1
00:00:10,990 --> 00:00:14,050
PROFESSOR: So we've just
discussed the mass balance that

2
00:00:14,050 --> 00:00:17,680
results from considering
ventilation and breathing

3
00:00:17,680 --> 00:00:20,650
of an infected individual
in a room leading

4
00:00:20,650 --> 00:00:23,560
to a build up and
then steady state

5
00:00:23,560 --> 00:00:28,750
of aerosol droplets that are
infectious in the indoor air.

6
00:00:28,750 --> 00:00:31,180
We've also briefly
talked about masks.

7
00:00:31,180 --> 00:00:34,540
I'd now like to introduce the
possibility of filtration,

8
00:00:34,540 --> 00:00:38,530
which is actually very common in
mechanical ventilation systems.

9
00:00:38,530 --> 00:00:41,380
And then arrive at a
very simple comparison

10
00:00:41,380 --> 00:00:46,180
of filtration versus mask use
as strategies for preventing

11
00:00:46,180 --> 00:00:48,390
indoor transmission.

12
00:00:48,390 --> 00:00:51,190
So here's a schematic
sketch of the air flows.

13
00:00:51,190 --> 00:00:53,700
So basically, we
still have this Q,

14
00:00:53,700 --> 00:00:55,240
which is the outdoor air flow.

15
00:00:55,240 --> 00:00:57,580
So that is the air which is
coming in from the outdoors.

16
00:00:57,580 --> 00:00:59,760
And for mass balance, it
also has to be leaving.

17
00:00:59,760 --> 00:01:02,500
And the air change rate
is based on that Q.

18
00:01:02,500 --> 00:01:06,660
And in fact, if I remember, if
there's a volume V of the room,

19
00:01:06,660 --> 00:01:13,710
then the air change
rate was Q/V. So that's

20
00:01:13,710 --> 00:01:16,060
of units of inverse time.

21
00:01:16,060 --> 00:01:18,800
So that's the time,
roughly, it takes for--

22
00:01:18,800 --> 00:01:20,430
the residence time
for the outdoor air,

23
00:01:20,430 --> 00:01:22,050
and also for the
changing of the air.

24
00:01:22,050 --> 00:01:23,670
Now, in addition to
that, though, there

25
00:01:23,670 --> 00:01:26,130
could be significant
recirculation of air.

26
00:01:26,130 --> 00:01:29,780
Now, if the air is recirculating
but not filtering the droplets

27
00:01:29,780 --> 00:01:31,470
in any way, then
it really doesn't

28
00:01:31,470 --> 00:01:33,690
concern our calculation,
which is basically

29
00:01:33,690 --> 00:01:34,759
just a mass balance.

30
00:01:34,759 --> 00:01:37,140
So if I'm just swirling the
air around, or even taking it

31
00:01:37,140 --> 00:01:38,820
outside and back in,
as long as I'm not

32
00:01:38,820 --> 00:01:40,910
losing some droplets
in the ducts,

33
00:01:40,910 --> 00:01:43,080
then it really doesn't
matter if it's recirculating.

34
00:01:43,080 --> 00:01:46,050
But what is of interest to us
is if in that recirculation

35
00:01:46,050 --> 00:01:47,820
we lose some droplets.

36
00:01:47,820 --> 00:01:49,740
So some droplets
could be lost simply

37
00:01:49,740 --> 00:01:53,259
to settling on the walls
of the ducts or the heating

38
00:01:53,259 --> 00:01:57,420
and ventilation and air
conditioning, HVAC, unit.

39
00:01:57,420 --> 00:02:00,660
But more interesting
is to consider

40
00:02:00,660 --> 00:02:02,910
what would happen if we
actually placed filters, which

41
00:02:02,910 --> 00:02:05,640
is very common in HVAC systems.

42
00:02:05,640 --> 00:02:08,699
So we could either have
one of those big filters

43
00:02:08,699 --> 00:02:11,910
that you stick into the
heating or ventilation ducts.

44
00:02:11,910 --> 00:02:15,900
And those typically
are given MERV

45
00:02:15,900 --> 00:02:19,860
ratings, which are Mean
Efficiency Rating Values.

46
00:02:19,860 --> 00:02:24,000
And we're interested in
the filtration of aerosols.

47
00:02:24,000 --> 00:02:28,090
And so if Pf is the fraction of
the aerosols that are blocked--

48
00:02:28,090 --> 00:02:30,390
and we roughly would look at
a size range, for example,

49
00:02:30,390 --> 00:02:33,180
less than 5 micron radius--

50
00:02:33,180 --> 00:02:35,460
then the difference
of ratings of filters

51
00:02:35,460 --> 00:02:39,180
give you anywhere from
20% to 90% filtration.

