We evaluate the epidemiological and cost effectiveness of a spectrum of school closure policies for mitigating an influenza pandemic in the US under four different pandemic scenarios: low transmission-low severity, low transmission-high severity, high transmission-low severity, and high transmission-high severity. In the low transmission scenarios, our model predicts a base case (no intervention) cumulative attack rate (CAR) of 41% for the school age population and 31% for the adult population. Analyzing 200 simulations with different samples of R0 for each scenario-policy combination, we found that the attack rates tend to decrease with the duration of the closure, and increase with the initial prevalence trigger, that is, with the delay in closing schools (Tables and ).
Average Cumulative Attack Rates (CAR) for school age population and adults under the low transmission scenarios (standard deviations in parenthesis)
Average Cumulative Attack Rates (CAR) for school age population and adults under the high transmission scenarios (standard deviations in parentheses)
For the low transmission-low severity and low transmission-high severity scenarios, only the lowest trigger value yields efficient strategies: a 0.5% SAP closure trigger followed by either a 12-week closure ($2.56 billion societal cost and total of 44,300 QALYs) or a 24-week closure ($5.12 billion societal cost and 51,900 QALYs) (Figure a and b). For the 12-week closure policy, as the severity increases from a case fatality rate of less than 0.2% to 2%, the incremental cost effectiveness ratio (ICER), that is, the cost per QALY gain, decreases from $57,700 to $4,500 and the expected number of deaths averted rises from 4,250 to 84,188 (however, the proportion of deaths averted increases more modestly from 0.67 to 0.73). For a 24-week closure policy, as the severity increases, the ICER decreases from $334,800 to $26,400 and the expected number of deaths averted increase from 4,981 to 96,702 (the proportion of deaths averted increases from 0.79 to 0.84) (Tables and ).
Figure 2 a: Cost and effectiveness comparison of school closure strategies with different closure triggers for low transmission-low CFR scenario. Red circles indicate efficient strategies. b: Cost and effectiveness comparison of school closure strategies with (more ...)
Incremental Cost Effectiveness Ratio (ICER) of the effective closure strategies under the low transmission-low severity scenario
Incremental Cost Effectiveness Ratio (ICER) of the effective closure strategies under the low transmission-high severity scenario
For the high transmission scenarios, our model predicts that 72% of the school age population and 52% of the adult population will become infected. Based on an evaluation of total costs and total QALYs for each school closure strategy, three efficient strategies emerged for the high transmission-low severity scenario (Figure a): (i) a 1.1% closure trigger coupled with a non-monitored prevalence-based reopening trigger (specifically, a decrease in SAP to 25% of the original value, that is, a decrease in SAP from 1.1% to 0.275%), (ii) a 0.5% closure trigger with non-monitored prevalence-based reopening trigger (50% decrease in the SAP from the closure trigger), and (iii) a 0.5% closure trigger followed by 24
weeks of closure. Under the first of these policies, the model predicts that schools will close for an average of 125
days (standard deviation 3.67
days) while prevalence declines to the re-opening threshold (Figure ). Thus, the closure duration falls between the fixed closure options of 12 and 24
weeks. A non-monitored (NM) policy assumes that accurate estimates of SAP are made throughout the closure period with a one-week lag. For the high transmission-high severity, two additional efficient strategies exist; these are 3% closure trigger with non-monitored prevalence-based reopening until SAP drops to 25% of the trigger and 0.8% closure trigger with monitoring (M) based reopening until SAP drops to 25% of the original trigger value (See Figure b).
Figure 3 a: Cost and effectiveness comparison of school closure strategies with different closure triggers for high transmission-low CFR scenario. Red circles indicate efficient strategies. b: Cost and effectiveness comparison of school closure strategies with (more ...)
Figure 4 Total influenza prevalence curves with and without school closures under low transmission (black) and high transmission (blue) scenarios. Dashed lines show a typical epidemic curve under a cost effective closure policy (based on one simulation). Vertical (more ...)
