The purpose of this article is to evaluate the cost-effectiveness of school closure during a potential influenza pandemic and to examine the trade-off between costs and health benefits for school closure involving different target groups and different closure durations.
Methods
We developed two models: a dynamic disease model capturing the spread of influenza and an economic model capturing the costs and benefits of school closure. Decisions were based on quality-adjusted life years gained using incremental cost-effectiveness ratios. The disease model is an age-structured SEIR compartmental model based on the population of Oslo. We studied the costs and benefits of school closure by varying the age targets (kindergarten, primary school, secondary school) and closure durations (1–10 weeks), given pandemics with basic reproductive number of 1.5, 2.0 or 2.5.
Results
The cost-effectiveness of school closure varies depending on the target group, duration and whether indirect costs are considered. Using a case fatality rate (CFR) of 0.1-0.2% and with current cost-effectiveness threshold for Norway, closing secondary school is the only cost-effective strategy, when indirect costs are included. The most cost-effective strategies would be closing secondary schools for 8 weeks if R0=1.5, 6 weeks if R0=2.0, and 4 weeks if R0= 2.5. For severe pandemics with case fatality rates of 1-2%, similar to the Spanish flu, or when indirect costs are disregarded, the optimal strategy is closing kindergarten, primary and secondary school for extended periods of time. For a pandemic with 2009 H1N1 characteristics (mild severity and low transmissibility), closing schools would not be cost-effective, regardless of the age target of school children.
Conclusions
School closure has moderate impact on the epidemic’s scope, but the resulting disruption to society imposes a potentially great cost in terms of lost productivity from parents’ work absenteeism.
The online version of this article (doi:10.1186/1471-2458-12-962) contains supplementary material, which is available to authorized users.
Competing interests
The authors declare that they have no competing interest.
Authors’ contributions
YX originated the idea and drafted the paper. YX and BFB constructed the mathematical model while YX and ISK conducted the health economic evaluation. BFB and ISK reviewed and revised the manuscript. All authors read and approved the final manuscript.
Background
Influenza pandemics occur at irregular intervals and cause significant mortality and morbidity as well as substantial economic losses [1]. School closure is a possible strategy for mitigating transmission during the early phase of a pandemic when vaccine is not yet available. School closure has three main consequences: reducing the total disease burden, postponing the peak of infection and lowering the peak prevalence of the disease. Postponing the pandemic increases the time available for strain-specific vaccine production and distribution, and allows for more time to prepare for the peak workload in health care settings. Lowering the peak of the pandemic reduces the risk for overloading of health services and shortage of health care personnel due to influenza sickness.
Schools are thought to play a special role in transmission due to high contact rates among school children combined with higher susceptibility among children compared with adults. During the A(H1N1) pandemic in 2009, the estimated infection rate among school children was significantly higher than that of the general population [2]. However, extended school closure is costly and may cause significant disruption to local communities by keeping working parents away from work and reducing school children’s learning time. Quantifying the costs and benefits of school closure might help inform pandemic policy making.
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There is currently no consensus about the expected health benefits of school closure [3]. Previous studies have investigated the impact of school closure either by analysing data from previous pandemics and epidemics or by computer simulation. The historical data approach includes studies of the 1918 influenza pandemic and suggests that school closure, combined with other interventions, lowered the disease burden and that the timing and duration of such interventions mattered [4, 5]. A 2009 study of eight European countries indicated that during holidays and weekends the social contact patterns of children and the basic reproductive number were reduced by almost a quarter [6]. However, little effect on transmission was observed during a two-week kindergarten and primary school closure in Hong Kong in 2008 [7]. The estimated impact of school closure from computer simulations varies widely depending on model assumptions about how children contribute to influenza transmission, virus transmissibility and illness threshold when school closure is triggered [8‐12]. Only a limited number of studies have explored the cost of school closure. Two studies focused on productivity loss of care-taking parents suggest that school closure for 12 weeks may cost 0.2-1% of GDP in the UK [13], and 4 weeks closure 0.1-0.3% of GDP in the US [14]. To reduce the economic loss from working parents, reactive short-term (1–4 weeks) school closure has been studied, where schools are shut when ICU units reach peak demand [15], but the optimal timing of such interventions may be difficult. Some studies have combined cost estimates with micro-simulation models [16‐19] or dynamic compartmental models [20]. While the assumptions used in the studies differ, the general picture in the cost-effectiveness is that school closure may be effective under high transmissibility, and/or high severity. Some of the studies were based on the characteristics of the 2009 H1N1 pandemic. Halder and co-workers [16] found that productivity losses due to sick leave and taking care of children when schools are closed were the dominating part of cost. A similar result was obtained in a study by Brown and co-workers [17] suggesting that the cost of school closure may far outweigh the cost saved from reducing the disease burden when the severity is low, regardless of the transmissibility.
In this study, we estimated potential costs and health benefits of school closure when implemented before substantial transmission of influenza among children has occurred (proactive school closure). We combined the cost estimates with a dynamic epidemiological transmission model, and determined the optimal closure strategy based on incremental cost-effectiveness ratios. Our study complements previous work on school closure by focusing on the age of the target school children, covering several scenarios for transmissibility, closure duration and severity. The study may be useful for public health authorities and may inform preparedness planning for future influenza pandemics.
Methods
Background
We modelled the impact of school closure in the context of a local community, using the capital city of Norway, Oslo, as the study setting. The city has a population size of 587 000, covering 12% of the Norwegian population. The unemployment rate is low (3.4%) and women’s participation in the labour force is high (70% of women aged 15–74 are employed) [21]. The education system is composed of primary school for children aged 6 to 12 years and secondary school for children aged 13 to 18 years. The attendance rate in kindergarten is approximately 90% for children aged 1 to 5 [21].
The disease model
We considered a closed population of size N=587 000, ignoring demography (births, deaths and immigration) since influenza epidemics are of very short duration. We divided the population into six age groups (i=1-6): 1–5 years (6.7%), 6–12 years (7.2%), 13–18 years (6.9%), 19–39 years (36.6%), 40–64 years (30.5%) and 65+ years (12.2%). We modelled a pandemic influenza using a deterministic dynamic SEIR (Susceptible-Exposed-Infected-Recovered) model [22]. People in each age group are divided into four mutually exclusive compartments: susceptible, infected symptomatically, infected asymptomatically, and recovered with immunity/dead from influenza (Figure 1). People progress from one compartment to another at the rates determined by the contact pattern and characteristics of the virus.