52
00:02:39,180 --> 00:02:40,950
And then a very
high quality filter

53
00:02:40,950 --> 00:02:42,660
would be a so-called
Hepa filter,

54
00:02:42,660 --> 00:02:48,040
which is a High Efficiency
Particle Air filtration unit.

55
00:02:48,040 --> 00:02:53,040
And that would give you
even as high as 99.97%.

56
00:02:53,040 --> 00:02:56,370
And also, it's worth emphasizing
that you could also have

57
00:02:56,370 --> 00:02:57,850
a freestanding filtration unit.

58
00:02:57,850 --> 00:02:59,790
There are a variety of different
kinds of filtration units.

59
00:02:59,790 --> 00:03:02,310
It could be a fan which is
blowing through a Hepa filter.

60
00:03:02,310 --> 00:03:04,660
And it could be a
freestanding unit in the room.

61
00:03:04,660 --> 00:03:07,380
It could also be
more exotic systems,

62
00:03:07,380 --> 00:03:10,200
such as electrostatic
precipitators, where the air is

63
00:03:10,200 --> 00:03:12,790
flowing into a chamber that
has a very high electric field,

64
00:03:12,790 --> 00:03:14,460
and the droplets are
basically projected

65
00:03:14,460 --> 00:03:16,500
and deposited onto a surface.

66
00:03:16,500 --> 00:03:20,340
It could be flowing the air
through a UV-concentrated light

67
00:03:20,340 --> 00:03:22,030
treatment to kill the virus.

68
00:03:22,030 --> 00:03:24,360
So you're not actually
removing the droplets, per se,

69
00:03:24,360 --> 00:03:26,070
but you are removing the virus.

70
00:03:26,070 --> 00:03:27,810
And since we've
been keeping track

71
00:03:27,810 --> 00:03:30,360
of the concentration
of virions, they

72
00:03:30,360 --> 00:03:32,240
could be deactivated
in that way.

73
00:03:32,240 --> 00:03:33,660
And so all of that
can essentially

74
00:03:33,660 --> 00:03:37,760
be lumped into this simple
picture of a recirculating flow

75
00:03:37,760 --> 00:03:41,329
rate Qf, and a filtration
efficiency, Pf.

76
00:03:41,329 --> 00:03:44,860
So let's revisit our
equations from last time.

77
00:03:44,860 --> 00:03:49,780
So our mass balance
is at V dC dt

78
00:03:49,780 --> 00:03:55,079
is P, which is the production
rate of infectious air

79
00:03:55,079 --> 00:03:57,490
by an infected person.

80
00:03:57,490 --> 00:04:01,460
We have the removal of air
by the outer flow rate,

81
00:04:01,460 --> 00:04:02,810
which we've already discussed.

82
00:04:02,810 --> 00:04:07,360
And now we have the new
term which is Pf Qf.

83
00:04:07,360 --> 00:04:12,040
So if Pf is 1, then the
entire filtration flow

84
00:04:12,040 --> 00:04:14,200
is removing droplets.

85
00:04:14,200 --> 00:04:17,440
On the other hand, if Pf
is 0, this term goes away.

86
00:04:17,440 --> 00:04:19,690
And that's the limit where
you're simply recirculating

87
00:04:19,690 --> 00:04:21,230
air, but you're not
actually removing

88
00:04:21,230 --> 00:04:24,550
any infectious droplets,
and it's playing no role.

89
00:04:24,550 --> 00:04:29,190
So this is basically
our only new term here.

90
00:04:29,190 --> 00:04:33,180
And so what this means is
we get the same calculation,

91
00:04:33,180 --> 00:04:38,030
same as before, but we just have
to make a little replacement.

92
00:04:38,030 --> 00:04:41,030
What was before Q is now--

93
00:04:41,030 --> 00:04:43,220
notice we can lock-- oops,
I've forgotten, actually,

94
00:04:43,220 --> 00:04:47,490
here there should be
a C here, actually.

95
00:04:47,490 --> 00:04:52,570
Because the flow rate-- or
the flux of infectious air

96
00:04:52,570 --> 00:04:54,760
is the concentration
of infectious air, so

97
00:04:54,760 --> 00:04:58,680
the concentration of virions
per volume times the flow rate,

98
00:04:58,680 --> 00:05:01,150
that thing gives me
the correct value.

99
00:05:01,150 --> 00:05:03,690
So the Pf a dimensionless
number between 0 and 1.

100
00:05:03,690 --> 00:05:10,290
So anyway, Q gets
replaced by Q plus Pf Qf.

