Covid-19 Risk Among Airline Passengers: Should the Middle Seat Stay Empty?
Abstract
We use recent data and research results to approximate the probability that an air
traveler in coach will contract Covid-19 on a US domestic flight two hours long, both
when all coach seats are full and when all but middle seats are full. The point estimates
we reach based on data from late June 2020 are 1 in 4,300 for full flights and 1 in 7,700
when middle seats are kept empty. These estimates are subject to both quantifiable
and nonquantifiable sources of uncertainty, and sustain known margins of error of a
factor about 2.5. However, because uncertainties in key parameters affect both risk
estimates the same way, they leave the relative risk ratio for “fill all seats” compared to
“middle seat open” close to 1.8 (i.e., close to 1/4,300)/(1/7,700). We estimate the
mortality risks caused by Covid-19 infections contracted on airplanes, taking into
account that infected passengers can in turn infect others. The point estimates—which
use 2019 data about the percentage of seats actually occupied on US flights--range from
one death per 400,000 passengers to one death per 600,000. These death-risk levels
are considerably higher than those associated with plane crashes but comparable to
those arising from two hours of everyday activities during the pandemic.
Arnold Barnett
Sloan School of Management
MIT
Cambridge, MA 02142
abarnett@mit.edu 617 686-1485 E62-568, MIT
(George Eastman Professor of Management Science, Professor of Statistics)
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2
Introduction
Among the many ways the Covid-19 crisis is unprecedented is a public disagreement
1
among US airlines on a safety question. As of July 2020, Alaska, Delta, jetBlue, and Southwest
2
Airlines are keeping middle seats open on their flights to limit infection risk, while Allegiant,
3
American, Spirit, and United Airlines are selling all seats when demand warrants. United
4
Airlines has vigorously defended its policy, describing “middle seats only” as a “PR strategy and
5
not a safety strategy.“ Its chief communications officer depicted social distancing as impossible
6
on an airplane, saying:
7
“When you're on board the aircraft, if you're sitting in the aisle, and the middle seat is
8
empty, the person across the aisle from you is within six feet of you. The person at the
9
window is within six feet of you. The people in the row in front of you are within six feet
10
of you. The people in the row behind you are within six feet of you."
11
Yet prominent experts have expressed dismay at the “fill all seats” policy. When
12
American Airlines announced that it would sell as many seats as it could, Dr. Anthony Fauci, the
13
top infectious diseases official at the US National Institutes for Health, told a Senate hearing
14
that "obviously, that's something that is of concern." Dr. Robert Redfield, the director of the US
15
Centers for Disease Control and Prevention, agreed, declaring that "I can tell you that when
16
they announced that the other day, obviously there was substantial disappointment with
17
American Airlines,"
18
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3
Motivated by this disagreement, this paper is an attempt to estimate the level of risk to
19
US airline passengers under both “middle seats empty” and “fill all seats” policies. Making
20
those estimates entails major complications and uncertainties, which can easily lead one to
21
throw up one’s hands. But even a rough approximation of the risks at issue seems preferable
22
to clashes of unsubstantiated conjectures. This paper strives for such an approximation.
23
As we will discuss, a first-order estimate is that coach passengers on full flights two
24
hours long on popular US jets suffer a 1 in 4300 risk of contracting Covid-19 from a nearby
25
passenger. Under “middle seat empty,” the risk is approximately 1 in 7700, a factor of 1.8
26
lower. Both these estimates are subject to sizable quantifiable and unquantifiable
27
uncertainties, though the factor of 1.8 is considerably less so. Given these estimates and some
28
others, one could expect approximately one death from Covid-19 per 400,000 passengers on
29
flights by airlines that would sell all seats if they could. Under “middle seat empty,” the
30
corresponding figure is about one death per 600,000 passengers.
31
Materials and Methods
32
To estimate the risk to an uninfected passenger from a passenger experiencing Covid-19, it
33
is necessary to consider three questions:
34
• What is the probability that a given passenger on board is contagious with Covid-19?
35
• What is the probability that universal masking can prevent a contagious passenger from
36
spreading the disease?
37
• How does the risk of infection depend on the locations on the aircraft of both the
38
contagious and uninfected passenger?
