1
00:00:10,450 --> 00:00:12,540
PROFESSOR: So this
brings us to the conclusion

2
00:00:12,540 --> 00:00:16,620
of our Massive Open Online
Course, 10.S9,5 Physics

3
00:00:16,620 --> 00:00:18,990
of COVID-19 Transmission.

4
00:00:18,990 --> 00:00:21,180
So let's briefly review
what we've learned.

5
00:00:21,180 --> 00:00:23,550
We began by talking about
respiratory pathogens,

6
00:00:23,550 --> 00:00:25,740
both bacteria and viruses.

7
00:00:25,740 --> 00:00:27,630
And, in particular,
we focused on viruses

8
00:00:27,630 --> 00:00:30,180
and understood how
they can be transmitted

9
00:00:30,180 --> 00:00:35,010
through aerosol particles
through infected indoor air.

10
00:00:35,010 --> 00:00:38,670
And this includes the
important case of SARS-CoV-2,

11
00:00:38,670 --> 00:00:41,790
the virus that causes COVID-19.

12
00:00:41,790 --> 00:00:44,280
We then went on to use
epidemiological models

13
00:00:44,280 --> 00:00:48,330
and fluid-mechanical
analysis of a well-mixed room

14
00:00:48,330 --> 00:00:51,420
to arrive at a universal
indoor safety guideline

15
00:00:51,420 --> 00:00:53,970
to limit transmission
of the disease.

16
00:00:53,970 --> 00:00:57,480
A very important
conclusion is that it's not

17
00:00:57,480 --> 00:00:59,790
possible to bound
a single variable,

18
00:00:59,790 --> 00:01:04,170
as in all of the current
safety guidelines

19
00:01:04,170 --> 00:01:06,190
from various official
organizations.

20
00:01:06,190 --> 00:01:09,630
So, for example, you cannot
only bound the distance between

21
00:01:09,630 --> 00:01:12,160
people, for example,
6 feet, 1 meter.

22
00:01:12,160 --> 00:01:16,050
You cannot bound only the
occupancy, say, 25 persons.

23
00:01:16,050 --> 00:01:18,390
You can't even bound the
ventilation rate, say,

24
00:01:18,390 --> 00:01:22,320
a minimum of 15 cubic feet
per minute per person.

25
00:01:22,320 --> 00:01:24,240
Or you can't bound
only the time--

26
00:01:24,240 --> 00:01:26,580
let's say 15 minutes
or one hour--

27
00:01:26,580 --> 00:01:29,970
because all of these variables
are, inevitably, linked.

28
00:01:29,970 --> 00:01:33,360
And the simplest way to see that
is through our universal safety

29
00:01:33,360 --> 00:01:35,700
guideline, which
shows you how to limit

30
00:01:35,700 --> 00:01:39,120
the cumulative exposure time,
(N-1)t, which

31
00:01:39,120 --> 00:01:40,830
is a product of the
number of susceptible

32
00:01:40,830 --> 00:01:43,020
people in a room times
the time they're together

33
00:01:43,020 --> 00:01:45,030
with an infected person.

34
00:01:45,030 --> 00:01:47,430
And there are a number
of factors that come in.

35
00:01:47,430 --> 00:01:49,860
So epsilon is a
tolerance you can choose.

36
00:01:49,860 --> 00:01:53,490
And then there are these factors
lambda_V over --

37
00:01:53,490 --> 00:01:56,789
Q_b^2 P_m^2 Cq.

38
00:01:56,789 --> 00:02:01,470
And we can discuss, based on
that formula and our analysis

39
00:02:01,470 --> 00:02:04,680
throughout this course,
the most important ways

40
00:02:04,680 --> 00:02:07,300
of mitigating transition
based on this formula.

41
00:02:07,300 --> 00:02:09,520
So I've, roughly, put
them in order here.

42
00:02:09,520 --> 00:02:12,450
So the first thing is to wear
masks and, in particular,

43
00:02:12,450 --> 00:02:13,950
try to wear good masks.

44
00:02:13,950 --> 00:02:17,610
So these might be
surgical masks, N95s,

45
00:02:17,610 --> 00:02:21,120
but even various cloth
or silk masks, especially

46
00:02:21,120 --> 00:02:23,760
double-layer fabrics,
can be quite effective

47
00:02:23,760 --> 00:02:27,150
because, as P_m goes to 0,
the mask penetration factor,

48
00:02:27,150 --> 00:02:29,220
you can see this bound
gets larger and larger,

49
00:02:29,220 --> 00:02:30,510
like P_m^2.