101
00:05:10,290 --> 00:05:13,910
And also, wherever we
saw a lambda a, that gets

102
00:05:13,910 --> 00:05:20,750
replaced by lambda a just
from the outdoor air plus

103
00:05:20,750 --> 00:05:28,150
lambda f, where
lambda f is Qf over V.

104
00:05:28,150 --> 00:05:31,840
So that's the recirculating
or filtration air change.

105
00:05:35,680 --> 00:05:46,200
So it's the recirculation or
filtration air change rate,

106
00:05:46,200 --> 00:05:52,970
whereas lambda a is the
outdoor air change rate.

107
00:05:56,010 --> 00:05:59,680
And we can also talk about
the balance between these two.

108
00:05:59,680 --> 00:06:02,610
And so that's also something
which is reported or measured

109
00:06:02,610 --> 00:06:04,200
for ventilation systems.

110
00:06:04,200 --> 00:06:06,390
And that's sometimes
called Z, which

111
00:06:06,390 --> 00:06:08,650
is the outdoor air fraction.

112
00:06:08,650 --> 00:06:13,440
So that would be lambda a
over lambda a plus lambda f.

113
00:06:13,440 --> 00:06:18,030
Or we could also write
it as Q over Q plus Qf.

114
00:06:18,030 --> 00:06:25,910
This is the outdoor air fraction
of the ventilation system.

115
00:06:25,910 --> 00:06:28,360
So another way to
talk about ventilation

116
00:06:28,360 --> 00:06:30,230
is you give the total flow rate.

117
00:06:30,230 --> 00:06:31,840
So as I sketched
here, there could

118
00:06:31,840 --> 00:06:34,540
be a fan which is in the
heating, ventilation,

119
00:06:34,540 --> 00:06:37,150
and air conditioning unit,
which is just pumping out

120
00:06:37,150 --> 00:06:38,830
air at a certain rate.

121
00:06:38,830 --> 00:06:41,830
That air is mixing
the recirculated air

122
00:06:41,830 --> 00:06:44,440
and the fresh air with
a fraction Z, which

123
00:06:44,440 --> 00:06:46,460
is the outdoor air fraction.

124
00:06:46,460 --> 00:06:49,750
And so actually, this might be,
for example, a typical value

125
00:06:49,750 --> 00:06:54,130
is around 20% for
many indoor spaces,

126
00:06:54,130 --> 00:06:57,580
such as businesses
or classrooms.

127
00:06:57,580 --> 00:06:59,620
And basically, you have
to tune this number

128
00:06:59,620 --> 00:07:01,180
to make sure that
enough fresh air is

129
00:07:01,180 --> 00:07:03,820
coming in for the
occupants that are present.

130
00:07:03,820 --> 00:07:06,310
And also, you don't want
this number too high,

131
00:07:06,310 --> 00:07:09,120
because typically the outdoor
air is not comfortable air.

132
00:07:09,120 --> 00:07:12,730
It either is too cold or too
hot or has the wrong humidity.

133
00:07:12,730 --> 00:07:15,970
And so you save a lot of energy
in your heating ventilating

134
00:07:15,970 --> 00:07:19,390
system by keeping this number
as low as it can be effectively,

135
00:07:19,390 --> 00:07:23,410
so that you're just
recirculating quality air that

136
00:07:23,410 --> 00:07:26,350
is at the right temperature
and the right humidity.

137
00:07:26,350 --> 00:07:31,690
However, that desire to save
energy, and hence also save

138
00:07:31,690 --> 00:07:34,900
carbon emissions and
other related things,

139
00:07:34,900 --> 00:07:36,700
goes against what we're
talking about here,

140
00:07:36,700 --> 00:07:38,600
though, is that when
you recirculate the air

141
00:07:38,600 --> 00:07:40,150
and you don't take
in fresh air, it's

142
00:07:40,150 --> 00:07:43,960
actually much worse for
any airborne pathogens that

143
00:07:43,960 --> 00:07:45,480
might be transferred.

144
00:07:45,480 --> 00:07:47,350
So there's a
competition here where

145
00:07:47,350 --> 00:07:50,500
you design an air ventilation
system to make sure

146
00:07:50,500 --> 00:07:53,110
that you're saving energy,
but also that you're

147
00:07:53,110 --> 00:07:56,560
keeping the place safe for
potential airborne transmission

148
00:07:56,560 --> 00:07:57,850
of disease.

149
00:07:57,850 --> 00:08:00,770
OK, so if we just
take this change here,

150
00:08:00,770 --> 00:08:02,940
we can replace these
quantities in the result

151
00:08:02,940 --> 00:08:03,940
that we already derived.