39
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4
The general formula for combining the answers to these questions is:
40
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"#$%$
&
%$
'
(I)
41
where P= the probability that a particular uninfected passenger contracts Covid-19 during the
42
flight
43
Q = the probability that a given passenger on the flight has covid-19
44
(It is assumed the Q is small enough that having two or more contagious passengers
45
near the uninfected one is a remote risk.)
46
Q
M
= the probability that universal mask-wearing on aircraft fails to prevent
47
transmission of Covid-19
48
Q
L
= the conditional probability that a contagious passenger transmits Covid-19 to the
49
uninfected one if the mask fails
50
Q
L
and thus P can depend on whether the operating policy is “fill all seats” or “middle seat
51
empty”
52
In the forthcoming analysis, we make estimates of these three quantities. Among the
53
primary assumptions underlying these estimates are:
54
1. The number of actual cases of Covit-19 in the US is a large multiple of the number of
55
confirmed cases. However, asymptomatic carriers of the disease are considerably less
56
contagious than pre-symptomatic and symptomatic ones, and air travelers are
57
considerably less likely to be contagious than the citizenry as a whole.
58
2. All passengers are wearing masks, and masks are highly effective at preventing
59
transmission of Covid-19.
60
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5
3. An uninfected passenger is only threatened with Covid-19 by a contagious passenger
61
sitting in the same row, the row ahead, or the row behind. Because of strong air-
62
purification mechanisms on aircraft, the risks posed by other passengers are of
63
secondary importance.
64
Specifically:
65
The Estimation of Q
66
For a given passenger from a particular American state, the risk of contagiousness is
67
estimated in several steps:
68
• First, one finds N
7
, the number of confirmed new Covid-19 infections in that state over
69
the last seven days [1)]. Seven days is chosen because that is the approximate length of the
70
contagiousness period for someone experiencing Covid-19. (The average such period is a
71
bit below seven days in asymptomatic cases and higher than seven in symptomatic ones;
72
see [2,3].)
73
• One then divides N
7
by N
POP
, the state’s estimated population in 2020, to obtain
74
N
7
/N
POP
as the state’s per capita rate of new confirmed cases over the last week.
75
• Then, in accordance with recent estimates from the US Centers for Disease Control [4] ,
76
one multiplies N
7
by ten to approximate the actual number of new infections in the state
77
over the previous week.
78
• Then one recognizes that people with Covid-19 who board airplanes are presumably
79
either asymptomatic, pre-symptomatic, or mildly symptomatic. (Those with severe
80
symptoms are unlikely to be flying.) Because of evidence that asymptomatic Covid-19
81
carriers constitute about 40% of all carriers and are only about 40% as contagious as the
82
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6
others [5], one multiplies the prior product by a factor of ¾. (This factor of ¾ arises because
83
the number of contagious passengers with Covid-19 is approximately .4*.4 + .6*1 = .76 of
84
the number of passengers with the disease.)
85
• Then one multiplies by a factor of ½ approximately to reflect of the premise that
86
passengers who fly are generally more affluent (and less likely to encounter Covid-19 risks)
87
than the citizenry at large. (This factor treats the half of the population less vulnerable to
88
the disease as 1/3 as likely to suffer it as the half that is more vulnerable. It further treats
89
air travelers as members of the less-vulnerable half.)
90
• Finally, one divides by N
POP
, the state’s estimated population in 2020, to obtain N
7
/N
POP
as
91
the state’s per capita rate of new confirmed cases over the last week.
92
The estimate of Q consistent with these specifications is:
93
!!!!!!!!!!!!!!!$!(!)*
+
%
)
!,-
.
%
/
0
1
2
%
/
3
4
2
.5*
676
!#!89:;*
+
5*
676
(I)
94
<=>!?@ABCDABEF!EG!$
&
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
95
96
Here we assume that all passengers wear masks. For Q
M
, a meta-analysis in The Lancet
97
by Chu et al [6] estimated that mask wearing cuts transmission risk given contagiousness from
98
17.4% to 3.1%, a reduction of 82%. Ignoring the possibility that the masks under study were
99
more effective than those worn by airline passengers, we estimate Q
M
as 1 - .82 = .18.
100
The Estimation of
$
'
101
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7
In this analysis, we focus on the coach section of a Boeing 737 or Airbus 320 jet and a
102
flight of two hours (which is about average for a US domestic flight). In a given row, there are
103
six seats: with A, B, and C (the window, middle, and aisle seats, respectively to the left of the
104
aisle,) and D, E, and F (respectively the aisle, middle and window sets right of the aisle).
