Background
Methods
Developing Wells-Riley model for several microenvironments
Filter Type | Range | Mean |
---|---|---|
MERV 4 | 7.7–12.7% | 10.5% |
MERV 7 | 35.5–47.4% | 42.2% |
MERV 13 | 81.6–89.2% | 85.9% |
MERV16 | 95.0% | 95.0% |
HEPA | 99.9% | 99.9% |
Estimating the number of susceptible individuals based on vaccination coverage and age
Back calculating quanta generation rate
Parameter | Primary School Best-Estimate [Range] | Secondary School Best-Estimate [Range] | Reference |
---|---|---|---|
No. of enrolled students during outbreaks | 868 | 1873 | Literaturea |
No. of first generation infected cases | 28 | 69 | Literaturea |
No. of index case/s | 1 | 1 | Literaturea |
Infection period in school (day) | 3 | 4 | Literaturea |
Portion of unvaccinated students | 3.3% | 0.3% | Literaturea |
Portion of students with 1-dose vaccination | 96.7% | 70.9% | Literaturea |
Portion of students with 2-dose vaccination | 0.0% | 28.8% | Literaturea |
No. of students in infector’s classroom | 24 | 30 | Literaturea |
No. of students in recirculation area | 592 | 1843 | Literaturea |
No. of students in common area | 664 | 1873 | Literaturea |
Average time spent in classroom/s (min) | 280 [270–290]b | 340 | Literaturea |
Average time spent in recirculation area (min) | 280 [270–290]b | 340 | Literaturea |
Average time spent in common area (min) | 20 [10–30]b | 70 | Literaturea |
HVAC system runtime fraction | 1 | 0.768 | Literaturea |
Recirculated air fraction | 0.438 | 0.05 | Literaturea |
Supply airflow rate of one classroom (m3/min) | 28.3 | 8.5 | Literaturea |
Total HVAC system capacity (m3/min) | 1019.4 | 595 | Literaturea |
Air filter removal efficiency (%) | 12 | 12c [10.5–42.2] | Literatured |
Occupancy density of classroom (m2/person) | 4 [3–5] | 4 [3–5] | DOEe |
Volume of recirculation area (m3) | 13,832 [10374–17,290] | 33,600 [25200–42,000] | Estimatedf |
Occupancy density of common area (m2/person) | 1.39 [1.04–1.74] | 1.39 [1.04–1.74] | DOEe |
Inhalation rate (m3/day) | 12.96[11.34–14.53] | 15.53 [13.93–17.45] | EPAg |
Deposition rate of measles bio-aerosols (1/h) | 1.7 [1.0–2.7] | 1.7 [1.0–2.7] | Literatured |
Natural ventilation rate (1/h) | 0.31 [0.12–0.49] | 0.31 [0.12–0.49] | DOEh |
Developing a nationwide representative school model for measles transmission risk
Parameter | Primary School Best-Estimate [Range] | Secondary School Best-Estimate [Range] | Reference |
---|---|---|---|
No. of educational institutions in US 2015–2016 | 88,665 | 26,986 | NCESa |
No. of Index case/s | 1 | 1 | Assumption |
Quanta generation rate (quanta / hour) | 1925 [1185–3345] | 2765 [1430–5140] | This Studyb |
No. of enrolled students before outbreak | 513 [175–825] | 854 [245–1394] | NCESc |
