We simulate the impact of near optimally timed school closures lasting from between one and four weeks, and for different basic reproductive ratios (R0 = 1.1, 1.4, 2.0), and measure the relative peak incidence in children, adults and the elderly for all 600 plausible parametrizations. The results for children and adults are plotted in ; results for the elderly resemble those for adults. These relatively short-duration school closures reduce the peak incidence by between 30 and 70 per cent, depending on both the duration and underlying epidemiological assumptions. Many results emerge from these simulations: first, as expected, a greater reduction in the peak can be achieved by either longer duration school closures or multiple closures of the same total duration. The corollary of this (which follows logically but is not explicitly modelled here) is that infections with a shorter generation time (shorter latent or infectious period) are more affected by school closures, as a closure of a fixed duration covers more generations of infection. Second, higher values of R0 lead to a greater impact for school closures, although the results are much more variable. In addition, the impact of school closures is generally greater on the peak incidence in children than in adults. Finally, it should be noted that we have been extremely optimistic in our timing of school closures, first in assuming that the optimum can be precisely calculated and second in assuming that school closures occur as close as possible to this optimum, although conditional on schools closing for whole days. If, for practical reasons, schools close for whole weeks (e.g. first closing on a Monday), then clearly there would often be a greater disparity between optimal and actual timings of the closure, reducing the impact on the epidemic peak. Surprisingly, the impact of alternative susceptibility profiles, such as those associated with seasonal influenza or the 1918 pandemic, is relatively minor.
Figure 3. Impact of duration of school closure and epidemiological assumptions on the peak incidence in adults and children relative to simulations without school closures. (a) For each colour, there are 6000 points reflecting uncertainty in the mixing matrix and (more ...)
shows the relative distribution of peak demand per ICU bed across all hospitals (assuming all regions experience identical peak levels of infection). We stress that the shape of this distribution is invariant under different epidemic profiles, it is merely that the absolute demand scales with the epidemic peak; in addition we find that there is generally insufficient age-structured heterogeneity between hospital catchment areas for these results to be strongly influenced by age-dependent severity of infection (see the electronic supplementary material). These results suggest that even if there is sufficient national capacity to deal with the peak demand during an outbreak, many hospital ICUs could be overwhelmed—an effect, which could potentially be exacerbated if some regions experience substantially higher epidemic peaks than the average.
Faced with this potential lack of capacity in some hospitals, we consider how closing schools and thereby reducing the local epidemic peak could be used to reduce the number of ICUs with excess demand, and we assess the scale at which such closures would need to be enacted. Three measures are used to capture the impact of these closures (): the percentage of hospitals where adult ICU demand from the local catchment area still exceeds capacity (a); the maximum number of adults requiring ICU above local capacity (b); and the total additional distance travelled if adults are moved from their primary hospital to the nearest secondary hospital with spare ICU capacity (c). d shows the impact of specially targeted school closures on the equivalent distance travelled by children.
Figure 4. Effect of school closures on pressure on capacity as a function of the percentage of schools closed. Red lines represent the scenario where school closures can reduce the local peak by 15%, green lines 30% and blue lines 60%. From top to bottom, in each (more ...)
Similar results are given in , for the situation when all schools under the control of an LA are closed simultaneously; obviously, this gives less benefit per school closure as there is less control over the targeting of closures, and significantly less benefit for the case of paediatric ICU.
Figure 5. Effect of school closures on pressure on capacity as a function of the percentage of LAs closing schools. Red lines represent the scenario where school closures can reduce the local peak by 15%, green lines 30% and blue lines 60%. From top to bottom, (more ...)
Considering the scenario where, in the absence of school closures, peak national demand equals national capacity (solid lines in ) we observe that 60 per cent of hospitals have a local demand that exceeds their capacity. Even with broadly optimistic assumptions about school closures (reducing the peak demand by 60%, blue line), the proportion of hospitals above capacity cannot be brought to zero and only achieves its lowest value of 12 per cent when there is a coordinated closure of at least 30 per cent of all English schools. While this coordinated closure still leaves 12 per cent of hospitals above capacity it does substantially reduce the amount by which the capacity is exceeded in these regions and, therefore, also reduces the distance patients needing ICU facilities have to be moved. Alternative, less optimistic assumptions concerning school closures (green and red lines) correspondingly have a more limited impact. Also shown in are corresponding results for more-severe (dashed lines) and less-severe (dot-dashed lines) epidemics, when peak demand reaches 150 and 67 per cent of national capacity, respectively. Although the public-health consequences of different epidemic severity are marked, the relative impact of localized school closures is remarkably consistent.