Cost-effective length and timing of school closure during an influenza pandemic depend on the severity

Abstract

Background: There has been a variation in published opinions toward the effectiveness of school closure which is implemented reactively when substantial influenza transmissions are seen at schools. Parameterizing an age-structured epidemic model using published estimates of the pandemic H1N1-2009 and accounting for the cost effectiveness, we examined if the timing and length of school closure could be optimized.

Methods: Age-structured renewal equation was employed to describe the epidemic dynamics of an influenza pandemic. School closure was assumed to take place only once during the course of the pandemic, abruptly reducing child-to-child transmission for a fixed length of time and also influencing the transmission between children and adults. Public health effectiveness was measured by reduction in the cumulative incidence, and cost effectiveness was also examined by calculating the incremental cost effectiveness ratio and adopting a threshold of 1.0 × 10⁷ Japanese Yen/life-year.

Results: School closure at the epidemic peak appeared to yield the largest reduction in the final size, while the time of epidemic peak was shown to depend on the transmissibility. As the length of school closure was extended, we observed larger reduction in the cumulative incidence. Nevertheless, the cost effectiveness analysis showed that the cost of our school closure scenario with the parameters derived from H1N1-2009 was not justifiable. If the risk of death is three times or greater than that of H1N1-2009, the school closure could be regarded as cost effective.

Conclusions: There is no fixed timing and duration of school closure that can be recommended as universal guideline for different types of influenza viruses. The effectiveness of school closure depends on the transmission dynamics of a particular influenza virus strain, especially the virulence (i.e. the infection fatality risk).

Figure 1

A scenario of school closure during the course of an influenza pandemic. School closure is implemented for 7 days from Day 50. The basic reproduction number is set at 1.4. Panel A. The average number of child-to-child secondary transmissions in the absence of the depletion of susceptibles. There is an abrupt 70% decline in the child-to-child secondary transmissions, while no compensatory contact with adults is assumed at the baseline. B. Age-dependent prevalence (i.e. the age-specific number of infectious individuals) as a function of calendar time.

Figure 2

Cumulative incidence of pandemic with different timing and lengths of school closure. Panels A, C and E examine the sensitivity of the cumulative incidence (i.e. final size) to different timing of school closure. Length of school closure in these panels is set at 7 days. Similarly, Panels B, D and F explore the sensitivity of the cumulative incidence to different lengths of school closure. Timing of school closure in these panels is set at Day 50. The basic reproduction number is set at 1.4. Panels A and B compare the final size among children to that of the entire population. Panels C and D vary the efficacy of school closure (i.e. the relative reduction in the child-to-child secondary transmissions) from 50% to 90%. No compensatory contact with adults is assumed in these panels. Panels E and F vary the proportion of child contact compensated with young adults, assuming that the compensation occurs for 0 to 50% of intervened within-child contacts. In these panels, the efficacy of school closure is set at 70%.

Figure 3

Cost effectiveness of school closure with different timing and lengths. Incremental cost effectiveness ratio (ICER), expressed as Japanese Yen per single life-year saved, is computed. Horizontal dashed grey line represents the threshold value of ICER, 1.0 × 10⁷ Yen/life-year, below which one may regard the intervention as cost-effective. Panels A and C examine the sensitivity of ICER to different timing of school closure. Length of school closure in these panels is set at 7 days. Similarly, Panels B and D explore the sensitivity of ICER to different lengths of school closure. Timing of school closure in these panels is set at Day 50. The basic reproduction number is set at 1.4. Panels A and B vary the efficacy of school closure (i.e. the relative reduction in the child-to-child secondary transmissions) from 50% to 90%. No compensatory contact with adults is assumed in these panels. Panels C and D vary the proportion of child contact compensated with young adults, assuming that the compensation occurs for 0 to 50% of intervened within-child contacts. In these panels, the efficacy of school closure is set at 70%.

Figure 4

Sensitivity of the cost effectiveness of school closure to the severity of influenza pandemic. Incremental cost effectiveness ratio (ICER), expressed as Japanese Yen per single life-year saved, is computed. Panel A examines ICER as a function of the reproduction number (ranging from 1.2 to 1.8) and the timing of school closure. Length of school closure in these panels is set at 7 days. It should be noted that the horizontal axis is at the ICER of 1.0 × 10⁷ Yen/life-year. Panel B shows ICER as a function of the risk of death relative to assumed baseline of H1N1-2009 pandemic and the length of school closure. The relative risk of death of assumed pandemic is expressed as multiplier to the infection fatality risk of H1N1-2009 (e.g. if the relative risk is 50, the assumed pandemic is 50 times more likely lethal upon infection). The basic reproduction number and the timing of school closure in these panels are set at 1.4 and Day 60, respectively. Horizontal dashed grey line represents the threshold value of ICER, 1.0 × 10⁷ Yen/life-year, below which one may regard the intervention as cost-effective.