152
00:08:03,940 --> 00:08:06,070
So I don't have to go
through all that again,

153
00:08:06,070 --> 00:08:09,850
but I can just say that the
disease transmission rate--

154
00:08:14,050 --> 00:08:17,300
and this would be
in steady state,

155
00:08:17,300 --> 00:08:19,910
just to give us something
concrete to look at--

156
00:08:19,910 --> 00:08:23,380
that's what I called beta bar.

157
00:08:23,380 --> 00:08:26,200
And let's now write
down the same result,

158
00:08:26,200 --> 00:08:28,130
but just make this change here.

159
00:08:28,130 --> 00:08:32,830
So we have Qb squared,
that's the breathing rate.

160
00:08:32,830 --> 00:08:36,460
We have Cq, that's the
concentration of infection

161
00:08:36,460 --> 00:08:42,049
quanta per volume in the exhaled
breath of a sick individual,

162
00:08:42,049 --> 00:08:43,650
an infected individual.

163
00:08:43,650 --> 00:08:45,530
There was Pm squared.

164
00:08:45,530 --> 00:08:48,370
I'll write different colors
just to emphasize that.

165
00:08:48,370 --> 00:08:51,100
And then in the denominator,
we had lambda a, but now

166
00:08:51,100 --> 00:08:55,920
it's going to be lambda
a plus Pf lambda f--

167
00:08:55,920 --> 00:08:57,550
and I'll write that
in a separate color

168
00:08:57,550 --> 00:09:00,500
in just a moment-- times volume.

169
00:09:00,500 --> 00:09:02,900
So here's Pf.

170
00:09:02,900 --> 00:09:07,890
So now, in this formula, we
have the effects of masks

171
00:09:07,890 --> 00:09:10,090
and the effects of air
filtration together.

172
00:09:10,090 --> 00:09:11,640
And so we can ask
the question that I

173
00:09:11,640 --> 00:09:13,950
posed at the beginning
is, which one

174
00:09:13,950 --> 00:09:17,430
is more effective in stopping
airborne transmission

175
00:09:17,430 --> 00:09:18,910
of disease?

176
00:09:18,910 --> 00:09:23,160
So you can see these two
factors do come in differently

177
00:09:23,160 --> 00:09:24,850
in the equations.

178
00:09:24,850 --> 00:09:28,350
So let's first consider
the effect our filtration--

179
00:09:32,780 --> 00:09:35,390
effective air filtration.

180
00:09:35,390 --> 00:09:37,130
So there's a lot
of interest today

181
00:09:37,130 --> 00:09:40,850
in installing Hepa filters or
other high quality filtration

182
00:09:40,850 --> 00:09:45,710
systems into vulnerable spaces,
such as nursing homes, and also

183
00:09:45,710 --> 00:09:49,010
in spaces such as classrooms,
where people fear transmission

184
00:09:49,010 --> 00:09:50,490
of COVID-19.

185
00:09:50,490 --> 00:09:52,910
So we can ask how
effective that can be.

186
00:09:52,910 --> 00:09:56,730
So one way look at that
would be to say, well,

187
00:09:56,730 --> 00:10:01,130
how does air filtration affect
the steady transmission rate?

188
00:10:01,130 --> 00:10:03,980
So that would be looking
at the transmission rate

189
00:10:03,980 --> 00:10:06,770
with the filter compared
to the transmission

190
00:10:06,770 --> 00:10:10,970
rate without the filter.

191
00:10:10,970 --> 00:10:13,310
So if we do that, you can
see all the terms here

192
00:10:13,310 --> 00:10:16,010
cancel except for this
one that has Pf in it.

193
00:10:16,010 --> 00:10:19,770
And so what we're left with
is, because in the denominator

194
00:10:19,770 --> 00:10:23,540
we're left with just--

195
00:10:23,540 --> 00:10:25,730
when Pf is equal to
0, it's just lambda a.

196
00:10:25,730 --> 00:10:28,370
That's in the denominator, so
it ends up in the numerator.

197
00:10:28,370 --> 00:10:34,920
And so it's just lambda a over
lambda a plus Pf lambda f.

198
00:10:34,920 --> 00:10:37,650
So the benefit of filtration
can be immediately seen right here.

199
00:10:37,650 --> 00:10:40,500
If you know the ratio
lambda a to lambda v,

200
00:10:40,500 --> 00:10:45,460
because I can also
write this as 1 plus--

201
00:10:45,460 --> 00:10:46,710
well, actually, I won't even--

202
00:10:46,710 --> 00:10:47,790
I won't do that right now.

