensors in a primary school [38]. The data show that children spend more time in contact with children of the same class (on average three times more than with children of other classes) and of their own grade [38]. This is expected to be a rather general qualitative feature of schools, due both to age homophily [40] and schedule constraints, and suggests that transmission events might take place preferentially within the same class or grade^a. We thus consider targeted and reactive mitigation strategies in which one class or one grade is temporarily closed whenever symptomatic individuals are detected. To evaluate the effectiveness of such micro-interventions we use our high-resolution contact network data [34],[38] to build an individual-based model of epidemic spread, and we compare, in simulation, the performance and impact on schooling of different targeted mitigation strategies with the closure of the whole school.

Here we provide results corresponding to the parameter values β=3.5·10⁻⁴ s ⁻¹ (1/β≈48m i n), β _com =2.8·10⁻⁹ s ⁻¹, 1/μ=2 days, 1/γ=4 days. The results for the other sets of parameters and other distributions of latent and infectious periods’ durations are qualitatively similar and are discussed in the Additional file 2.

Figures 1 and 2 display the temporal evolution of the median number of infectious individuals for several mitigation strategies, when only realizations leading to an attack rate higher than 10% are considered. Figure 1 shows the effect of closure duration for the targeted class and targeted grade strategies at a fixed closure-triggering threshold of 3 symptomatic cases. Longer closures lead to shorter and smaller epidemic peaks. Closure durations of 5 or 6 days (120 and 144 hours, respectively) lead to very similar epidemic curves. Figure 2, on the other hand, compares the epidemic curves for the targeted class, targeted grade and whole school strategies at fixed closure-triggering threshold and closure duration parameters. The targeted class closure strategy already yields a large reduction of the epidemic peak, and this reduction is only slightly improved by the targeted grade closure and whole school closure strategies (for the same closure durations).

Effect of the risk of infection in the community

As mentioned in the Methods section, to assess the role of the risk of infection due to contacts in the community (as opposed to those at school), we consider a set of parameter values where β _com is increased five-fold with respect to the previous results. That is, we use the values β=3.5·10⁻⁴ s ⁻¹, β _com =1.4·10⁻⁸ s ⁻¹, 1/μ=2 days, 1/γ=4 days, p _A =1/3. Tables 4 and 5 report the results we obtain with this higher value of β _com for the targeted closure strategies. The probability of a large outbreak is much higher than in the previous case (as shown by comparing Table 4 with Table 1). This probability is reduced by the targeted closure strategies, but remains comparatively large. As observed for the smaller β _com , the decrease in the probability of a large outbreak is larger for longer closure durations, for smaller closure-triggering thresholds, and for closures involving more classes.

Closure strategy	Targeted	Targeted	Whole
(threshold, duration)	class	grade	school
No closure	65.9	65.9	65.9
3, 24 h	65.0	62.4	64.1
3, 48 h	58.7	59.0	58.9
3, 72 h	58.0	57.4	53.7
3, 96 h	58.1	56.3	44.0
3, 120 h	56.4	51.2	38.9
3, 144 h	55.3	51.0	38.7
2, 24 h	65.7	59.0	60.7
2, 48 h	57.3	56.1	53.2
2, 72 h	49.7	49.5	45.3
2, 96 h	46.7	46.2	43.3
2, 120 h	44.0	37.7	35.9
2, 144 h	41.5	36.8	31.7

The baseline case given by the simple isolation of symptomatic children is indicated as “No closure”. Parameter values: β = 3.5 · 10^-4 s ^-1, β _com = 1.4 · 10^-8 s ^-1, 1/ μ = 2 days, 1/ γ = 4 days, p _A = 1/3.

