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In the event of an influenza pandemic, health authorities can choose from among a number of interventions to reduce the spread of infection. Closing schools is one intervention that has been used during past influenza pandemics.1 However, the disruption to the community that results2 makes its use controversial. Before a decision to close schools is taken, it is essential to assess its likely impact, as well as the circumstances under which it is most effective.
There is evidence that interventions targeted at children are effective for endemic influenza. In Japan, excess mortality rates dropped after the introduction of a policy of vaccinating school children and increased again when the vaccination policy was discontinued. The changes in mortality rates were largely attributable to adult deaths from influenza and pneumonia.3 In Israel, the incidence of respiratory illness in school children decreased by around 40% during a 2-week period in which schools were closed because of a labor dispute by teachers.4 However, there is less evidence supporting closure of schools during an influenza pandemic, where adults may have little or no immunity to the pathogen. A recent review of pandemic influenza interventions1 noted that “data on the effectiveness of school closures are limited”; the review cited situations in which closing schools was believed to have been effective at reducing transmission as well as situations in which case numbers were higher when children were not at school. Modeling studies have suggested that vaccination of children could be an effective intervention during an influenza pandemic.5 Modeling analyses of school closures have variously shown that closing schools may have primary use in flattening a pandemic, rather than reducing the overall attack rate,6 or that complete isolation of school children can be very effective at reducing the attack rate.7
In this paper, we assess the impact of closing schools on the attack rate in children and the overall attack rate in the population. We do so using a stochastic household model of 1 million households with sizes and composition of adults and children matching Australian census data. This model incorporates heterogeneity in household size, and takes account of the fact that transmission between children is an important route through which large households infect one another. The main focus of this work is to calculate the likely impact of closing schools during an influenza pandemic. In the process, we consider a range of reproduction numbers and levels of immunity in adults and children that is wider than the range considered plausible for pandemic influenza. This lets us compare the effect of closing schools during an influenza pandemic with closing schools during an outbreak of an endemic infection.
Stochastic Simulation Model
We use a stochastic model of transmission in 1 million households with 2 types of individuals: adults and school children. Household sizes and compositions are based on data from the 2001 Australian census, as outlined in eTable 1 (available with the online version of this article at www.epidem.com.) School children make up 18% of the population, and their households have 3.1 other members on average; adults have an average of 1.6 other individuals in their household. The population contains around 2.6 million individuals in total. Within the household, disease spreads according to a Reed-Frost model.8 Mixing time outside the household is split between time spent at work or school, and time spent mixing in the community. Mixing at school or work is assumed to be with individuals of the same type, while mixing within the community includes both types. Full details of the model structure and assumptions are provided in the online Appendix, together with a discussion of alternative mixing assumptions, and the sensitivity of the model to the main parameters.
Closing schools is modeled by eliminating all transmission among children at school, while increasing transmission between school children within the household in proportion to the extra time spent at home. This represents an “ideal” school closure, in which children are kept at home during school hours. Similar modifications are made to take account of some adults staying home to care for children, assuming that one adult stays home from work in every household with school children and no nonworking adult. As we do not distinguish between adults in the household, this role might be assumed by one adult, or shared by more than one. Immunization of children is implemented by assuming that all school children are immune before the epidemic begins. Again, this represents an ideal case, used for the purposes of comparison.
In the early stages of the outbreak, it may be possible to isolate all diagnosed cases (both children and adults) in hospitals, thus greatly reducing the spread of infection after isolation. Isolation of cases was incorporated by expanding the model to identify health care workers who care for diagnosed and isolated cases. This expanded model is considered both with and without the use of additional protection for health care workers. Where protection is included, transmission between the case and health care worker is reduced to 2% of the unprotected value, representing a combination of antivirals for both case and caregiver9 and personal protective equipment for health care workers.10
Model Reproduction Number and Attack Rate Approximations
To obtain general results for a wide range of reproduction numbers and immunity levels, we used theoretical results11 that allow a reproduction number for the household model to be expressed in a relatively simple form. This reproduction number was used to compare the effectiveness of interventions under different levels of adult and child immunity. The expected attack rates without intervention were derived analytically from an analogous differential equation model, again allowing for differing levels of immunity in adults and children. See the online Appendix for details of these calculations.