Infection period in school (day) | 3 [2–4] | 3 [2–4] | Literatured |
Portion of unvaccinated students | 9% [8–10%] | 9% [8–10%] | CDCe |
Portion of students with ≥2-dose vaccination | 91% [90–92%] | 91% [90–92%] | CDCe |
No. of students in infector’s classroom | 21 [18–26] | 23 [18–30] | SASSf |
Occupancy density of classroom (m2/person) | 4 [3–5] | 4 [3–5] | DOEg |
Occupancy density of common area (m2/person) | 1.39 [1.04–1.74] | 1.39 [1.04–1.74] | DOEg |
Average time spent in school (mins) | 400 [375–425] | 400 [375–425] | SASSh |
Average time spent in common area (mins) | 20 [15–30] | 30 [20–45] | NFSMIi |
Heating and cooling periods in US schools (day) | H: 200 & C: 90 | H: 200 & C: 90 | Assumptionj |
HVAC system type | See Table 4 | See Table 4 | CBECSk |
HVAC recirculation rate in classrooms (per hour) | 6.4 [3.3–8.5] | 6.4 [3.3–8.5] | Literaturel |
Outdoor air ventilation in classrooms (L/s-person) | 6.7 [4.0–9.5] | 6.7 [4.0–9.5] | ASHRAEm, |
Outdoor air ventilation in common area (L/s-person) | 4.9 [4.7–5.1] | 4.9 [4.7–5.1] | ASHRAEm |
HVAC runtime for applicable systems | 1 | 1 | Assumption |
Air filter removal efficiency (%) | 72% [44–86%] | 72% [44–86%] | NAFAn |
Infiltration rate (1/h) | 0.31 [0.12–0.49] | 0.31 [0.12–0.49] | DOEg |
Deposition rate of measles bio-aerosols (1/h) | 1.7 [1.0–2.7] | 1.7 [1.0–2.7] | Literatureo |
Inhalation rate (m3/day) | 12.96 [11.34–14.53] | 15.53 [13.93–17.45] | EPAp |
School Type | HVAC System Type | Heating | Cooling |
---|---|---|---|
Primary School | Central-Forced-Air | 41% | 26% |
Ductless with Air Filter | 47% | 63% | |
Ductless without Air Filter | 12% | 10% | |
Secondary School | Central-Forced-Air | 43% | 35% |
Ductless with Air Filter | 41% | 54% | |
Ductless without Air Filter | 16% | 11% |
Evaluating the effects of vaccination and airborne infection control strategies on measles transmission risk
Improving removal efficiency of HVAC air filters
Increasing ventilation rate
Using air purifiers in classrooms
Results
Estimates of quanta generation rate
Transmission risk of measles in U.S. schools
Effects of selected infection control strategies on measles transmission
Discussion
Comparing the risk model assumptions and results with existing epidemiological studies
School Location [outbreak year] – Type | NO. Students | No Vac. Record | 1-Dose Vaccination | 2-Dose Vaccination | ARU | ARI-1- Dose | ARI-2- Dose | ARI-General | Susceptible Students | NO. First Gen. Cases | Total NO. Cases |
---|---|---|---|---|---|---|---|---|---|---|---|
New York, US [1945–46] ES I [44] | 367 | 100.0% | 0.0% | 0.0% | 77.6% | N/A | N/A | N/A | 170 | 26 | 132 |
New York, US [1945–46] ES II [44] | 530 | 100.0% | 0.0% | 0.0% | 83.9% | N/A | N/A | N/A | 249 | 64 | 209 |