105
We focus on a particular passenger who is traveling alone, and assume that the primary
106
infection risk for this passenger arises from other passengers in the same row. We further
107
assume that additional risk arises from passengers in the row ahead and row behind. For two
108
reasons, we treat the risk posed by other passengers as negligible:
109
• We posit that the airlines are correct when they contend that the powerful
110
air-purification systems on jet aircraft largely negate the risk of aerosol
111
transmission of Covid-19. Thus, when a contagious passenger is in her seat in
112
row 22, she poses little risk to another traveler seated in row 14.
113
• A study by Hertzberg et. al. in the Proceedings of the National Academy of
114
Sciences [7] suggested that infection risk depends on the duration of exposure to
115
contagious person (as did Brundage [8]). We accept this premise, which implies
116
there is limited risk posed by (say) a contagious passenger who passes one’s row
117
en route to the lavatory. Moreover, we treat the risks associated with boarding
118
the aircraft, leaving the aircraft, visiting the lavatory, and touching surfaces in
119
the passenger cabin, as second-order effects. If this assumption understates
120
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8
such risks, then the infection estimates presented here would be construed as
121
lower-bounds on Covid-19 risk.
122
A given passenger can get infected, however, by droplets from a contagious passenger
123
in the same row. But here the risk depends on the distance between the two passengers. The
124
meta-analysis of more than 100 studies in The Lancet (Chu et al, 2020; [6]) yields the
125
approximation that infection risk is about 13% given physical contact with the contagious
126
person, and that it falls by essentially a factor of two as the distance from that person increases
127
by one meter. The equation reflecting this pattern of exponential decay is:
128
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!H
I
!(-9,8%>
J9KLM
(II)
129
where d = distance in meters between contagious and uninfected person
130
This formula assumes no barriers between the contagious and uninfected persons. If
131
there were (say) a layer of plexiglass between the two, then transmission risk would essentially
132
drop to zero.
133
In each coach row in a Boeing 737 or an Airbus 320, the individual seats are
134
approximately 18 inches wide, while the aisle width is about 30 inches. Under the “fill all seats”
135
policy on a full flight, all six of the ABCDEF seats will be occupied. Under “no middle seats,” A/C
136
and D/F will be occupied on a full flight but not B/E. Assuming that (II) refers to passengers
137
without masks, one can use it to estimate the transmission risk posed by others in the same
138
row to an A-seat passenger, given that the contagious passenger’s mask fails (as happens with
139
probability Q
M
):
140
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9
$
'
)
N!@DC>!OEP
.
(!!
Q
H
I
)
NRS
.
T!H
I
)
NRU
.
T!H
I
)
NRV
.
!WFX>O!
middle seat open
!
!H
I
)
NRY
.
TH
I
)
NRS
.
TH
I
)
NRU
.
T!H
I
)
NR?
.
TH
I
)
NRV
.
!WFX>O!ZGB[[!D[[!@>DA@Z
!!!!!!
141
(III)
142
where
H
I
)
NR\
.
#!
transmission probability absent masks given a contagious passenger in seat X
143
of a given row and an uninfected passenger in seat A of that row
144
Equation (III) taken literally treats infections caused by passengers in different seats as
145
mutually exclusive events. But they are not mutually exclusive: it is possible that
146
contagious persons are seated in both seats 16C and 16F. The actual assumption –
147
consistent with data--is that Q is small enough that having several contagious people
148
close to one another is a second-order effect, with probabilities involving Q
2
or higher
149
powers of Q. In practical terms, therefore, the events of interest are mutually
150
exclusive.
151
We therefore make the approximation that:
152
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!H
I
)
NR\
.
!(!9,8>
J9KLM)]R^.
!!!!!!!
(IV)
153
where d(A,X) = distance from a person’s head in the middle of seat A to another
154
person’s head in the middle of seat X.
!
155
For the jets under consideration, the quantity d(A, B) is about 18 inches, while
156
d(A,C) is 18+18= 36 inches, d(A, D) =36 + 9 + 30 + 9 = 84 inches, d(A, E) =84+18= 102
157
inches, and d(A,F) = 102 + 18= 120 inches Because a meter is 39.37 inches, d(A,B) in
158
meters is 18/39.37 = .457
!R_`a9!!