Closure strategy	Targeted	Targeted	Whole
(threshold, duration)	class	grade	school
No closure	187 [161,192]	187 [161,192]	187 [161,192]
3, 24 h	173 [142,196]	176 [155,200]	181 [153,200]
3, 48 h	155 [114,185]	157 [69,191]	178 [143,203]
3, 72 h	131 [52,170]	137 [40,188]	169 [37,200]
3, 96 h	118 [100,182]	120 [28,182]	161 [30,200]
3, 120 h	103 [35,164]	100 [29,174]	145 [28,196]
3, 144 h	102 [39,161]	89 [28,173]	126 [26,196]
2, 24 h	176 [145,201]	177 [149,202]	183 [160,203]
2, 48 h	151 [89,186]	158 [89,196]	180 [155,201]
2, 72 h	118 [37,177]	136 [32,189]	179 [149,201]
2, 96 h	111 [30,180]	120 [31,191]	176 [141,202]
2, 120 h	102 [27,168]	106 [27,188]	176 [155,198]
2, 144 h	93 [28,167]	94 [27,185]	174 [88,205]

The baseline case given by the simple isolation of symptomatic children is indicated as “No closure”. In square brackets we provide the 5^th and 95^th percentiles. Parameter values: β = 3.5 · 10^-4 s ^-1, β _com = 1.4 · 10^-8 s ^-1, 1/ μ = 2 days, 1/ γ = 4 days, p _A = 1/3.

In the case of epidemics reaching more than 10% of the population, however, Table 5 shows that the targeted class and targeted grade closure strategies lead to smaller attack rates than the whole school closure strategy. Figure 3 gives more insight into this point by showing the epidemic curve for realizations with a final attack rate larger than 10%, for the targeted and school closure strategies with a closure duration of 144 hours and a closure-triggering threshold of 3 infectious individuals. The effect of the targeted class and grade closure strategies is similar to the case of a smaller β _com : these strategies lead to a smaller and shorter epidemic peak with respect to the baseline strategy. The epidemic curve for the whole school closure strategy on the other hand is changed and has now two successive peaks; even if the first one is smaller than for the targeted strategies, the presence of the second peak, due to the end of the school closure, leads overall to a larger final attack rate. Such poor performance of the whole school closure might thus occur because the intervention is being applied and relaxed too early and because of its a priori limited duration.

Since the contacts of children at school play an important role for the propagation of many infectious diseases in the community, it is crucial to devise efficient and cost-effective mitigation strategies as an alternative to the closure of whole schools, whose socio-economic costs are often considered excessive. Inspired by the empirical evidence collected in European primary and high schools [28],[38],[52] that children did not mix homogeneously but rather spent much more time in contact with their classmates and with other children of the same age, we have designed targeted closure strategies at the class or grade level that are reactively triggered when symptomatic cases are detected. We have simulated the dynamics of epidemic spread among school children by using an SEIR model on top of a high-resolution time-resolved contact network measured in a primary school. The model included asymptomatic individuals and a generic risk of infection due to random contacts with the community when children are not at school. Using this model we have studied the targeted strategies for class and grade closure both in terms of their ability to mitigate the epidemic and in terms of their impact on the schooling system (and therefore indirectly on the whole community), measured by the number of cancelled days of class.

All targeted strategies lead to an important reduction in the probability of an outbreak reaching a large fraction of the population. In the case of large outbreaks, targeted strategies significantly reduce the median number of individuals affected by the epidemic. The reduction is stronger if the strategies are triggered by a smaller number of symptomatic cases, and if longer closures durations are used. While the closure of one class yields a smaller mitigation effect than the closure of the whole school, the closure of the corresponding grade (two classes) leads to a reduction of large outbreak probability and a reduction of epidemic size that are similar to those obtained by closing the entire school. The less efficient results of the benchmark strategies (iv) and (v) involving closure of randomly chosen classes (given in the Additional file 2) also show that the effect of the class-targeting strategies is due to the targeting of contacts of cases, and not just to the size of the closure (i.e., the number of children involved by the closure). Targeted strategies, moreover, come at a much smaller cost in terms of lost class days. Such decrease in the cost of the intervention might also imply a smaller global impact of the spread on the whole community. In the case of large outbreaks and large risk of infection in the community, whole-school closure might even lead to a smaller mitigation effect than targeted grade closure, as more susceptible children would spend more time in the community, acquiring the infection and subsequently bringing it back into the school upon re-opening.