Figure 1
The dynamic influenza transmission model.
×
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A susceptible individual (Si) becomes infected according to the age-specific force of infection λi. Newly infected individuals first enter the exposed state (Ei) where they are infected, but not yet contagious, before developing either symptomatic infection (ISi) or asymptomatic infection (IAi). To obtain more realistic distributions of the exposed and infectious periods, we divided these periods into ni stages, where the progression from each stage occurs at a rate ri = ni/Di, where Di is the mean duration of period i = E, IS, IA. This gives gamma distributed waiting times with shape parameters k = ni and scale parameters θ = Di/ni. The mean duration of the exposed period was set to 1/σ = 1.9 days (17;18) and modelled in nE = 3 stages. Individuals in the last exposed stage were assumed to be infectious with infectivity 50% compared to the infectivity of symptomatic infection, as viral shedding increases after one day following transmission [23]. We assumed that a proportion p=0.67 will become symptomatically infected while a proportion (1-p)=0.33 develop asymptomatic infection [24, 25]. The average duration of the symptomatic infectious period was set to 1/γc =7 days for children (i=1, 2) and 1/γa = 5 days for adolescents/adults (i=3-6) [23, 24, 26] and modelled in nI = 5 stages. Infectivity during the stages was set at 100%, 100%, 50%, 30% and 15% in accordance with data showing that viral transmission peaks during the early period after symptoms develop [23, 27]. We assumed that asymptomatic infections are 50% as infectious per contact as symptomatic infections [23], but with similar duration and infectivity profile as symptomatic infections. However, other studies have found that asymptomatically infected individuals might be less important for transmission [28]. At the end of the infectious stage, people either recover or are removed from the system due to death. Individuals who have recovered from infection (Ri) are assumed be protected from re-infection during the course of the simulation. The system can be described by a set of differential equations for each age group i=1-6:
Where λi is the per capita force of infection for a susceptible individual in age group i to become infected and βij is the transmission rate from age group j to age group i The age-specific force of infection λi is a product of age-specific contact rates, the prevalence of the infectious people (Ii) and the probability of transmission given contact (q). We obtained the contact rates based on conversational data from a study in the Netherlands [29]. We employed a WAIFW matrix (“Who-acquires-infection-from-whom” matrix) based on the contact rates between age groups. The basic reproductive number (R0) was calculated as the largest eigenvalue in the next generation matrix (23). The basic reproductive number is “the average number of secondary cases arising from an average primary case in an entire susceptible population” [22]. Through varying the value of q, we can produce the desired R0.
The differential equations were solved numerically using a fourth-order Runge–Kutta method with adaptable step size in Matlab 2009. It is unclear whether cross-immunity from past exposure to influenza will provide protection against a future pandemic strain. We assumed that the population was fully susceptible to the novel pandemic strain at the beginning of the simulation. Transmission was initiated at day ti=1 by moving a proportion of 10-6 of susceptible in each age class into the exposed class. The simulation was run for a period of t=250 days.
The transmissibility of a future pandemic strain is a major source of uncertainty. For this reason, we tested the model with three different basic reproductive numbers R0=1.5, 2.0 and 2.5. The school closure intervention was initiated when the prevalence of symptomatic infections had reached 1% of the population and was assumed to have full impact from this point in time. In the baseline scenario (scenario A), we assumed a 90% reduction in contacts among isolated children/adolescents with individuals in their own age group and a 25% decrease in contacts with other age groups. We did not consider changes in the contact patterns of affected parents taking care of children at home in this baseline scenario.
One-way sensitivity analysis
To account for some of the uncertainty in the model, we performed additional simulations varying assumptions about: the behaviours of care-taking parents, the behaviours of dismissed student during school closure and the case fatality rate (CFR).
In Scenario B, we introduced a 50% reduction in same age contacts among care-taking parents absent from work; in Scenario C we reduced the same age contact of dismissed children by 50% instead of 90% in the base case, and by 10% with other age groups instead of 25% to simulate low compliance among affected children; in Scenario D we increased the case fatality rate (CFR) by a factor of 10 compared to the baseline scenarios, using CFR of 1-2% in children and adults below 65 years similar to the level observed during the Spanish flu [30]; in Scenario E we reduced the CFR by a factor of 10 relative to the baseline scenarios, using CFR of 0.01-0.02% to simulate a mild pandemic. Finally, in Scenario F we modelled a pandemic with similar characteristics as the 2009 H1N1 pandemic. In these simulations, we assumed an R0 of 1.3. 60% of the populations in the 65+ year old age group and 10% of the 40–64 year old age group were assumed to have prior immunity. We also reduced the case fatality rate in accordance with Norwegian data showing that approximately 30 people died from H1N1 influenza (http://www.fhi.no/dokumenter/6cbae0eece.pdf).
The economic model
The costs of school closure comprised parents’ productivity losses and students’ loss of learning. Avoided costs resulted from less use of health care resources, less loss of productivity and less use of energy in school buildings. Health benefits were expressed as gained quality-adjusted life-years (QALYs). Productivity loss due to illness and health benefits were included for cases of mortality and cases of morbidity. We used 2008 data (US$1.00=NOK7.00 [21]) for all economic calculations. All future costs and health outcomes were discounted by 4% as recommended by the Ministry of Health.
Costs of school closure
Absence from school means lost learning hours and potentially permanent loss of learning and income [31, 32]. We searched the literature and databases, and contacted experts in education and educational economics. We were unable to identify any studies that directly address the issue of learning consequences of school closure. We assumed that this was the case only for students in upper secondary schools while children in kindergarten, primary and lower secondary school have no loss of learning from some weeks’ school closure. Most schools in Norway are public and free of charge, but some private schools offer upper secondary school education. Here, the tuition fee for one school year comprising 40 weeks was $8143, which is equivalent to $203 per week. We used this amount as an estimate of the value of lost learning.