50
00:02:30,510 --> 00:02:33,300
So a factor of 10%
transmission can still

51
00:02:33,300 --> 00:02:35,610
give you a factor of 100
compared to not wearing

52
00:02:35,610 --> 00:02:37,380
masks in terms of filtration.

53
00:02:37,380 --> 00:02:39,780
That's a very
significant amount.

54
00:02:39,780 --> 00:02:42,220
Secondly, we can
improve ventilation.

55
00:02:42,220 --> 00:02:45,480
And this can be by imposing
faster mechanical ventilation

56
00:02:45,480 --> 00:02:48,000
with more fresh air coming in.

57
00:02:48,000 --> 00:02:51,010
It could also be by opening a
window and turning on a fan.

58
00:02:51,010 --> 00:02:52,740
And that's increasing lambda_a.

59
00:02:52,740 --> 00:02:56,130
We can also try to spend more
time in larger rooms or even

60
00:02:56,130 --> 00:02:58,920
outside, which is,
basically, increasing V

61
00:02:58,920 --> 00:03:02,020
and, thereby, diluting
the air that is present

62
00:03:02,020 --> 00:03:04,320
and all the infectious aerosols.

63
00:03:04,320 --> 00:03:06,640
We can also look at
imposing air filtration.

64
00:03:06,640 --> 00:03:08,520
We've shown that there
is some benefit there.

65
00:03:08,520 --> 00:03:10,520
Although, it might not
be as large as you think.

66
00:03:10,520 --> 00:03:12,990
Even very good air
filtration doesn't

67
00:03:12,990 --> 00:03:15,390
buy you many orders of
magnitude because it's only

68
00:03:15,390 --> 00:03:17,310
filtering some of the
air, but not all of it,

69
00:03:17,310 --> 00:03:20,010
compared to masks, which
are filtering at the source

70
00:03:20,010 --> 00:03:23,760
and at the target and, thereby,
are much more effective.

71
00:03:23,760 --> 00:03:28,950
We can also try to make sure the
occupants of the room maintain

72
00:03:28,950 --> 00:03:30,560
lower activity
levels if possible.

73
00:03:30,560 --> 00:03:31,980
So they're breathing
less heavily.

74
00:03:31,980 --> 00:03:35,730
So they're exchanging air with
the space and with other people

75
00:03:35,730 --> 00:03:38,290
less frequently and
at a lower rate.

76
00:03:38,290 --> 00:03:42,570
We can also try to avoid
vocal exertions, which

77
00:03:42,570 --> 00:03:45,600
tend to lead to much larger
emissions of droplets,

78
00:03:45,600 --> 00:03:48,060
for example, singing being
a particularly bad case,

79
00:03:48,060 --> 00:03:51,480
but even loud voices can be a
lot worse than quiet voices.

80
00:03:51,480 --> 00:03:56,040
So, generally, keeping the
noise in the room down--

81
00:03:56,040 --> 00:03:59,079
I know this will be welcome
news for many teachers--

82
00:03:59,079 --> 00:04:00,720
but, in general,
that is a good way

83
00:04:00,720 --> 00:04:05,190
to try to limit transmission
to keep people calm.

84
00:04:05,190 --> 00:04:07,080
We can also take measures
to try to enhance

85
00:04:07,080 --> 00:04:10,350
the deactivation, the
natural elimination

86
00:04:10,350 --> 00:04:13,590
of the infectiousness
of the virus.

87
00:04:13,590 --> 00:04:14,970
One way to do that
is to maintain

88
00:04:14,970 --> 00:04:17,070
an intermediate, comfortable
range of humidity

89
00:04:17,070 --> 00:04:18,390
from 50% to 80%.

90
00:04:18,390 --> 00:04:21,779
So very dry air turns
out to be worse,

91
00:04:21,779 --> 00:04:24,660
and that is one of the reasons
that viral diseases tend

92
00:04:24,660 --> 00:04:26,720
to be seasonal, like the
seasonal flu, typically,

93
00:04:26,720 --> 00:04:28,890
worse in winter, in addition
to the fact that you're

94
00:04:28,890 --> 00:04:30,890
spending more time indoors.

