For some infectious diseases spread by person-to-person, school children are responsible for a disproportionate amount of disease transmission, and opening or closing schools can have a considerable impact on the spread of infection. This is particularly the case for existing highly infectious diseases that confer lasting immunity, where the adult population is almost entirely immune. It is not clear whether school children are responsible for a disproportionate amount of disease transmission of pandemic influenza. A recent review of pandemic influenza interventions [WHO (2006)] noted that ‘data on the effectiveness of school closures are limited’, and cited examples where it was believed to have been beneficial, in addition to examples where it appears to have been detrimental.

We model the effect of school transmission in the SEIRH model by assuming that all individuals spend time in three different venues, namely (i) at work or school, (ii) in the community, and (iii) at home. We assume different mixing patterns in each of these venues, and allow for a larger transmission rate between children at school. We also allow for different levels of immunity between adults and school children. To calibrate the model, we use age-specific influenza attack rates measured for south west high-school families in the US during the 1968/69 and 1957 pandemics [Davis (1970)]. In the 1957 pandemic, the influenza attack rate in school children was around 46% compared to 23% in adults. In 1968/69, the influenza attack rate in school children was 42%, while that of adults was 37%. We assume that the mixing patterns in these communities did not vary considerably between the two pandemics, but that there was a higher level of immunity in adults in the 1957 pandemic, and that the reproduction numbers of the two pandemics may have differed.

We assume that the effect of closing schools is that children spend no mixing time within the school, and instead spend all this time within the household. The fraction of time spent mixing in the community is unchanged. This represents the ‘best case’ scenario for closing schools – in reality, some children may continue to mix with individuals outside the household during school time. Initially, we assume that only school children change their behaviour, and then we consider the effect of some parents staying home to care for their children. As the form of the infectivity function does not change the relative effectiveness of the measures, we assume a flat infectiousness function. Figure 4.5 shows the epidemic curves under these interventions for the model calibrated to 1968/69 age-specific attack rates with R0 = 1.5, 2.5 and 3.5. In order to reproduce the age-specific attack rates seen in 1957, it is necessary to assume relatively high levels of immunity in adults, which is then not consistent with high estimates of R0. In Figure 4.6, we show the epidemic curves for the model calibrated to 1957 age-specific attack rates with R0 = 1.5 only.

The results suggest that school closure could assist in reducing the epidemic size if the reproduction number is relatively low, and if children stay at home when schools are closed. For higher values of the reproduction number, there is much less effect. However, it should be noted that closing schools will assist in reducing the attack rates in school children even when it has a limited effect on the overall attack rate. For example, with an R0 of 3.5 and flat infectivity, closing schools reduces the overall attack rate from 94% to 91%, largely by reducing the attack rate in school children from 97% to 84%. It appears that ‘parents staying home to care for their children’ does not have a noticeable impact on the outbreak.

The impact of school closure, with a proportion of parents caring for them, on conditions under which the effective R is 1, is illustrated by Strategy D of Figure 4.18 (see below). While not as effective as alternative strategies shown in Figure 4.18, this strategy does have a moderate impact.

Roughly speaking, the effectiveness of closing schools is similar to the effectiveness of isolating cases soon after diagnosis. Closing school has the advantage that its effectiveness is relatively robust against alternative forms of the infectiousness function, in contrast to isolating cases.

Epidemic curves for the SEIRH model with flat infectivity calibrated to the age-specific influenza attack rates of 1968/69

    Figure 4.5 Epidemic curves for the SEIRH model with flat infectivity calibrated to the age-specific influenza attack rates of 1968/69, with R0 = 1.5, 2.5 and 3.5. Each figure compares: no intervention (red dotted line), schools closed (blue dashed line), and schools closed and some parents staying home from work (green solid line). Solid lines show the median, and shaded regions contain 90% of the simulations.

Epidemic curves for the SEIRH model with flat infectivity calibrated to the age-specific influenza attack rates of 1957

    Figure 4.6 Epidemic curves for the SEIRH model with flat infectivity calibrated to the age-specific influenza attack rates of 1957, with R0 = 1.5. The figure compares: no intervention (red dotted line), schools closed (blue dashed line), and schools closed and some parents staying home from work (green solid line). Solid lines show the median, and shaded regions contain 90% of the simulations.

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Using Mathematical Models to Assess Responses to an Outbreak of an Emerged Viral Respiratory Disease(PDF 873 KB)