School closure will keep working parents at home to care for children who are affected by the intervention. We assumed that students over 12 years do not need parental care during school closures. Similar to Sadique’s study [13], we assumed that only one parent is needed to care for children in a single household during school closure. Consequently, we distinguished between children living together with a single parent and with two parents. The percentages of both parents working were 66% among married couples with children and 78% among co-habitant couples with children (personal communication with Statistics Norway, 12 March, 2010). The percentage of working single parents was assumed to be the same as the percentage of working people in the same gender group (90% for men and 85% for women) [21]. We multiplied these percentages by the number of married couples, co-habitant couples and single parents, respectively. The sum of the products was taken as the number of individuals who would be absent from work during school closure.
We estimated the productivity losses from parents’ work absenteeism by multiplying the number of individuals that would need to be away from work during school closure with the number of days when schools are closed under different scenarios. The value of one day’s work was set equal to the national average wage rate (US$290 per day) plus 40%, which accounts for the value of productivity that is not returned to the worker as wages, including employer tax, payment for holiday and pension contributions.
Reduction of total cost due to school closure
The model outcome for symptomatically infected was divided into four types: mild cases who receive no medical care, moderate cases who receive outpatient service, severe cases who are hospitalized and fatal cases. Since the severity of a future pandemic is unknown, we used estimates of case fatality rates and health outcomes based on data from previous pandemics [33] (Table 1). We assumed that people with asymptomatic infection incur no economic costs, and therefore they were ignored in the economic analyses. The medical costs were estimated as the sum of mild, moderate and severe cases, multiplied by their respective unit costs. The unit costs were taken from a recent study of influenza costs in Norway [34].
Table 1
Model parameters
Mean
Distribution
Parameter
References
Demographic data
Population by age
15
1--5 years old
6.63%
6—12 years old
7.17%
13—19 years old
6.86%
20—39 years old
36.65%
40—64 years old
30.46%
65+ years old
12.24%
Percentage of adult population affected by school closure:
15
kindergarten (1-5 years old)
4.54%
kindergarten/primary school (1-11 years old)
10%
Disease parameters
Basic reproductive number (R0)
1.5, 2.0, 2.5
31; 32; 8
Mean duration of exposed period
1.9 days
17; 18
Mean duration of infectious period
7 days (<12 years) 5 days (12+ years)
17; 18; 19
Proportion asymptomatic (p)
33%
Infectivity (last exposed stage)
50%
19
Infectivity (in the five infectious stages)
100%, 100%, 50%, 30%, 15%
19;20
Mixing assumptions
Scenario A (baseline)
Reduction in contact rate between dismissed children of same/other age groups
90%/25%
Reduction in contact rate among care-taking parents and same age group
0%
Scenario B
Reduction in contact rate between dismissed children of same/other age groups
90%/25%
Reduction in contact rate among care-taking parents and same age group
50%
Scenario C
Reduction in contact rate between dismissed children of same/other age groups
50%/10%
Reduction in contact rate among care-taking parents and same age group
0%
Disease outcomes
Outcomes per 1000 cases by age groupsa
25
Outpatient
(534, 389, 497)
Uniform
((494-574), (369-410), (487-506))
Inpatient
(4, 8, 29)
((1-8), (2-13), (21-37))
Death
(1, 2, 13)
((0-2),(0-4),(11-15))
Economic parameters
Cost of energy saving (1000 US$)
1 439
Gammab
α=16; β=90
Oslo Municipality
Cost of lost learning (1000 US$)
25 797
Gamma
α=16; β=1 612
Bjørknes private school
Proportion of productivity loss catching up
15%
Uniform
range [0: 30%]
Average cost per self-care person (US$)
43
Normal
σ=3.57
26
Average cost per out-patient (US$)
59
Normal
σ=4.92
Den norske legeforening
Average cost per in-patient (US$)
5 211
Normal
σ=434
26
Average wage per day (US$)
290
Normal
σ=24
15
aAge groups were grouped by 1—18 years old, 19—64 years old and 65+years old.
b
where Γ is the Gamma function.
Loss of productivity associated with influenza has two components: the loss of working hours for the symptomatically infected and the loss of potential productivity for the fatal cases. Productivity losses due to morbidity were valued in the same way as parents’ work absenteeism. Productivity losses due to mortality were valued according to the remaining life expectancy at the relevant ages, discounted by 4% and with the assumption that people participate in the work force until age 65.
The avoided school heating cost was estimated using data from the Educational Buildings and Property Department in Oslo municipality.
Health benefits
Assuming that school closure will reduce the number of symptomatic and fatal influenza cases, we expressed the health benefits from school closure in terms of quality-adjusted life years (QALYs). For those who are symptomatically infected, we used utility scores from a Canadian study [35]. These utility scores represent the utility people have on each of the seven days since the onset (0 for worst possible health and 1 for normal health). The utilities are 0.41, 0.47, 0.58, 0.67, 0.73, 0.78 and 0.81 for day 1 to day 7, respectively. For those who died due to the illness, the QALY loss was calculated from the remaining life expectancy at the age of death predicted by the disease model and the discount factor.
Intervention strategy scenarios
We explored the costs and benefits of intervention policies with different durations (from 1 to 10 weeks) and for different target groups (closing kindergarten alone, primary school alone, secondary school alone, kindergarten and primary school or all three).
Uncertainty in cost-effectiveness estimates
To quantify the uncertainty in the cost-effectiveness ratios, we performed a probabilistic sensitivity analysis (number of simulations=1000) on the selected strategy for R0= 1.5, 2.0 and 2.5, incorporating the uncertainty in the demographic parameters, disease parameters, disease outcomes and economic parameters (Table 1). In addition, we reduced the work loss of care-taking parents by 0-30% (uniform distribution) assuming that some children were cared for by relatives or other persons, or that part of their work loss could be carried out through work from home or through work at a later time. The results were presented graphically by means of cost-effectiveness acceptability curves (Additional file 1: e-Figure 1).