159
Analogous expressions arise when the uninfected passenger is in the B, C, ..F seat.
160
One can use (III) and (IV) to obtain:
161
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10
$
'
)
N!@DC>!OE P
.
(!!
Q
!!-9,,;!!bcd_e!
middle seat empty
!
-9f8f!!!!!!Wcd_e!Zghii!jii!k_j`kZ
!
162
Using similar reasoning, one can likewise determine that:
163
$
'
)
Y!@DC>!OEP
.
!(9flf!bcd_e!Zghii!jii!k_j`kZ
164
$
'
)
S!@DC>!OEP
.
(!!
Q
!!!-9,;;!!bcd_e!
middle seat empty
!
-9fm,!!!!!!Wcd_e!Zghii!jii!k_j`kZ
!
165
$
'
)
U!@DC>!OEP
.
#!$
'
)
S!@DC>!OEP
.
n!!
166
$
'
)
?!@DC>!OE P
.
#!$
'
)
Y!@DC>!OEP
.
n!!
167
$
'
)
V@DC>!OEP
.
#!$
'
)
N!@DC>!OEP
.
n!!
168
Averaging across all the passengers in a given row yields:
169
$
'
)
@DC>!OEP
.
#!
Q
9fol!WFX>O!Zghii!jii!k_j`kZ!!!!!!!!!!!
!
9,8;!WFX>O!CBXX[>!@>DA!>CpAq
170
Hertzberg et al [7} concluded from their computer simulations that, for droplet-
171
mediated respiratory diseases, contagious passengers pose appreciable transmission risk to
172
uninfected travelers within one meter. They therefore concluded that, beyond the same row,
173
transmissions can occur from passengers in the row ahead of an uninfected passenger and in
174
the row behind. Here we process distances using (III) rather than a one-meter yes/no
175
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11
threshold, but we concur that passengers in the two neighboring rows pose first-order
176
transmission risk.
!
177
In Hertzberg et. al. all contagious passengers within one meter pose equal levels of
178
transmission risk, regardless of whether they are in the same row as the uninfected passenger.
179
However, the authors noted that they did not consider the possibility that seatbacks would
180
impede transmissions between rows. Here we do not ignore that possibility.
181
While seatbacks can somewhat block droplets from a contagious passenger, they are
182
presumably less effective than plexiglass, which all but eliminates transmission. Lacking
183
available studies about the benefit conferred by seatbacks, we make the estimate that they are
184
about ¾ as effective as plexiglass. More specifically, we assume that:
185
• When the flight is full, the six passengers one row ahead of the uninfected passenger
186
collectively pose ¼ the transmission risk of the five passengers in the same row.
187
• When the flight is full, the six passengers one row behind the uninfected passenger
188
collectively pose ¼ the transmission risk of the five passengers in the same row.
189
• When the flight follows “middle seats empty” but is otherwise full, the four passengers
190
one row ahead of the uninfected passenger collectively pose 2/3 the transmission risk of
191
the six passengers in that row had the flight been full.
192
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12
• When the flight follows “middle seats empty” but is otherwise full, the four passengers
193
one row behind the uninfected passenger collectively pose 2/3 the transmission risk of
194
the six passengers in that row had the flight been full.
195
If this factor-of-four reduction overstates the effectiveness of the seatbacks against contagion,
196
then our risk estimates tied to neighboring rows could well be too low.
197
Under these approximations:
198
$
'
)
GW[[!G[Br=A
.
#,9;$
'
)GW[[!G[Br=AR@DC>!OEP.
$
'
)
CBXX[>!@>DA!>CpAq
.
#$
'
)
CBXX[>!@>DA!>CpAqR@DC>!OEP
.
T
s
f
8
t
%
s
,
f
t
$
'
)
GW[[!G[Br=A!@DC>!OEP
.
199
Thus:
200
$
'
#!
Q
!!!!9u-f!!GEO!GW[[!G[Br=A!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!9ffu!!P=>F!CBXX[>!@>DA!>CpAq!!!!!!!!!!!!!!