95
00:04:30,890 --> 00:04:33,400
There's also ultraviolet
treatments that might be used,

96
00:04:33,400 --> 00:04:36,820
which is, effectively, like
another form of filtration.

97
00:04:36,820 --> 00:04:38,200
And then, finally,
we spent a lot

98
00:04:38,200 --> 00:04:41,140
of time talking about the fluid
mechanics of indoor spaces

99
00:04:41,140 --> 00:04:43,420
and of human respiration
and movement,

100
00:04:43,420 --> 00:04:47,530
and those considerations take
us beyond the well-mixed room.

101
00:04:47,530 --> 00:04:49,090
And the main thing
to remember there

102
00:04:49,090 --> 00:04:52,300
is, thinking back to our example
of people who are smoking,

103
00:04:52,300 --> 00:04:55,630
if someone is exhaling right
after breathing in a cigarette,

104
00:04:55,630 --> 00:05:01,350
there's sort of a narrow plume
of turbulent, very smoky air,

105
00:05:01,350 --> 00:05:02,680
which you want to avoid.

106
00:05:02,680 --> 00:05:04,330
And the same thing
is true when dealing

107
00:05:04,330 --> 00:05:05,920
with a respiratory
pathogen. You don't

108
00:05:05,920 --> 00:05:08,770
want to spend a lot of time in
the respiratory jet of a person

109
00:05:08,770 --> 00:05:12,520
who is not wearing a mask if
you don't know if they are sick,

110
00:05:12,520 --> 00:05:14,850
potentially, even asymptomatic.

111
00:05:14,850 --> 00:05:17,020
So that's an important just
general piece of advice,

112
00:05:17,020 --> 00:05:19,960
and we've given some insight
into how to quantify that.

113
00:05:19,960 --> 00:05:23,920
Although, any treatment of
short-range transmission

114
00:05:23,920 --> 00:05:25,960
through respiratory
jets is, inevitably,

115
00:05:25,960 --> 00:05:29,300
dependent upon assumptions
about the activity of the room.

116
00:05:29,300 --> 00:05:30,760
How much are you
turning your head?

117
00:05:30,760 --> 00:05:31,760
Where are people placed?

118
00:05:31,760 --> 00:05:34,630
And so, hence, you can't really
get a universal guideline,

119
00:05:34,630 --> 00:05:37,330
as opposed to this boxed
formula, which is, essentially,

120
00:05:37,330 --> 00:05:38,830
the mass balance
for the whole room.

121
00:05:38,830 --> 00:05:40,870
And that is a
universal guideline.

122
00:05:40,870 --> 00:05:43,180
We've also talked a bit
about types of ventilation.

123
00:05:43,180 --> 00:05:46,240
And, as opposed to ventilation
that seeks to mix the space,

124
00:05:46,240 --> 00:05:48,790
there may be situations
where having high ceilings

125
00:05:48,790 --> 00:05:52,720
and trying to take advantage of
buoyancy-driven thermal flows

126
00:05:52,720 --> 00:05:56,320
that you can sort of target the
airborne aerosols to be sitting

127
00:05:56,320 --> 00:05:58,720
higher in a room where
they could then be removed

128
00:05:58,720 --> 00:06:01,630
by ventilation at the top, which
is displacement ventilation.

129
00:06:01,630 --> 00:06:04,010
That's another strategy
that may be useful.

130
00:06:04,010 --> 00:06:06,620
So these are all different
strategies one can use.

131
00:06:06,620 --> 00:06:08,290
And which one is most
effective or makes

132
00:06:08,290 --> 00:06:12,040
the most sense in a given space
really depends on the details.

133
00:06:12,040 --> 00:06:15,250
And, in order to facilitate the
application of the guideline,

134
00:06:15,250 --> 00:06:18,610
we have provided an
online app and, also,

135
00:06:18,610 --> 00:06:21,250
a spreadsheet, which you
can use to adapt this

136
00:06:21,250 --> 00:06:23,200
to your own space.

137
00:06:23,200 --> 00:06:25,330
And I hope that you will
find the principles you've

138
00:06:25,330 --> 00:06:27,190
learned in this class
useful and that,

139
00:06:27,190 --> 00:06:29,200
perhaps, even you'll
find these tools useful,

140
00:06:29,200 --> 00:06:33,070
specifically, to combat the
transmission of COVID-19

141
00:06:33,070 --> 00:06:36,630
and, in the future, other
respiratory diseases.