An analysis12 of influenza data from Tecumseh13 was used to calibrate the relative amount of transmission between and within households. Outside the household, individuals are assumed to spend 60% of their time at work or school, although results remained broadly similar across the range 40–80%. (See the Appendix for a discussion of the sensitivity of the model to these mixing assumptions, available with the electronic version of this article.)
The model includes a school-mixing parameter to take account of extra transmission between children at school. This parameter was estimated by fitting the model to age-specific attack rates from Kansas City from the 1957 and 1968–1969 influenza pandemics,14 adjusting for the fact that all adults included in this study were family members of school children. The age-specific attack rates for the 2 pandemic years show different patterns: the 1957 data have relatively high attack rates in children, while the 1968–1969 data have a fairly flat age-specific attack rate curve. We estimated 2 values of the school-mixing parameter corresponding to the 2 pandemics, and used the model with these values to compare the 1957 and 1968–1969 scenarios. We then cross-checked the estimated values by calculating the percentage of households in which a school-aged child was the index case. The model showed good agreement with the data, although the percentage of child index cases was slightly lower in the model because of smaller household sizes in Australia. See the online Appendix for further details.
It seems likely that immunity from previously circulating strains of influenza partly accounts for the lower attack rates in adults seen in the 1957 pandemic (as has been assumed previously15). When adult immunity was incorporated into the model, closing schools under the 1957 scenario became less effective, although still more effective than under the 1968–1969 scenario. For reasons of space, we present results only from the 1957 scenario without immunity. However, we note that this scenario represents an extreme case, where heightened attack rates in school children are entirely attributed to extra mixing at school. Unless otherwise stated, we assume that all individuals in the population are susceptible.
The Reproduction Number
The reproduction number is a measure of the infectiousness of a disease. In a population where individuals mix homogeneously, it is defined as the mean number of infections generated by a single infected individual over the course of his or her infectious period. The basic reproduction number (R0) is in the absence of control measures, while the effective reproduction number (R) is calculated once control measures have been introduced. Estimates of the basic reproduction number for pandemic influenza vary, with recent estimates lying between 1.4 and 3.75.16–20 Although high attack rates in past pandemics suggest that the basic reproduction number in some isolated communities may be much higher,21,22 it seems likely that the reproduction number in a typical western population lies between 1.5 and 3.5. When we consider the impact of school closure on infections spread person-to-person in general, we use a wider range of possible basic reproduction numbers. This allows us to compare the pandemic influenza scenario with that of an endemic childhood infection.
Figure 1 shows the effect of closing schools at the start of the outbreak on the epidemic curve for values of the basic reproduction number (R0) of 1.5 and 2.5, comparing the model calibrated to age-specific attack rates from the1968-1969 and the 1957 pandemics. As the model is stochastic, there is some variability in the timing and the size of the epidemic peak. In each plot, the curve shows the median of 100 simulations, and the shaded area contains 90% of the simulations, with the upper and lower 5th percentiles omitted. This shaded region indicates the variability seen over different realizations of the stochastic model. The case with no intervention (red dotted line) is compared with the case where schools are closed (blue solid line), and the case where schools are closed and some parents stay home from work to care for their children (black dashed line).
Closing schools has most effect when R0 is low, and is more effective if there is a high attack rate in children (as in 1957) than if attack rates in adults and children are similar (as in 1968–1969). When R0 is 2.5, closing schools has only a moderate effect on the epidemic curve, and the effect is even less noticeable for higher values of the basic reproduction number. The situation in which parents stay home from work to care for children has little impact on the spread of the infection in the model. Although the final attack rates under no intervention are the same for the 1957 and 1968–1969 scenarios, the baseline epidemics (red dotted lines) under the 1957 scenario take off faster and have a higher epidemic peak than those under the 1968–1969 scenario. This is a consequence of the greater spread of infection between children in the 1957 scenario, which boosts the initial take-off of the outbreak.
Figure 2 shows the effect of the timing of school closure on the final attack rate in adults (dashed lines), children (solid lines), and overall (dotted lines) for a range of values of the basic reproduction number, and for the 1957 and the 1968–1969 scenarios. In each plot, the horizontal axis is the prevalence in school children at the time when schools are closed in the population of 1 million households. This axis is shown on a log scale, and extends to 0.8 for visual clarity although the prevalence never reaches that level. Where the intervention threshold for closing schools (shown on the horizontal axis) exceeds the maximum prevalence achieved during the epidemic, the intervention is never introduced.