201
We should stress that Equation (II) summarizes the experiences reported in many
202
disparate studies, probably none of which reflects the exact conditions in a US jet flight two
203
hours long. The risk of infection presumably relates to duration of exposure, but the durations
204
in the summarized studies are often unknown. Moreover, US airlines have argued convincingly
205
that ventilation during their flights suppresses disease spread more effectively than that in a
206
typical indoor setting. Yet the mix of environments in the studies that contributed to (II) is not
207
clear. It is also understood that disease spread is greater when the contagious person is
208
speaking than when he is silent. But the proportional breakdown of exposure time between
209
speaking and silence is unavailable, both for airplanes and in the summarized studies.
210
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13
A further complication is that, while we are assuming that Equation (II) arises when the
211
contagious person wears no mask, there were apparently some masked individuals in the
212
studies that generated the equation (private communication from Dr. Chu). As noted, we
213
apply an 82% reduction in infection risk because of masks, but (II) already reflects the benefit of
214
masks to some extent.
215
These circumstances need not compromise the exponential-decay factor in (ii), under
216
which transmission risk drops by a factor of two per meter of distance. But the 13% factor
217
could well be affected, with some considerations suggesting the factor is too high and others
218
that it is too low. This analysis offers a baseline risk estimate using the Chu et al. results at face
219
value, which seems reasonable absent further information about the combinations of
220
conditions that underlie those results.
221
When the estimates of Q, Q
M
, and Q
L
are at hand, they are multiplied under (I) to obtain
222
a point estimate of P.
223
Confidence Intervals for the Point Estimates
224
The point estimates of Covid-19 risk are subject to various sources of uncertainty, some
225
of them subject to quantification. The basic relationship:
226
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"!($%$
&
%$
v
(I)
227
can be rewritten as: !
228
[F"!([F$T
14
roughly half the point estimate to double that estimate), and the estimation errors for different
232
variables can be considered independent. Thus, lnP would be essentially normal, and a 95%
233
confidence interval for P can be obtained through exponentiating the 2.5%ile and 97.5%ile of
234
lnP. The calculated confidence intervals pertain to known uncertainty in the risk estimates,
235
and not to the uncertainties in Equation (II) discussed above.
236
Results
237
Point Estimates
238
New confirmed covid-19 cases were sharply increasing in many American states during
239
the last week of June 2020, but continuing to decline in others. Exemplifying the states
240
experiencing spikes was Texas, with 42,254 new cases over 6/24/20 to 6/30/20, while typifying
241
states long past their peaks of new infections was New York, with 5,200 cases over that period.
242
Because the population of Texas in 2020 was estimated at 29.1 million in mid-2020, its per
243
capita rate of new infections that week (i.e., N
7
/N
POP
) was 1/689. For New York, with a
244
population of 19.5 million, the corresponding rate was 1/3750.
245
Under (I), the probability a passenger from a particular state has contagious covid-19 is
246
approximated by:
247
!
Q
(!
3.75(N
7
/N
POP
)
248
Meaning that:
249
$!(!
w
3
3x1
!!GEO!<>y D@!!!!!!!
!
3
3zzz
!!GEO!*>P !{EO|
250
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15
For US domestic jet flights as a group, one might approximate Q by taking the average of
251
these estimates for higher-infection-rate Texas and lower-rate New York, which yields
$!(
3
03z
252
Even on a flight from Dallas to New York City, there will be Texas natives, New York natives, and
253
transfer passengers who originated elsewhere, so a mid-range estimate seems suitable. Had
254
we instead used new infections over a week in mid-July 2020 (when this is written), the
255
estimate of Q would have increased by a factor of 1.6. We use the late June estimate in the
256
hope that the mid-July upsurge is temporary.
257
As noted, the probability Q
M
for mask failure is estimated as 0.18, while .402 and .224 are
258
treated as, respectively, the transmission probabilities absent masks (Q
L
) under “fill every seat”
259
and “middle seat empty.” In consequence, Equation (I) generates the following estimates for
260
dates around 6/30/20:
261
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)
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.
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•
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•
•
,
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,
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262
The first of these risk estimates is the average for the passengers in the six filled seats in each
263
row. The second is the average for passengers in the four seats occupied under “middle seat
264
empty.”
