ASHRAE Journal - June 2021 - 16

TECHNICAL FEATURE
of NACH =1.34 h-1. For each of the scenarios,
the mask effective filtration
rate of 0 corresponds to the no-mask
baseline for all room occupants.
Unremarkably, Scenario A (instructor
infectious with student susceptible)
had the highest trajectory of
conditional probability of infection
due to the higher quanta emission
rate for the instructor. As the
mask effective filtration efficiency
increases, the conditional probability
of infection decreases modestly
until filtration efficiencies greater
than about 0.6 (60%) are reached,
after which it decreases rapidly with
incremental improvements in filtration
efficiency.
At a mask effective filtration efficiency
of 0.5 (50%), the conditional
infection probability is reduced by
a factor of 4 relative to the no-mask
baseline. With all occupants wearing
a mask with an effective filtration
efficiency of 0.9 (90%), the
conditional infection probability
is reduced by a factor of 100 relative
to the no-mask baseline. This
is due to the 10× decrease in quanta
discharged into the room due to
mask capture combined with the 10×
decrease in quanta inhaled through
the mask, resulting in a total reduction
of a factor of 100.
Figure 2 shows the effect of ventilation
rate in a well-mixed room on
the conditional probability of infection
when no occupants are wearing
masks. As the ventilation rate
increases from the no airflow case,
the conditional probability of infection
decreases at a somewhat rapid
rate, but then begins to level out.
For example, increasing the ventilation
rate by a factor of ~3.8, from the
baseline case of 1.34 ach to 5.05 ach,
yields a conditional probability of
16
ASHRAE JOURNAL ashrae.o rg
TABLE 1 Fixed and variable parameters included in the modified Wells-Riley model to predict conditional probability
of infection for each of the three scenarios.
PARAMETER
VR
NACH
λS
k
λ
tD
ηf,M
DESCRIPTION
Room Volume
Room Air Change Rate
Particle Settling Loss Rate
Virus Decay (Inactivation)
Rate
Total Loss Rate
Duration Occupant is in
Room
Effective Mask Filtration
Efficiency
VALUE
362.64 m3
1.34 h-1
0.35 h-1
0.63 h-1
2.32 h-1
60 min.
-
FIXED/VARIABLE
Fixed
Variable
Fixed
Fixed
Variable
Fixed
Variable
SOURCE
Facility Information
Current Study,
Field-Measured
Current Study
Buonanno, et al.,6 and
van Doremalen, et al.7
λ = NACH+λS + k
50 min. Class Period +
10 min. Before/After
Baseline = 0, Other Values
As-Measured
FIGURE 1 Conditional probability of infection for each of the three case scenarios as a function of effective
mask filtration efficiency. KCM-knit cotton mask, PM-procedure mask, SM-surgical mask, EOCM-emergency
operations committee mask, -C = commercial brace, -U = UW fitter.
0.18
6
4
2
0.018
6
4
2
0.0018
6
4
2
0.0001
0.00
0.10
0.20
0.30
0.40
.050
ηf,M (-)
FIGURE 2 Conditional probability of infection for each of the three case scenarios as a function of ventilation
rate in a well-mixed room.
0.18
6
4
2
0.018
6
4
2
0.0018
6
4
2
0.0001
0.0
1.0
2.0
3.0
4.0
5.0
NACH (h-1)
J U N E 2021
6.0
7.0
8.0
9.0
10.0
NACH (1.34 h-1)
NACH (5.05 h-1)
Scenario A
Scenario B
Scenario C
0.60
0.70
0.80
0.90
1.00
EOCM-C
KC PM KCM-U KCM-C
M
SM EOCM
EOCM-U
Scenario A
Scenario B
Scenario C
PM-U
SM-U
PM-C
SM-C
P (-)
P (-)
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ASHRAE Journal - June 2021

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