Modelling the impact of local reactive school closures on critical care provision during an influenza pandemic

Abstract

Despite the fact that the 2009 H1N1 pandemic influenza strain was less severe than had been feared, both seasonal epidemics of influenza-like-illness and future influenza pandemics have the potential to place a serious burden on health services. The closure of schools has been postulated as a means of reducing transmission between children and hence reducing the number of cases at the peak of an epidemic; this is supported by the marked reduction in cases during school holidays observed across the world during the 2009 pandemic. However, a national policy of long-duration school closures could have severe economic costs. Reactive short-duration closure of schools in regions where health services are close to capacity offers a potential compromise, but it is unclear over what spatial scale and time frame closures would need to be made to be effective. Here, using detailed geographical information for England, we assess how localized school closures could alleviate the burden on hospital intensive care units (ICUs) that are reaching capacity. We show that, for a range of epidemiologically plausible assumptions, considerable local coordination of school closures is needed to achieve a substantial reduction in the number of hospitals where capacity is exceeded at the peak of the epidemic. The heterogeneity in demand per hospital ICU bed means that even widespread school closures are unlikely to have an impact on whether demand will exceed capacity for many hospitals. These results support the UK decision not to use localized school closures as a control mechanism, but have far wider international public-health implications. The spatial heterogeneities in both population density and hospital capacity that give rise to our results exist in many developed countries, while our model assumptions are sufficiently general to cover a wide range of pathogens. This leads us to believe that when a pandemic has severe implications for ICU capacity, only widespread school closures (with their associated costs and organizational challenges) are sufficient to mitigate the burden on the worst-affected hospitals.

Figure 1.

Different administrative regions and hosptial locations in England. Local authorities (LAs) are shown using grey lines for Scotland and Wales, and black lines for England. Strategic health authorities (SHAs) are shown using similar hues, and within these, primary care trusts (PCTs) are shown by different hue intensities and saturations. Acute trusts are shown by a circle at the location of the main hospital, with red indicating a larger number of total beds and yellow indicating a smaller number of total beds, as shown in the colourbar.

Figure 2.

(a,b) Local authorities are shown using grey lines for Scotland and Wales, and black lines for England. English NHS trusts with (a) non-zero adult ICU capacity and (b) non-zero paediatric ICU capacity is shown by a circle at the location of the main hospital, with red indicating a larger number of ICU beds and yellow indicating a smaller number of ICU beds, as shown in the colourbars. The assumed catchment areas for these hospitals are shown using black lines containing coloured dots located at the population-weighted centroids of lower super output areas (LSOAs) to indicate population density. (c,d) The heterogeneity in local ICU capacity in these catchments for (c) adults and (d) children is also shown. The impact of local demand at a level consistent with certain levels of national demand is shown using coloured lines. y-axis intercepts give the number of hospitals locally over capacity at a given national level of demand. (c,d) Circles with solid line, cumulative distribution; orange line, 67% of national capacity; red line, 100% of national capacity; pink line, 150% of national capacity.

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 imperfection in the timing of closures as they would have to coincide with whole days. The default model has R₀ = 1.4 and a single continuous closure of four weeks; for clarity, the convex hull around the default points is shown as a solid black line. Alternative values of R₀ are shown in turquoise (R₀ = 1.1) and green (R₀ = 2.0). Orange, crimson and dark red points indicate shorter continuous closures of one, two and three weeks; while purple represents an optimally timed strategy of two closures of two weeks each. (b) Impact of different timings of closure at the most probable parameter values. Dots are spaced a day apart, with no intervention at the extreme top right of each polygon, and motion clockwise around each polygon representing later closures. Note that the inset has linear axes while the main plot has logarithmic axes. In comparing the two panels, the minimum peak incidence for a coloured polygon in (b) divided by the maximum peak incidence on that polygon is a number comparable to the location of the corresponding coloured region in (a). (a,b) Black circles, default; yellow circles, closure = 7 days; red circles, closure = 14 days; maroon circles, closure = 21 days; purple circles, two closure; blue circles, R₀ = 1.1; green circles, R₀ = 2.0.

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 graph, the series of lines represent different levels of national peak adult ICU demand as a percentage of adult ICU demand relative to national capacity: 150% (dashed line), 100% (solid line) and 67% (dashed-dotted line). No red dashed line is shown in (c,d) because no amount of travel satisfies ICU demand in this scenario. (a) Percentage of hospitals whose capacity is saturated, (b) number of adult patients whose local hospital's ICU capacity has been saturated, and (c) total distance travelled by adults to their nearest hospitals (in grey) and the secondary distance travelled to a hospital with available ICU beds (mean as a dark-coloured line on top of fainter lines for each realization). (d) Smoothed means for 10³ realizations of total distance travelled by children, who do not make a primary journey, but are allocated an under-capacity ICU through national coordination. The absence of a red line (and the truncation of green and blue lines) in the upper region of (c,d) represents the absence of any allocation strategy that will satisfy all demand for 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, in each graph, the series of lines represent different levels of national peak adult ICU demand as a percentage of adult ICU demand relative to national capacity: 150% (dashed line), 100% (solid line) and 67% (dashed-dotted line). No red dashed line is shown in (c,d) because no amount of travel satisfies ICU demand in this scenario. (a) Percentage of hospitals whose capacity is saturated, (b) number of adult patients whose local hospital's ICU capacity has been saturated and, (c) total distance travelled by adults to their nearest hospitals (in grey) and the secondary distance travelled to a hospital with available ICU beds (mean as a dark-coloured line on top of fainter lines for each realization). (d) Smoothed means for 10³ realizations of total distance travelled by children, who do not make a primary journey, but are allocated an under-capacity ICU through national coordination. The absence of a red line (and the truncation of green and blue lines) in the upper region of (c,d) represents the absence of any allocation strategy that will satisfy all demand for ICU.