New York, US [1945–46] ES III [44] | 492 | 100.0% | 0.0% | 0.0% | 69.4% | N/A | N/A | N/A | 193 | 123 | 134 |
Kansas, US [1970] ES [102] | 690 | 14.2% | NR | NR | 30.3% | NR | NR | 2.6% | 122 | 3 | 35 |
New York, US [1974] ES [33] | 868 | 3.3% | NR | NR | 20.7% | NR | NR | 6.4% | 113 | 28 | 60 |
Texas, US [1985] JHS I [103] | 1141 | 0.6% | 87.6% | 11.9% | 10.0% | 4.5% | 1.4%a | 4.1% | 107 | 10 | 21 |
Texas, US [1985] JHS II [103] | 1122 | 1% | NR | NR | NR | NR | NR | NR | 122 | NR | 34 |
East Sussex, UK [1992–93] E-M-HS [104] | 1673 | 31.5% | NR | NR | 17.8% | NR | NR | 1.52% | 528 | 41 | 66 |
687 | < 1% | 45% | 44% | NR | NR | NR | < 2.18% | 41 | 4 | 15 | |
525 | < 1% | 45% | 44% | NR | NR | NR | < 1.33% | 31 | 4 | 7 | |
Reuler, Luxembourg [1996] PS [106] | 363 | 22.8% | NR | NR | 54.7% | NR | NR | 4.6% | 102 | 28 | 45 |
Wincrage, Luxembourg [1996] PS [106] | 343 | 28.0% | NR | NR | 51.9% | NR | NR | 1.0% | 110 | 15 | 43 |
Disburg City Germany [2006] E-M-HS [107] | 1250 | 3.8% | 24.5% | 58.4% | 52.8% | 1.0% | 0.4% | 0.5% | 81 | NR | 53 |
California, US [2008] ES [108] | 377 | 10.9% | NR (< 50%) | NR (> 50%) | 9.8% | 0.0% | 0.0% | 0.0% | 62 | 2 | 4 |
Beijing, China [2014] ES [109] | 1245 | 0.5% | 1.7% | 97.8% | 0.0% | 0.0% | 0.9% | 0.9% | 20 | 3 | 11 |
School Location [outbreak year] – Type | NO. Students | No Vac. Record | 1-Dose Vaccination | 2-Dose Vaccination | ARU | ARI-1- Dose | ARI-2- Dose | ARI, General | Susceptible Students | NO. First Gen. Cases | Total NO. Cases |
---|---|---|---|---|---|---|---|---|---|---|---|
Massachusetts, US [1984] SHS [59] | 2098 | 0.6% | 42.3% | 57.1% | 22.9% | 1.7% | 0.5% | 1.0% | 117 | 5 | 24 |
Texas, US [1985] HS [103] | 1796 | 0.6% | 87.6% | 11.9% | 10.0% | 4.5% | 1.4% | 4.1% | 99 | 3 | 5 |
Illinois, US [1985] HS [22] | 1873 | 0.3% | 71.1% | 28.9% | 0.0% | 4.5% | 1.7% | 3.7% | 100 | 69 | 69 |
New Mexico, US [1987] HS [110] | 2012 | 1.9% | 76.5% | 21.6% | 0.0% | 2.8% | 1.7% | 2.6% | 137 | 24 | 49 |
Texas, US [1989] HS [111] | 2243 | 0.0% | 95.2% | 4.8% | N/A | 3.2% | 1.9% | 3.2% | 112 | 58 | 71 |
Honkajoki, Finland [1989] HS [112] | 144 | 63.8% | 29.5% | 6.7% | 22.4% | 29.0%a | 14.3%a | 26.3%a | 69 | 22 | 25 |
Gwynedd, North Wales [1991] SHS [113] | 723 | 38.5% | NR | NR | 33.1% | NR | NR | 1.0% | 140 | 12 | 45 |
127 | < 1% | 45.0% | 44.0% | NR | NR | NR | < 3.94% | 7 | 3 | 5 | |
Alaska, US [1996] HS I [114] | 2192 | 0.0% | 48.8% | 50.4% | 0.0% | 1.5% | 0.0% | 0.7% | 110 | 16 | 17 |
Alaska, US [1996] HS II [114] | 1486 | 0.5% | 53.9% | 45.5% | 0.0% | 0.1% | 0.3% | 0.1% | 81 | NR | 2 |
Pennsylvania, US [2003] SBS [115] | 663 | 0.5% | 3.9% | 94.9% | 66.7% | 0.0% | 1.0% | 0.9% | 36 | 5 | 8 |
Quebec, Canada [2011] HS [116] | 1306 | 4.7% | 9.0% | 85.5% | 82.0% | 4.6% | 3.7% | 4.7% | 123 | 10 | 110 |