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Results
Epidemiological impact of school closure
Figures 2, 3 show the epidemiological results of school closure. In the absence of intervention, our baseline model predicts 216 000, 300 000 and 340 000 symptomatic infections in the Oslo population for R0 =1.5, 2.0 and 2.5 pandemics, corresponding to clinical attack rates (AR) of 37%, 51% or 58%, respectively (Table 2). The relative effectiveness of the interventions increased with lower R0 values but required longer closure time to achieve the health benefits (Figure 3). School closure lowers the attack rate with up to 7-22%, 4-13% and 2-9% with R0=1.5, 2.0 or 2.5; these reductions are achieved after approximately 10, 8 and 7 weeks of closure (Figure 3). The peak prevalence of symptomatic infections was reduced correspondingly with up to 7-36%, 6-26% and 5-20%. To reach maximum reduction, school closure must be maintained for some weeks and beyond the point in time when the mitigated pandemic passes through its natural peak (Additional file 1: e-Figure 2). If schools are re-opened earlier, the pandemic will rebound. This will also happen if the intervention stops in the wake of the pandemic, provided the effective reproductive number of the un-mitigated pandemic is still above 1. Consequently, the maximum delay of the peak occurred for intermediate closure durations. The peak was delayed by up to 8–10 days (R0 =1.5), and to 4–5 days for R0 =2.0, 2.5. To avoid restarting the epidemic, we found that closure must be effective for at least 3–4 week for R0 =1.5, and 2–3 weeks when the transmissibility is higher.
Figure 2
Epidemic curves showing the prevalence of symptomatic infections for unmitigated pandemic versus implementing a 12-week school closure withR0=1.5, 2.0 and 2.5.
Figure 3
The relative attack rate compared to an unmitigated pandemic as function of school closure duration (number of closure weeks).
×
×
Table 2
Disease outcomes givenR0=1.5, 2.0 and 2.5
School closure of 12 weeks
R0=1.5
R0=2.0
R0=2.5
outp.
inp.
deaths
AR(%)
outp.
inp.
deaths
AR(%)
outp.
inp.
deaths
AR(%)
No intervention
92779
1929
584
37
128932
2738
844
51
146088
3150
983
58
Scenario A (baseline)
K
87388
1846
560
35
123904
2673
825
49
141642
3098
968
56
P
83081
1779
540
33
121245
2638
815
49
140075
3080
962
56
S
85718
1813
550
34
123784
2665
822
49
142328
3101
968
57
K+P
77605
1692
514
31
115823
2566
793
47
135161
3022
945
54
K+P+S
69989
1559
474
29
109800
2477
767
44
130661
2962
927
53
SENSITIVITY ANALYSIS
R0=1.5
R0=2.0
R0=2.5
outp.
inp.
deaths
AR(%)
outp.
inp.
deaths
AR(%)
outp.
inp.
deaths
AR(%)
Scenario B
K
85200
1798
546
34
122669
2645
817
49
140911
3082
963
56
P
79765
1707
519
32
119377
2597
803
48
138986
3056
955
55
S
85718
1813
550
34
123784
2665
822
49
142328
3101
968
57
K+P
71608
1559
475
29
112224
2487
770
45
133028
2975
932
53
K+P+S
64030
1423
434
26
105671
2387
740
43
128221
2910
912
52
Scenario C
K
89954
1885
572
36
126502
2707
835
50
144110
3127
976
57
P
87441
1847
560
35
125354
2691
830
50
143677
3121
974
57
S
89346
1873
568
36
126696
2706
835
50
144607
3131
977
57
K+P
84498
1801
547
34
122774
2657
820
49
141574
3097
967
56
K+P+S
80744
1738
528
33
120292
2621
810
48
139934
3075
961
56
Outp= outpatient. Inp= inpatient. AR=attack rate.
Scenario A is the base case scenario; scenario B included a 50% reduction in contacts among care-taking parents absent from work based on scenario A; scenario C reduced the compliance to 50% from scenario A.
The baseline scenarios gave an estimated 93 000–147 000 outpatient visits, 1 900–3 100 hospitalizations and 590–990 deaths (Table 2). The simulation runs showed that a 12-week school closure would reduce the attack rate by up to 22%, 14% and 7% for R0=1.5, 2.0 and 2.5 pandemics. The reductions in disease outcomes followed the reductions in attack rate, with slightly higher reductions in outpatients (6%–25%) and slightly lower reductions in inpatients and deaths (4%–20%) for a 12-week closure with R0=1.5, 2.0 or 2.5 in the base case.
Economic impact
Without school closure, the total health care costs would be $21 million, $29 million and $33 million, productivity losses due to mortality would be $313 million, $428 million and $480 million and productivity losses due to morbidity $102 million, $139 million and $155 million, for basic reproductive numbers of 1.5, 2.0 and 2.5 (Tables 3, 4 and 5). Depending on the type and duration of school closure, the cost of lost learning would be $0–32 million, while the cost of lost productivity were in the range of $0–630 million, and reduction in school heating costs varied between $0.18 and 5.4 million. The total influenza related costs would range from $435 million to $1285 million from the societal perspective (Tables 3, 4 and 5).