The model indicates that most of the effect of closing schools can be achieved in this population if schools are closed by the time the prevalence reaches around 2% in school children; in contrast, if the intervention is delayed until 20% of children are infected, most of the effect of closing schools will be lost. If the model is run with fewer households, the threshold is still 2%. The horizontal axis represents the true prevalence in the population. If there is a high proportion of asymptomatic or undiagnosed cases, the number of diagnosed cases will underestimate this true prevalence, and the timing of school closure should be adjusted accordingly.
As there is extra mixing between children in the model, attack rates in children are higher than in adults if schools are kept open, and the difference is particularly large under the 1957 mixing assumptions. For values of the basic reproduction number of 2.5 or 3.5, nearly all children become infected even though the average attack rates for the population are 89% and 97%, respectively. Figure 2 shows that closing schools reduces the attack rate in school children to a much greater extent than the overall average attack rate. The greatest effect is seen for a basic reproduction number of 1.5 under the 1957 scenario, where closing schools reduces the attack rate in children from 84% to 32%, and the overall attack rate from 58% to 38%. This is the most optimistic scenario for closing schools, as it assumes a high level of mixing in schools, and a low basic reproduction number. The other cases considered here show a reduction in the attack rate in children of 10–35%, and a reduction in the overall attack rate of 3–15%. All plots in Figure 2 were created under the assumption that, once closed, schools remained closed until the epidemic was over. We also considered the effect of reopening schools as the epidemic dies out. Provided the prevalence in children is less than 1% when schools are reopened, most of the benefit of having closed the schools is retained.
In Figure 3, the effect of closing schools is compared with that of successfully immunizing all school children. While such an intervention is unlikely to be achievable in practice, it represents the effect of completely removing all transmission from children. Figure 3 compares these interventions under the 1968–1969 scenario, assuming that all diagnosed cases (both adults and children) are isolated, with Figure 3A representing the case where patients and health-care workers caring for these isolated cases are not protected, and Figure 3B the case where patients and health-care workers are given antivirals, and health-care workers are given personal protective equipment. Both plots show the contours where the effective reproduction number is equal to 1 under the interventions, so that the regions below the curves include all parameter values for which the intervention will bring transmission under control. In each plot, the vertical axis shows the basic reproduction number, and the horizontal axis represents the fraction of infectiousness experienced by cases before isolation. The position on the horizontal axis will depend both on the timeliness of isolation and on the profile of infectiousness in an individual after infection. If the typical infectiousness profile for influenza resembles that estimated by Ferguson et al,17 then most of an individual's infectiousness will occur before isolation. See the Appendix for a more detailed discussion of this point.
Figure 3 clearly shows the effectiveness of isolating cases and providing protection for health-care workers if individuals can be isolated before they have experienced much of their infectivity. In reality, values on the horizontal axis below 0.5 are unlikely to be achievable in practice, and even values in the range 0.5–0.8 may be impractical if individuals are very infectious in the early stages of infection. Figure 3 confirms that immunizing all school children is more effective than closing schools, but suggests that much of the benefit of eliminating transmission from children can be achieved by closing schools, provided that school children can be kept at home when schools are closed. Each intervention is only moderately effective at reducing transmission under the 1968–1969 scenario, indicating that if attack rates in children are similar to those in adults, interventions targeted at children will have limited ability to reduce transmission. The model fitted to 1957 attack rates shows a greater absolute effect for both interventions, but shows similar relative effects of immunization and closing schools.
In Figure 4, we broaden the study to look at the effect of closing schools on the effective reproduction number of a pathogen for which there may be existing immunity in the population and the level of immunity may differ between adults and school children. One example of such an alternative scenario is a local outbreak of measles in a country in which measles is not fully controlled by vaccination. Under this scenario, the basic reproduction number is likely to be high, and adult immunity would be expected to be very much greater than immunity in children. In Figure 4, the vertical axis shows the fractional reduction in the reproduction number when schools are closed, while the horizontal axis indicates the extent to which children are disproportionally affected before intervention; a value of 1 indicates that attack rates are equal in adults and children, and a value close to 0 indicates that hardly any cases occur in adults. To create the graph, we compared the reproduction number before and after schools are closed for values of the initial reproduction number ranging up to 18, and initial immunity in adults ranging from 0% to 90%, assuming that immunity in children is no greater than in adults. Each cross on the graph represents one such calculation. As this model is intended to compare the effect of closing schools for a range of infectious diseases spread in a similar manner to influenza, we performed a thorough sensitivity analysis on the parameters in the model that remained fixed, and also tested the effect of clustered immunity in households. This analysis confirmed that the results presented here are robust to changes to the mixing and immunity assumptions.