265
Confidence Intervals
266
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16
As noted earlier, there is nonquantifiable uncertainty in our use of Equation (II), related to
267
ventilation, speech/silence, duration of exposure, and mask usage. But the literature offers
268
margins of error in addition to point estimates for three parameters in the risk calculations:
269
• The 95% confidence interval for the rate of exponential decay with distance extends
270
from a factor of 1.08 per meter to a factor of 3.76. (We have used a point estimate of
271
two, corresponding to -0.69 in (II).)
272
• The 95% confidence interval for the failure probability of masks extends from .07 to
273
.34 (point estimate .18)
274
• The 95% confidence interval for the ratio of actual cases of Covid-19 to confirmed
275
cases extends from 8.7 to 12.7. (point estimate 10).
276
These confidence intervals suggest that the distributions for the parameter estimates can
277
be approximated as lognormal. For example, the interval for exponential decay goes from
278
about half the point estimate of two to roughly double that estimate. Treating
279
uncertainties in the three parameters as independent, we can estimate the overall degree
280
of imprecision that they (alone) cause in the estimate of P.
281
In the relationship based on (I):
282
In P = lnQ + lnQ
M
+ lnQ
L
,
283
the independence and normality of the three random variables on the right implies that lnP
284
itself is normally distributed. First we find the mean and standard deviations of lnQ, lnQ
M
, and
285
lnQ
L,
and then we use them to find the mean, standard deviation, and 95% confidence interval
286
for lnP.
287
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17
For lnQ
M
, we note that its 2.5
th
percentile is ln(.07) and its 97.5
th
percentile is ln(.34).
288
From this information and the assumption of lognormality, we readily deduce that the mean of
289
lnQ
M
is the average of ln(.07) and ln(.34), while its standard deviation is (ln(.34) – ln(.07))/3.92.
290
Because ln(.34) = -1.08 and ln(.07) = -2.66, ln(Q
M
) is approximately normal with mean -1.87
291
and standard deviation 0.40. The calculations for lnQ and lnQ
L
proceed similarly, with the
292
distribution for lnQ
L
dependent on whether the policy under study is “fill all seats” or “middle
293
seats empty.”
294
The 95% confidence intervals for P are:
295
Š
3
3zR‹zz
!AE
3
3R+zz
!!!GEO!GW[[!G[Br=A@!WFX>O!GB[[!D[[!@>DA@9!!!!!!!!
!
3
3LR0zz
!AE
3
0Rzzz
!GEO!GW[[!G[Br=A@!WFX>O!CBXX[>!@>DA!>CpAq
296
In both instances, there is factor-of-2.5 uncertainty in the point estimates offered earlier ( i.e.
297
3
1R0zz
!
for fill all seats,
3
+R+zz
!
for middle seats empty). It important to note, however, that the
298
two estimates of P arise from the same parameters, and that the uncertainty in those
299
parameters affects both estimates in essentially the same way. The upshot is that the ratio of
300
P(fill all seats) to P(middle seat empty), which is 1.8 based on the point estimates. i.e.,
301
(1/4,300)/(1/7,700)), would stay stable despite the considerable uncertainty that affects the
302
numerator and denominator of the ratio.
303
Discussion
304
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18
The reason that Covid-19 is so fearsome is that it entails a risk of death. For a coach
305
passenger with a 1% chance of dying from the virus—which is slightly above the chance of 0.7%
306
now assumed to apply to the full population [9]-- the estimated mortality risk on a full flight
307
two hours long would be about 1 in 430,000 and about 1 in 770,000 million when all but middle
308
seats are full. But even an airline willing to fill every seat does not expect to do so: it
309
presumably aspires to a passenger load factor (passenger miles divided by seat miles) around
310
85.1%, which prevailed in 2019 on US flights. Having 85.1% of seats taken is consistent with
311
roughly 55% of middle seats full and 45% empty. With that load factor, a 1% chance of dying
312
from Covid-19 given infection would yield a death risk under “fill all seats” of about 1 in 540,000
313
rather than 1 in 430,000. Airlines that keep middle seats empty could well try to fill nearly all of
314
them, so their mortality risk would remain about 1 in 770,000.
315
Actually, covid-19 infections on planes can cause deaths to some people who were not
316
passengers (e.g., a 22-year traveler gets infected, and passes the virus on to his elderly
317
grandparents). A quantity familiar in this pandemic is R
0,
the average number of new
318
infections generated directly by an infected person. The quantity E(Further Inf), the mean total
319
number of further infections that person causes, follows:
320
?