Table 3
Cost and health outcome according to type and duration of school closure whenR0=1.5
Target school
Duration (weeks)
Cost of lost learning ($1000)
Lost productivity due to school closure ($1000)
Energy savings ($1000)
Health care costs ($1000)
Lost productivity due to fatal cases ($1000)
Lost productivity due to sickness ($1000)
Total cost ($1000)
QALY gains (compared to no intervention)
Cost per QALY (compared to no intervention)
ICER
0
0
0
0
0
20 591
312 958
101 576
435 125
0
3
6
19 350
0
1 080
19 557
298 239
97 846
433 912
507
−2 395
3
7
22 575
0
1 260
19 410
296 139
97 312
434 175
579
−1 641
3 648
3
5
16 125
0
900
19 766
301 213
98 600
434 804
404
−796
Dominated
3
8
25 800
0
1 440
19 318
294 825
96 978
435 481
624
570
28 929
3
4
12 900
0
720
20 008
304 661
99 474
436 323
286
4 193
Dominated
3
1
3 225
0
180
20 509
311 792
101 278
436 625
40
37 316
Dominated
3
9
29 025
0
1 620
19 264
294 064
96 784
437 517
650
3 679
77 819
3
3
9 675
0
540
20 235
307 897
100 293
437 560
174
13 962
Dominated
3
2
6 450
0
360
20 403
310 287
100 897
437 678
92
27 727
Dominated
3
10
32 250
0
1 800
19 237
293 672
96 684
440 043
664
7 412
187 991
2
1
0
26 795
188
20 495
311 614
101 261
459 977
47
531 474
1
1
0
36 194
174
20 530
312 120
101 383
470 054
29
1 193 056
2
2
0
53 591
376
20 385
310 094
100 909
484 603
100
496 745
4
1
0
62 989
362
20 440
310 857
101 085
495 009
73
817 647
5
1
3 225
62 989
542
20 367
309 817
100 816
496 672
109
564 499
1
2
0
72 388
348
20 453
311 044
101 138
504 674
67
1 039 847
2
3
0
80 386
564
20 210
307 651
100 342
508 024
185
395 026
2
4
0
107 181
752
19 950
304 039
99 504
529 922
310
305 814
1
3
0
108 582
522
20 323
309 257
100 729
538 369
129
798 460
2
5
0
133 976
940
19 645
299 793
98 516
550 991
457
253 333
4
2
0
125 979
724
20 263
308 401
100 517
554 436
159
751 538
5
2
6 450
125 979
1 084
20 109
306 200
99 944
557 598
234
522 386
1
4
0
144 776
696
20 148
306 836
100 173
571 237
214
636 557
2
6
0
160 772
1 128
19 356
295 758
97 575
572 332
597
229 715
2
7
0
187 567
1 316
19 117
292 419
96 793
594 579
713
223 637
1
5
0
180 970
870
19 971
304 374
99 606
604 051
300
563 630
4
3
0
188 968
1 086
19 989
304 590
99 632
612 092
291
607 281
5
3
9 675
188 968
1 626
19 736
300 952
98 673
616 377
416
435 391
2
8
0
214 362
1 504
18 961
290 230
96 279
618 327
789
232 250
1
6
0
217 164
1 044
19 812
302 170
99 095
637 197
377
536 585
2
9
0
241 157
1 692
18 858
288 799
95 942
643 065
838
248 040
4
4
0
251 957
1 448
19 608
299 290
98 394
667 801
476
489 135
2
10
0
267 953
1 880
18 803
288 023
95 759
668 657
865
269 909
1
7
0
253 358
1 218
19 703
300 654
98 742
671 239
429
549 816
5
4
12 900
251 957
2 168
19 239
293 960
96 967
672 854
658
361 133
1
8
0
289 552
1 392
19 639
299 767
98 536
706 101
460
588 611
4
5
0
314 946
1 810
19 151
292 916
96 892
722 096
697
411 700
5
5
16 125
314 946
2 710
18 630
285 363
94 847
727 200
955
305 707
1
9
0
325 746
1 566
19 605
299 302
98 427
741 514
477
642 905
4
6
0
377 936
2 172
18 702
286 631
95 396
776 493
915
373 065
1
10
0
361 940
1 740
19 585
299 025
98 363
777 173
486
703 475
5
6
19 350
377 936
3 252
18 018
276 690
92 681
781 422
1 255
275 997
4
7
0
440 925
2 534
18 330
281 412
94 143
832 277
1 096
362 429
5
7
22 575
440 925
3 794
17 426
268 283
90 555
835 970
1 544
259 543
4
8
0
503 914
2 896
18 058
277 580
93 217
889 873
1 228
370 185
5
8
25 800
503 914
4 336
16 965
261 700
88 870
892 913
1 771
258 490
4
9
0
566 903
3 258
17 885
275 152
92 627
949 309
1 312
391 782
5
9
29 025
566 903
4 878
16 627
256 878
87 624
952 179
1 937
266 957
4
10
0
629 893
3 620
17 789
273 802
92 297
1 010 161
1 359
423 098
5
10
32 250
629 893
5 420
16 386
253 424
86 726
1 013 259
2 056
281 259
Note: The maximum willingness to pay is set to be NOK 500,000 or US$71,500 based on the government guidance28. The most cost-effective option is shown with bold font.
Table 4
Cost and health outcome according to type and duration of school closure whenR0=2.0
Target school
Duration (weeks)
Cost of lost learning ($1000)
Lost productivity due to school closure ($1000)
Energy savings ($1000)
Health care costs ($1000)
Lost productivity due to fatal cases ($1000)
Lost productivity due to sickness ($1000)
Total cost ($1000)
QALY gains (compared to no intervention)
Cost per QALY (compared to no intervention)
ICER
0
0
0
0
0
28 890
428 137
138 654
595 682
3
4
12 900
0
720
28 215
419 135
136 843
596 374
321
2 155
3
5
16 125
0
900
28 049
416 920
136 411
596 604
400
2 306
2 921
3
1
3 225
0
180
28 846
427 542
138 529
597 961
21
106 854
3
3
9 675
0
540
28 491
422 813
137 570
598 009
190
12 224
Dominated
3
6
19 350
0
1 080
27 985
416 062
136 245
598 562
431
6 686
64 224
3
2
6 450
0
360
28 732
426 018
138 216
599 056
76
44 470
Dominated
3
7
22 575
0
1 260
27 964
415 780
136 190
601 248
441
12 628
267 404
3
8
25 800
0
1 440
27 957
415 695
136 173
604 186
444
19 161
975 711
3
9
29 025
0
1 620
27 955
415 672
136 169
607 201
445
25 907
3 654 485
3
10
32 250
0
1 800
27 955
415 664
136 167
610 236
445
32 714
11 358 909
2
1
0
26 795
188
28 844
427 532
138 545
621 528
22
1 179 444
1
1
0
36 194
174
28 853
427 657
138 575
631 105
17
2 029 542
2
2
0
53 591
376
28 735
426 112
138 297
646 358
73
691 761
4
1
0
62 989
362
28 810
427 096
138 472
657 005
38
1 622 566
5
1
3 225
62 989
542
28 769
426 546
138 354
659 342
58
1 107 041
1
2
0
72 388
348
28 752
426 362
138 363
665 517
65
1 082 646
2
3
0
80 386
564
28 481
422 818
137 732
668 853
192
380 871
2
4
0
107 181
752
28 108
417 981
136 924
689 442
366
256 079