Figure 4 shows a clear association between relative attack rates in adults and children and the effect of closing schools; furthermore, this association is robust across this wide range of parameter values. If attack rates in the 2 groups are similar, the reproduction number is reduced by around 20% by closing schools, whereas if the attack rate in children is much higher than in adults, closing schools can reduce the reproduction number by as much as 75%. The ratio of attack rates in adults to attack rates in children calculated from pandemic influenza data14 from 1957 and 1968–1969 lies between 0.5 and 0.9, indicating that closing schools is only moderately effective for pandemic influenza. In comparison, closing schools could be very effective in reducing the reproduction number of an endemic childhood infection where cases are predominantly among children.
Closing schools is moderately effective at reducing transmission during an influenza pandemic, particularly if attack rates in children are high in comparison to adults, or if the basic reproduction number is low. Even when the intervention has little effect on the overall attack rate, closing schools can be helpful in protecting children from infection. To provide maximum benefit, schools should be closed by the time that around 2% of children are currently infected; if the intervention is delayed until 20% of children are infected, very little will be gained. In agreement with other modeling work,6 we find that as the epidemic dies out, it is safe to reopen schools when the prevalence in children has returned to low levels (less than 1%, say).
Although closing schools does not reduce transmission as effectively as immunizing all school children, much of the benefit of full immunization is achieved by closing schools. This indicates that a large proportion of transmission between children occurs at school. However, to implement school closure successfully, children must be kept at home during school hours, which may require parents to stay home from work. A table giving the distribution of working and nonworking adults in Australian households is provided in the online Appendix (Table 2, available with the electronic version of this article at www.epidem.com). Roughly 50% of households containing children have no nonworking adult. If one adult stayed home from work in each of these households, about 14% of the workforce would be unavailable for work. Although this would cause considerable disruption, it does not lead to much additional benefit in terms of reduced transmission. Many adults do not work, so the change in behavior affects only around 8% of the total adult population (that is, both working and nonworking adults). Recent modeling work has found large differences in the effectiveness of closing schools according to the extent to which children can be segregated from the community.7 Here, we have assumed that the level of community mixing is unchanged, as this seems more likely to be achievable. If families succeed in isolating themselves from the community, these measures would be more effective, but if community mixing were to increase following closure of schools, the benefit of closing schools is reduced. When assessing the most effective means of protecting children, the benefits of closing schools must be weighed against the likely disturbance to the community. Should a vaccine effective for school children become available early enough in the pandemic, immunization of children may provide a less disruptive method of protecting children from infection.
Previous modeling studies of pandemic influenza identify some differences in the likely benefit of closing schools. Ferguson et al6 found that school closure can reduce peak attack rates by up to 40%, but has little impact on overall attack rates. In contrast, Glass et al7 found that closing schools with 90% compliance reduces the overall attack rate by 22%. It seems likely that assumptions about baseline age-specific attack rates will at least partly explain this discrepancy. Glass and colleagues assume a baseline attack rate in children of 78% compared with an attack rate of 44% in adults, while the Ferguson model does not appear to include enhanced mixing among children, suggesting that baseline attack rates in children are similar to adults. In this paper, we show that a comparison of attack rates in adults and children provides a good indication of the likely benefits of closing schools, with much greater benefits seen when children are disproportionately affected. Monitoring age-specific attack rates during the early stages of an influenza pandemic will provide valuable information concerning the likely benefit of closing schools. This finding is robust over a wide range of parameter values and levels of immunity, and thus has more general implications for infectious diseases that are similar to influenza. In general, closing schools will be more effective against infections that show high attack rates in children, including childhood infections (to which most adults are immune), than against novel infections for which all age groups are similarly susceptible.
We thank Niels Becker, Jodie McVernon, and James McCaw for their valuable feedback on the manuscript.
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