)
VWOA=>O!ŒFG
.
#
H
z
,•H
z
!!!!GEO!!H
z
!Ž, !!!!!!!!!!!!!!)•.
321
Using the conservative estimate that
H
z
#-9;R?
)
!VWOA=>O!ŒFG
.
#,!bcd_e!
)
•
.
9!
Assuming a
322
0.7% death risk for both the person infected on a flight and the people further infected, the
323
expected total number of deaths would be 0.007 + 1*.007 = .014. Thus, if a given passenger on
324
a full flight has a 1 in 4,300 chance of getting infected, the resulting number of deaths would on
325
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19
average be about (1/4300)*.014. = 1 in 310,000. If the flight is 85.1% full, the estimate would
326
decline to 1 in 390,000. If the flight is 66.7% full under middle seat empty, the estimate would
327
decline further to 1 in 550,000.
328
All these death-risk estimates are considerably higher than the risk of perishing in a US
329
air crash unrelated to Covid-19, which is about 1 in 34 million [10]). It is not clear, however,
330
that two hours spent on an airplane entails higher infection risk (or mortality risk) than two
331
hours of everyday activities. In late June 2020, approximately 45,000 Americans were
332
confirmed to have contracted Covid-19 each day. Given that actual infections are estimated to
333
be about ten times confirmed ones [4], roughly 450,000 new infections arose per day among
334
the 330 million Americans. That works out to a daily infection probability of
335
450,000/330 million, which is 1/733. Assuming 16 waking hours, the chance of infection over a
336
two-hour period would be approximately (2/16)*(1/733) = 1/5900, which is quite close to our
337
infectionrisk estimates for a two-hour flight. (If air travelers have lower Covid-19 risk than
338
average citizens—as we have assumed—that could be because they engage in relatively few
339
everyday activities (e.g. fewer rides on buses or visits to supermarkets)). But that circumstance
340
does not affect the risk estimate for such activities.)
341
Final Remarks
342
Calculations like the ones here are highly approximate and, as has been evident during
343
this pandemic, projections about it often fall far from the mark. It would therefore be
344
desirable to use actual passenger outcomes to determine what fraction of travelers contracted
345
Covid-19 on their flights. If, averaged over US carriers, the risk level per passenger is estimated
346
as (say) 1 in 6,500, then approximately 90 cases of Covid-19 should emerge each day at a time
347
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20
(like early July 2020) when 600,000 US passengers are flying daily. In reality, load factors fell
348
below 50% in July 2020 even on “fill all seats” airlines, meaning that the number of cases that
349
actually arose would be closer to 50 per day.
350
But it would not be easy to determine how many Covid-19 cases arose on US flights on a
351
given day. If only 10% of infections are confirmed, 50 infections would yield five confirmed
352
ones. Is it plausible that five of the 45,000 confirmed US infections per day arose during air
353
journeys over the previous week? Because follow-ups of known Covid-19 infections are now
354
weak in the US, it is not clear that the circumstances of those five infections would be
355
identified. Further complicating the situation is the fact that air passengers who subsequently
356
get Covid-19 may have been infected elsewhere besides the airplane. Despite these difficulties,
357
it would be worth some effort to substantiate or refute projections that are tied to strong
358
assumptions.
359
The calculations here, however imperfect, do suggest a measurable reduction
360
in Covid-19 risk when middle seats on aircraft are deliberately kept open. The question is
361
whether relinquishing 1/3 of seating capacity is too high a price to pay for the added
362
precaution.
363
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21
364
Acknowledgements
To be supplied
References
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Droplet-Mediated Respiratory Diseases During Transcontinental Airline Flights, Proceedings
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82: pp 819–823.)
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(8) E. Brundage (2020), “The Risks: Know Them, Avoid Them,” available at
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(10) A. Barnett (2020), “Aviation Safety: A Whole New World?” Transportation Science
54(1), pp. 84-96, January-February 2020,
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The copyright holder for this preprint this version posted August 2, 2020. ; https://doi.org/10.1101/2020.07.02.20143826doi: medRxiv preprint
23
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is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted August 2, 2020. ; https://doi.org/10.1101/2020.07.02.20143826doi: medRxiv preprint