1
3
0
108 582
522
28 535
423 576
137 909
698 080
166
618 250
2
5
0
133 976
940
27 795
413 930
136 260
711 021
512
225 466
4
2
0
125 979
724
28 618
424 608
138 047
716 527
128
944 416
5
2
6 450
125 979
1 084
28 494
422 945
137 687
720 470
187
665 879
1
4
0
144 776
696
28 275
420 231
137 363
729 949
287
467 968
2
6
0
160 772
1 128
27 636
411 869
135 925
735 074
585
238 117
2
7
0
187 567
1 316
27 576
411 079
135 797
760 703
614
268 896
1
5
0
180 970
870
28 108
418 079
137 011
763 298
365
459 401
4
3
0
188 968
1 086
28 179
418 930
137 085
772 075
333
529 302
5
3
9 675
188 968
1 626
27 906
415 233
136 270
776 425
465
388 791
2
8
0
214 362
1 504
27 557
410 834
135 758
787 007
622
307 365
1
6
0
217 164
1 044
28 044
417 253
136 876
798 292
395
513 250
2
9
0
241 157
1 692
27 551
410 765
135 746
813 528
625
348 587
4
4
0
251 957
1 448
27 555
410 851
135 722
824 637
624
366 634
5
4
12 900
251 957
2 168
27 050
403 997
134 214
827 950
868
267 629
1
7
0
253 358
1 218
28 022
416 976
136 830
833 968
405
588 668
2
10
0
267 953
1 880
27 550
410 744
135 743
840 109
626
390 639
1
8
0
289 552
1 392
28 017
416 902
136 818
869 897
407
672 986
4
5
0
314 946
1 810
27 034
404 084
134 582
878 837
868
326 324
5
5
16 125
314 946
2 710
26 272
393 758
132 340
880 731
1 234
230 988
1
9
0
325 746
1 566
28 015
416 881
136 815
905 892
408
759 953
4
6
0
377 936
2 172
26 753
400 417
133 965
936 898
999
341 470
5
6
19 350
377 936
3 252
25 798
387 502
131 192
938 526
1 457
235 261
1
10
0
361 940
1 740
28 015
416 876
136 814
941 904
408
847 747
4
7
0
440 925
2 534
26 645
399 011
133 728
997 774
1 050
383 078
5
7
22 575
440 925
3 794
25 597
384 843
130 703
1 000 849
1 552
261 045
4
8
0
503 914
2 896
26 611
398 573
133 654
1 059 855
1 065
435 700
5
8
25 800
503 914
4 336
25 521
383 838
130 518
1 065 255
1 588
295 719
4
9
0
566 903
3 258
26 600
398 435
133 631
1 122 311
1 070
492 048
5
9
29 025
566 903
4 878
25 494
383 489
130 454
1 130 488
1 600
334 181
4
10
0
629 893
3 620
26 597
398 391
133 623
1 184 883
1 072
549 693
5
10
32 250
629 893
5 420
25 486
383 386
130 435
1 196 030
1 604
374 276
Table 5
Cost and health outcome according to type and duration of school closure whenR0=2.5
Target school
Duration (weeks)
Cost of lost learning ($1000)
Lost productivitydue to school closure ($1000)
Energy savings ($1000)
Health care costs ($1000)
Lost productivity due to fatal cases ($1000)
Lost productivity due to sickness ($1000)
Total cost ($1000)
QALY gains (compared to no intervention)
Cost per QALY (compared to no intervention)
ICER
0
0
0
0
0
32 961
479 607
155 079
667 646
3
1
3 225
0
180
32 928
479 185
155 005
670 162
16
160 991
3
3
9 675
0
540
32 544
474 295
154 205
670 179
195
12 994
3
4
12 900
0
720
32 367
472 045
153 864
670 456
277
10 150
3 380
3
2
6 450
0
360
32 801
477 565
154 728
671 184
75
47 003
Dominated
3
5
16 125
0
900
32 318
471 424
153 771
672 739
299
17 011
101 226
3
6
19 350
0
1 080
32 308
471 296
153 752
675 626
304
26 248
620 315
3
7
22 575
0
1 260
32 306
471 271
153 749
678 641
305
36 059
3 386 921
3
8
25 800
0
1 440
32 306
471 267
153 748
681 681
305
46 005
20 007 697
3
9
29 025
0
1 620
32 306
471 266
153 748
684 725
305
55 979
126 703 892
3
10
32 250
0
1 800
32 306
471 266
153 748
687 770
305
65 955
289 245 859
2
1
0
26 795
188
32 929
479 210
155 022
693 768
15
1 764 356
1
1
0
36 194
174
32 929
479 216
155 031
703 195
15
2 442 399
2
2
0
53 591
376
32 811
477 750
154 823
718 598
69
738 185
4
1
0
62 989
362
32 899
478 844
154 977
729 347
28
2 168 767
5
1
3 225
62 989
542
32 871
478 484
154 908
731 936
42
1 538 432
1
2
0
72 388
348
32 797
477 600
154 839
737 276
75
934 187
2
3
0
80 386
564
32 504
473 932
154 337
740 595
210
348 001
2
4
0
107 181
752
32 174
469 835
153 856
762 295
359
263 354
1
3
0
108 582
522
32 532
474 332
154 456
769 379
196
520 297
2
5
0
133 976
940
32 013
467 836
153 631
786 516
432
275 032
4
2
0
125 979
724
32 671
476 022
154 614
788 561
133
907 803
5
2
6 450
125 979
1 084
32 558
474 572
154 337
792 811
187
670 647
1
4
0
144 776
696
32 315
471 663
154 148
802 206
294
457 624
2
6
0
160 772
1 128
31 970
467 302
153 571
812 487
452
320 722
1
5
0
180 970
870
32 242
470 771
154 046
837 160
327
518 523
2
7
0
187 567
1 316
31 962
467 200
153 560
838 973
455
376 283
4
3
0
188 968
1 086
32 117
469 165
153 760
842 924
386
453 852
5
3
9 675
188 968
1 626
31 806
465 143
153 021
846 987
533
336 228
2
8
0
214 362
1 504
31 960
467 181
153 558
865 557
456
434 015
1
6
0
217 164
1 044
32 226
470 573
154 023
872 943
334
614 247
2
9
0
241 157
1 692
31 960
467 177
153 557
892 159
456
492 180
4
4
0
251 957
1 448
31 531
461 895
152 891
896 827
653
351 186
5
4
12 900
251 957
2 168
30 971
454 663
151 625
899 947
916
253 572
1
7
0
253 358
1 218
32 224
470 539
154 019
908 922
335
719 170
2
10
0
267 953
1 880
31 960
467 176
153 557
918 766
456
550 486
1
8
0
289 552
1 392
32 223
470 532
154 019
944 934
336
825 928
4
5
0
314 946
1 810
31 242
458 297
152 470
955 145
784
366 760
5
5
16 125
314 946
2 710
30 530
449 119
150 906
958 916
1 118
260 600
1
9
0
325 746
1 566
32 223
470 531
154 019
980 953
336
933 116
4
6
0
377 936
2 172
31 161
457 290
152 353
1 016 567
821
425 217
1
10
0
361 940
1 740
32 223
470 531
154 019
1 016 972
336
1 040 374
5
6
19 350
377 936
3 252
30 395
447 425
150 689
1 022 542
1 179
300 960
4
7
0
440 925
2 534
31 145
457 092
152 330
1 078 958
828
496 882
5
7
22 575
440 925
3 794
30 360
446 990
150 633
1 087 690
1 195
351 506
4
8
0
503 914
2 896
31 142
457 055
152 326
1 141 540
829
571 548
5
8
25 800