As in the low transmission scenarios, the efficient policies save more lives and have considerably lower ICERs under the high severity scenario than under the low severity scenario (Tables and ). For example, for the 1.1% SAP trigger coupled with reopening after a reduction in SAP to 25% of its original value (1.1%, NM25%), the incremental cost per QALY gained decreases from $56,000 to $3,100 and the number of deaths averted with school closure increases from 4,081 to 187,307 (the proportion of deaths averted increases from 0.27 to 0.42).
Incremental Cost Effectiveness Ratio (ICER) of the effective closure strategies under the high transmission-low severity scenario
Incremental Cost Effectiveness Ratio (ICER) of the effective closure strategies under the high transmission-high severity scenario
Our analyses suggest that efficient strategies depend on the transmission rate of the strain (Tables , , , , ). Although there is some overlap in the efficient sets for the low and high transmission rate scenarios, there are also notable differences. For a relatively slowly spreading strain, an early implementation and relatively long closure (0.5%, 12w or 0.5%, 24w) is efficient. For more rapidly spreading strains, later closures (prevalence thresholds ranging from 0.5% to 3%) are viable, but require variable durations. Specifically, the 3%,NM 25%; 1.1%,NM25%; 0.8%,M25%; and 0.5%,NM50% strategies are predicted to last 59, 125, 145, and 155
days, respectively (with standard deviations of 2.50, 3.28, 3.50, and 4.12 respectively). The ICERs of the efficient strategies are generally predicted to be lower with higher transmissibility and higher severity (Tables , , , ).
The World Health Organization (WHO) suggests that health interventions be designated cost-effective if they deliver QALYs at a cost less than three times a nation’s per capita GDP and very cost-effective if the cost per QALY is less than the country’s per capita GDP . To assess the cost effectiveness of school closure policies, we considered closure durations relative to the US per capita GDP in 2009 (approximately $46,000 according to ). Our analyses show that for the low transmission-low severity scenario, a 0.5% prevalence closure trigger followed by a 12-week closure ($57,700 per QALY gain) is the only effective and cost effective strategy (i.e., its ICER is less than three times the US per capita GDP). For the low transmission-high severity scenario, a 0.5% prevalence closure trigger followed by either a 12-week closure ($4,500 per QALY gain) or 24-week closure ($26,300 per QALY gain) meets the very cost effective threshold. Thus, the 5%, 24w would be the preferred policy, as it is the largest one (conferring the greatest number of QALYs) with a cost-effectiveness ratio below the willingness-to-pay threshold.
For the high transmission-low severity scenario, a 1.1% closure trigger coupled with a non-monitored prevalence-based reopening trigger (a decrease in SAP to 0.275%), and a 0.5% closure trigger with non-monitored prevalence-based reopening trigger (50% decrease in the SAP to 0.25%) are cost effective but not very cost effective, with costs of $56,000 per QALY gain and $60,200 per QALY gain, respectively. The latter of the two is larger (higher total QALY’s gained), and thus would be the preferred choice. Finally, for the high transmission-high severity scenario, all five efficient strategies meet the very cost effective threshold, with the 0.5% SAP trigger, 24-week closure being the preferred program. Our cost estimates are comparable to published values (Table ). For the low transmission-low severity scenario, influenza is predicted to cost the State of Texas 0.023–0.5% of its GDP.
Comparison to published analyses
For both high and low transmission pandemics, the predicted ICER values varied considerably with the percentage of working adults who will miss work due to influenza, average daily salary, and case fatality rate (CFR). For example, we illustrate this with a tornado diagram for the preferred strategy under the high transmission-high severity pandemic scenario (Figure ). Increases in any of the parameters, except the CFR, lead to increases in the ICER of the school closure policies. Conversely, decreases in pandemic severity (CFR) lead to increases in ICER of the closure policy. None of these parameter perturbations cause the policy to lose its very cost effective
designation, that is, the ICER remains well below the willingness-to-pay threshold of $46,000. The parameters influence the ICER values similarly for the cost effective policies under the other three pandemic influenza scenarios (Figures A4.1-A4.3 in Additional file 1
). While none of the perturbations cause the preferred policies rise above the cost effectiveness willingness-to-pay threshold, some extreme parameter perturbations are predicted to move policies from very cost effective to cost effective (by increasing the ICER) or, vice versa, from cost effective to very cost effective (by reducing the ICER).