A few important points need to be stressed. First, the reactive character of all strategies we studied, which are triggered by the detection of symptomatic individuals, limits the impact on the schooling system with respect to a closure of schools scheduled in a top-down fashion by public health authorities: the latter would be enforced even for schools that are free of infectious individuals. Second, targeted grade closure has in all cases a much lighter burden, in terms of lost class days, than whole-school closure. Given also its good performance in the mitigation of outbreaks, it thus represents an interesting alternative strategy. Finally, we recall that grade closure corresponds to closing the class in which symptomatic children are detected and the class which has the most contacts with it. To assess this relation between classes, we do not need the very detailed knowledge of the contact patterns we used in this study: rather, readily available information such as class schedules and classroom locations [53] may be sufficient to retrieve this information. This has important public health consequences, as it implies that the targeted mitigation strategies studied here might actually be carried out in the general case, without high-resolution contact network data.

Some limitations of this study are worth mentioning. While the strategies we discussed could be designed and implemented with limited information, they were only tested using one specific dataset corresponding to one particular school. Different schools, either concerning different ages (e.g., high schools [36],[52]) or in different countries, might lead to either more or less structured contacts between children or students of different classes. The high-resolution contact network data we used only spans two days of school activity, and had to be extended longitudinally by using a repetition procedure. This technique is commonly used to simulate epidemic spread on temporal data, but it does introduce strong temporal correlations in the extended dataset and it may fail to correctly model the day-to-day heterogeneity of contact patterns [41]. While variations in the repetition of contacts from one day to the next are known to modify the attack rate of an epidemic [50], we expect that the relative efficiency of the strategies we considered should be robust with respect to other temporal extensions strategies [41]^d. Moreover, this limitation should be less of an issue in school settings, where mixing patterns are shaped by a regular activity schedule and have a strong periodic character.

Another limitation of this study is the simplistic coupling with the community that we used: our high-resolution contact network does not include contacts happening outside of school, so we introduced in our model a free parameter that describes a generic risk of transmission from the community. Even though our results are robust with respect to important variations in this parameter, it would be desirable to inform the model with empirical data on the contacts that children have with members of the community, or with one another outside of school. Moreover, while we have established the effectiveness of the class closure measures in reducing the spread within the school population, the effect of these measures on the spread in the rest of the population is not modelled nor quantified. In fact, effective interventions at the school level might even have a further beneficial effect by leading to a decrease of the spread in the whole community, given the role of children in such spread.

The limitations described above point to several directions for further research. It would be interesting to validate the targeted class and grade closure strategies using high-resolution data describing the contacts of children in other schools and over longer timescales, if such datasets become available in the future. In particular it would be interesting to consider larger schools, for which the closure of more than two classes may represent an efficient intervention. An expansion of the model in order to refine the coupling with the community would also represent an important step, on the one hand to check that the simplistic coupling used here does not impact our results, and on the other hand to quantify the possible feedback effect of the mitigation of the spread within the school on the spread in the community. To this aim, high-resolution measurement of contact patterns within a school could for instance be coupled with surveys administered to the same children, to estimate their contact rates off-school and to model their contacts with other individuals of different age classes in the community. Such data could be used to refine the model used here, but also to design agent-based models at a larger scale (e.g., urban or geographic), spanning several schools [19]. This would allow to generalize the strategies introduced in this paper to the case of multiple schools, and to evaluate their relative efficiency, in particular comparing targeted strategies with the general closure of all schools in the relevant geographical region. Finally, we have discussed how targeted interventions can be guided by readily-available information on the school activities and organisational structure. New techniques to tease apart meso-scale activity patterns in high-resolution contact data [54] could be used to design and guide targeted intervention aimed not just at closing classes but, for example, at suspending or modifying specific activities in the school that involve the shared use of spaces (e.g., sports activities, time in the playground, lunch at the cafeteria, etc.).

^aThe quantitative extent of this effect might depend on school specificities and in particular might differ between primary schools and high schools, or between countries [28],[36].

^bif a susceptible is in contact with n infectious individuals, the forces of infection add as each possible transmission event is evaluated independently.

^cWe consider values of β close to the ones used in [41],[48], which lead to a reproductive number R ₀ close to 1.5.

^dAn indication that this is indeed the case is given by the fact that additional simulations, in which we consider only one of the two days of data and repeat it yield very similar (qualitative and quantitative) results.