503 914
4 336
30 354
446 910
150 623
1 153 266
1 198
405 402
4
9
0
566 903
3 258
31 142
457 047
152 325
1 204 158
829
646 844
5
9
29 025
566 903
4 878
30 353
446 893
150 621
1 218 917
1 199
459 966
4
10
0
629 893
3 620
31 141
457 045
152 324
1 266 783
829
722 298
5
10
32 250
629 893
5 420
30 352
446 889
150 620
1 284 584
1 199
514 689
Health benefits from school closure would range from 15 QALYs to 2056 QALYs depending on R0, the age target group and the duration of school closure (Tables 3, 4 and 5). Our results indicate that in the baseline scenario, closing secondary schools for 8, 6 and 4 weeks, when R0 is 1.5, 2.0 and 2.5 respectively, is the most cost-effective strategy when indirect costs are accounted for. Closing secondary schools is cost-effective given a wide range of cost-effective threshold ratios, as shown by cost-effectiveness acceptability curves (Additional file 1: e-Figure 1). The strategy of closing secondary was also cost-effective for varying closure durations (data not shown).
Anzeige
Sensitivity analyses
The sensitivity analyses confirm that closing secondary schools is the optimal strategy from a societal perspective, unless the case fatality rate (CFR) is very high.
Scenario B: Reduced (adult-adult) contact among care-taking parents. We found increased effect of school closure relative to the baseline scenarios. The estimated reduction in the attack rate compared to an unmitigated pandemic was 8-30%, 4-16%, and 3-10%, for R0=1.5, 2.0 and 2.5 pandemics, respectively (Table 2). The corresponding optimal strategies were closing secondary schools with durations of 8 weeks, 6 weeks and 4 weeks, identical to the findings in the baseline scenario (Additional file 1: e-Table 1; I-III).
Scenario C: Reduced compliance of dismissed children/students to stay at home. The simulations showed an overall small effect of school closure. The estimated maximum reduction in the attack rate compared to an unmitigated pandemic ranged between 3-11%, 2-6% and 2-3% for R0=1.5, 2.0 and 2.5, respectively (Table 2). The optimal strategies were closing secondary schools for 7, 4, and 3 weeks (Additional file 1: e-Table 2; I-III), indicating a shorter optimal period of one week compared with the baseline model for R0=1.5 and 2.5.
Scenario D: Increasing the case fatality rate by a factor of 10. This means increasing the severity of the pandemics to levels similar to those observed during the Spanish Flu [36]. In this case, the optimal strategies were closing kindergartens, primary and secondary schools for 9 weeks if R0=1.5, 7 weeks if R0=2.0, and 5 weeks if R0= 2.5 (Additional file 1: e-Table 3).
Anzeige
Scenario E: Decreasing the case fatality rate by a factor of 10. In this case, when R0=1.5, closing secondary school for 6 weeks is most cost-effective. Otherwise, there is no cost-effective strategy among the strategies we examined (Additional file 1: e-Table 4).
Scenario F: Pandemic with 2009 H1N1 characteristics. The results show that the added cost of school closure was higher than not closing schools, regardless of the age target of school children. Consequently school closure would not have been cost-effective during the 2009 H1N1 pandemic (Additional file 1: e-Table 5).
Discussion
Our study shows that school closure during influenza pandemic has a moderate impact on the total disease burden. The cost-effectiveness of school closure varies considerably across different strategies with different target groups and durations. Generally we found that for R0=1.5, 2.0 and 2.5 pandemics with case fatality rates of 0.1-0.2%, only those strategies involving closure of secondary schools were cost-effective from a societal point of view. The study shows that optimal school closure depends on the transmissibility and severity of the pandemic and may provide guidance to local policy planning. The optimal duration of closing secondary schools is shorter (4 weeks) with R0=2.5 compared to 8 weeks with R0=1.5. In contrast, school closure involving primary schools and kindergartens incur substantial economic costs due to lost productivity of care-taking parents. Consequently, most school closure strategies cannot be considered cost-effective (Tables 3, 4 and 5) at current values of quality adjusted life-years in Norway [37]. However, school closure involving children in need of parental care may be indicated when case fatality rates are high, for instance in the event of a future pandemic with an avian (H5N1) virus.
We also simulated a pandemic with characteristics of the 2009 H1N1 pandemic. Our results suggest that school closure as a single intervention would not have been cost-effective during the recent pandemic. This finding is in agreement with results by Brown and co-workers [17], who found that the net costs of school closure during the 2009 H1N1 pandemic would have been substantially higher than the cost savings from preventing influenza disease. However, other studies indicate that school closure might have been cost-effective, despite the low severity and low transmissibility of the 2009 H1N1 pandemic. Halder and co-workers [16] found that short-duration school closure of 2 to 4 weeks would be relatively cost-effective while in general school closure intervention as a single strategy would be less efficient than strategies involving widespread use of antivirals, and Araz and co-workers found that a 0.5% prevalence closure trigger followed by a 12 week closure would be cost-effective [20].