Figure 5 Tornado diagram comparing the relative impact of input variables on the ICER for the preferred closure policy (0.5% SAP trigger, 24-week) under the High transmission-High severity scenario. The width of the bars indicates the uncertainty associated with (more ...)
Discussion and conclusions
School closure interventions, in general social distancing interventions and population behavior changes, will lead to a delayed impact of the overall pandemic by reducing the peak of the current pandemic wave and overall epidemic size. However, it is expected that the temporarily spared susceptible population during the first wave can be affected during subsequent second or third pandemic waves. It is also important to note that it may take number of weeks before reliable estimates of pandemic severity could be inferred and this could impact the effectiveness of policy decisions on whether school closures should be triggered. This was the case during the 2009 A/H1N1 pandemic in Mexico; when the Mexican government decided to close schools across the country based on the available information, there was no reliable estimate of the case fatality ratio.
According to our model, school closures can significantly reduce the total number of influenza cases, but the epidemiological impact and societal costs of a school closure critically depend on the timing and duration of the closure. In the early days of a pandemic, there is typically considerable uncertainty about its transmission rate (or R0
) and its severity (or CFR). Policy makers face two interrelated decisions: (1) whether or not to implement a school closure policy; and (2) if so, which one. The answer to the first question depends on the predicted effectiveness and cost effectiveness of the effective policy options. We find that relatively few closure policies are efficient under the low transmissibility scenarios, while several are efficient under the high transmissibility scenarios. The answer to the second question depends on both the transmission rate and severity of the pandemic. Slower spreading pandemics call for early triggers and relatively long duration closures (12
weeks and 24
weeks), regardless of severity; and more rapidly spreading pandemics allow for higher triggers (e.g. 1.1% and 3%) coupled with moderate durations (averages of 125
days and 59
days, respectively), depending on the severity of the strain (see Additional file 1
for timing of the triggers for both cases). Although we assumed that the SAP estimates are exact in the model and single step errors, e.g. a policy intending to close school at a SAP of 0.8% actually closing school at 0.5% or 1.1%, do not make large differences in CARs, it is worth mentioning that these kind of errors can generate dramatic switches in the effectiveness of policy implementation, e.g. a switch from a cost effective strategy to a dominated or weakly dominated strategy (e.g. see low transmission, low CFR scenario in the Additional file 1
The policy options included fixed duration closures and re-opening triggers based on decreases in school-aged disease prevalence, both with and without additional surveillance to improve real-time prevalence estimates. Our model assumed that, in the absence of monitoring, decision-makers receive accurate estimates of prevalence with a one-week delay, and monitoring simply removes the delay. Although the direct cost of monitoring is assumed to be low, most of the efficient policies are either fixed duration or have non-monitored reopening triggers. This suggests that slightly lower reopening thresholds than those considered may provide a better balance between costs of closure and health outcome. Similarly, the efficiency of several trigger-based re-opening policies may indicate that there are better fixed durations than the values considered.
In summary, we have integrated a mathematical model of influenza transmission dynamics into a cost-effectiveness analytic framework for evaluating a wide range of school closure and reopening policies with respect to their societal costs and health impacts. The presented rigorous approach of this paper can be adapted to evaluate and compare a variety of non-pharmaceutical, vaccine, and antiviral policy options for influenza. We have found that the transmission rate and case fatality rate of a spreading pandemic can dramatically impact whether or not a school closure policy is efficient and cost effective. Although not surprising, this highlights the importance of obtaining early and reliable estimates of pandemic severity to public health decision-making.