Our findings are similar to other computer simulation studies [8‐10, 17, 36] and a surveillance data study from Hong Kong [7], all of which indicate that the impact of school closure on the pandemic is modest. In general we found that school closure peak timing was delayed with only few days compared with that of an unmitigated pandemic. The delay increased with lower transmissibility. The maximum delay was observed for intermediate closure durations, when the epidemic re-started influenced by the higher transmissibility of the unmitigated pandemic (Reff > 1). A micro-simulation study by Lee and co-workers [9] also show that intermediate duration closure produces the longest delays. However, their observed delay for long closure duration was longer: 4–8 days for system wide school closure for R0=1.4-2.4. One possible explanation for the shorter delay in our study is that we assume that the whole population is interacting, while we did not model the individual transmission processes. In addition, individuals in our model generally mix most with individuals in their own age group. Therefore, there is a tendency that the epidemic in school children develops “independently” of how the epidemic develops in the other age groups, and school closure has only small impact on the disease burden in the population that is not directly affected by the intervention. We have performed additional simulations using a lower closure trigger of 0.5% instead of the 1% assumed in the baseline scenario (results not shown). These simulations show that an earlier trigger increases the maximum delay by approximately one third, while the peak timing during long duration closure increased only little.
Our approach is analogous to a recent study by Araz and co-workers [20], using a dynamic compartmental model combined with calculations of incremental cost-effectiveness ratios to select the preferred policy. They studied pandemics with transmissibility in the range R0=1.1-2.1, using various closure triggers and fixed school closure durations of 1–24 weeks or prevalence-based reopening triggers. They found that in low transmissibility scenarios, early triggers combined with long closure duration of 12–24 weeks were preferred, regardless of severity; for high transmissibility scenarios, later triggers combined with 8–18 weeks closure were preferred. In comparison, our selected strategies involved much shorter closure durations of 4–8 weeks. One reason for this large discrepancy could be that they used early triggers. In addition, their model has a very long serial interval of 9 days, whereas our model has a serial interval of approximately 4 days due to the infectious profile, which we believe is more in agreement with data [38].
The present work highlights the potential importance of school closure among students who do not need parental care. The benefit of school closure interventions targeting this group appears to have escaped notice in the literature. Our results suggest that closing secondary school alone can decrease the peak prevalence of symptomatic infection by 10–20% while incurring no loss of productivity for parents. Hence, school closure for children over 12 years could have important implications for the functioning of the healthcare system during the surge of a pandemic, when the capacity of health services may be pressured. We note that in Norway laptop computers are mandatory equipment in secondary schools and an organized computer network (“Fronter”) for communication between students and teachers in primary and secondary schools is already in place. It would therefore be possible to plan for sustained teaching and learning during an extended school closure, making secondary school closure even more cost-effective. However, for the strategy to be effective, it is important that students actually follow the recommendations and isolate themselves. This may be difficult to achieve for extended periods of time.
The health-economic evaluation in this study was based on estimates of age-specific health-outcome from previous pandemics [26]. If we scale up the results in the baseline scenarios for R0=1.5-2.5 pandemics to the national level (Oslo comprises approximately 12% of Norwegian population), our results correspond to 16 000–26 000 hospitalizations and 4 900–8 200 deaths in Norway with an attack rate ranging from 37-58%. In comparison, the yearly influenza epidemics (attack rate of 5-10%) results in approximately 2 700 cases of hospitalizations [34] and approximately 1 000 deaths [39]. Adjusting for the difference in attack rates, this indicates that our results are in reasonable agreement with findings from the seasonal epidemics; however, the numbers are difficult to compare because the seasonal epidemics primarily affect the elderly population.
Our study has several limitations. Firstly, the age-specific contact rate data were adopted from a Dutch study, as no Norwegian data on social mixing is currently available. The contact pattern in Norway may differ, in particular due to the high attendance rates in kindergarten and high employment rate of women. Secondly, the effect of school closure on the contact pattern in the population is not well documented in the literature and is uncertain. However, our choices were guided by observation from weekends and holidays and previous school closures in Oslo due to strikes, etc. Thirdly, the cost of lost learning is uncertain. We used tuition fees as a proxy for the value of learning, but private schools are primarily used by people with higher incomes and the tuition fee may therefore overstate the value of lost learning. Fourthly, productivity losses may be overestimated because some parents who are away from work may be absent anyway because they have influenza themselves. Fifthly, energy savings in schools during school closure may be partly off-set by higher energy use in homes. However, energy in Norway is cheap and only small proportions of households have day-time energy saving systems according to the governmental energy saving organization. Lastly, we have considered school closure as a single strategy. Combining school closure with other interventions such as use of antiviral medications or other social distancing measures might change the conclusions about optimal duration of school closure, and the target group.
Conclusions
School closure has moderate impact on influenza disease and may incur substantial economic costs in terms of lost productivity from care-taking parents absent from work. Closing secondary schools, assuming children above 12 years would not need parental care, is a cost-effective strategy from a societal perspective. With the current willingness to pay in Norway, closing kindergartens and primary schools is not a cost-effective policy to mitigate an influenza pandemic, unless the case fatality rates are high. Reliable information on influenza mortality is therefore of primary importance to inform decision-making on school closure. Finally, we note that the perspective of the policy maker is crucial for optimal design of school closure. If the policy maker disregards productivity losses, the optimal strategy is to close as many school as possible for as long time as possible.
Funding source
Yiting Xue was supported by the Norwegian Research Council through project number 177401/V50 and Birgitte Freiesleben de Blasio was supported by the Norwegian Research Council through project number 166056/V50.
Acknowledgements
We are grateful to Kirsten E. Dybendal at Statistics Norway for providing detailed data on population statistics and to Gianpaolo Scalia Tomba at the Department of Mathematics, University of Rome for suggestions in the disease modelling. Arna Desser at Department of Health Management and Health Economics, University of Oslo, has provided valuable suggestions on heath economics and helped to improve the language.
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Competing interests
The authors declare that they have no competing interest.
Authors’ contributions
YX originated the idea and drafted the paper. YX and BFB constructed the mathematical model while YX and ISK conducted the health economic evaluation. BFB and ISK reviewed and revised the manuscript. All authors read and approved the final manuscript.