203
00:10:47,790 --> 00:10:50,490
But you can see how
this is related.

204
00:10:50,490 --> 00:10:53,160
It's related to this quantity
Z. but basically, the ratio

205
00:10:53,160 --> 00:10:55,470
of the lambda a to
lambda v is related to Z.

206
00:10:55,470 --> 00:10:56,850
And that obviously
comes in here.

207
00:10:56,850 --> 00:10:58,590
And Pf comes in as well.

208
00:10:58,590 --> 00:11:00,180
But an interesting
question we can ask

209
00:11:00,180 --> 00:11:02,010
is, well, what if you
have a perfect filter?

210
00:11:02,010 --> 00:11:04,260
So let's say we have something
even better than Hepa.

211
00:11:04,260 --> 00:11:06,300
Let's say it's 100% filtration.

212
00:11:06,300 --> 00:11:08,440
That's like best case scenario.

213
00:11:08,440 --> 00:11:14,640
So this fraction here is larger
than if I just set Pf equals 1.

214
00:11:14,640 --> 00:11:17,400
So this is a perfect filter.

215
00:11:17,400 --> 00:11:20,050
So we have the most expensive
filter on the planet,

216
00:11:20,050 --> 00:11:23,520
and it's going to definitely
filter everything.

217
00:11:23,520 --> 00:11:25,050
And so what we're
left with, then,

218
00:11:25,050 --> 00:11:28,620
is just lambda a over
lambda a plus lambda f.

219
00:11:28,620 --> 00:11:30,480
Now I can make the
connection here.

220
00:11:30,480 --> 00:11:37,150
That is simply Z. So basically,
the effect of air filtration

221
00:11:37,150 --> 00:11:40,630
is never better than the
outdoor air fraction itself.

222
00:11:40,630 --> 00:11:43,210
But I already told you, the
outdoor air fraction here

223
00:11:43,210 --> 00:11:46,540
cannot be too small or you're
not delivering enough oxygen

224
00:11:46,540 --> 00:11:47,860
to the occupants of the room.

225
00:11:47,860 --> 00:11:50,180
So basically, there are
standards for that as well.

226
00:11:50,180 --> 00:11:56,750
For example, you need to
have, for outdoor air,

227
00:11:56,750 --> 00:11:59,330
there is an additional
requirement is that you need,

228
00:11:59,330 --> 00:12:01,880
at least in the United
States, 15 cubic feet

229
00:12:01,880 --> 00:12:05,220
per minute per person.

230
00:12:10,270 --> 00:12:12,660
So basically, this Q
can't be too small,

231
00:12:12,660 --> 00:12:14,620
because you have to be
delivering, essentially,

232
00:12:14,620 --> 00:12:16,330
enough oxygen for a
person to breathe.

233
00:12:16,330 --> 00:12:19,520
And so this is one way
this standard is decided.

234
00:12:19,520 --> 00:12:21,980
And so basically, the
Z can't be that small.

235
00:12:21,980 --> 00:12:24,940
And so if I ask myself, what's
the effect of filtration,

236
00:12:24,940 --> 00:12:27,640
an interesting conclusion
to this calculation

237
00:12:27,640 --> 00:12:32,650
is that this is not really
smaller than about 10

238
00:12:32,650 --> 00:12:33,700
to the minus 1.

239
00:12:33,700 --> 00:12:36,910
So if we just think of an order
of magnitude, roughly speaking,

240
00:12:36,910 --> 00:12:40,270
gaining a factor of 10,
maybe, out of air filtration,

241
00:12:40,270 --> 00:12:41,470
but not that much more.

242
00:12:41,470 --> 00:12:43,180
Now, you might say,
how is that possible?

243
00:12:43,180 --> 00:12:45,040
My filter is a perfect filter.

244
00:12:45,040 --> 00:12:46,900
I'm filtering everything.

245
00:12:46,900 --> 00:12:50,560
The problem is seen right
here, is that in reality,

246
00:12:50,560 --> 00:12:54,910
what we really want is we
want to protect a person who's

247
00:12:54,910 --> 00:12:57,490
over here, maybe
who is susceptible,

248
00:12:57,490 --> 00:13:01,420
from another person over
here who is infected.

249
00:13:01,420 --> 00:13:04,630
And you see the problem is
that if it's a well-mixed room,

250
00:13:04,630 --> 00:13:07,570
then the infected
person is breathing

251
00:13:07,570 --> 00:13:11,260
all these infectious
droplets everywhere.

252
00:13:11,260 --> 00:13:13,040
And this other person
is breathing them.

253
00:13:13,040 --> 00:13:16,060
And even if you perfectly filter
the piece of the flow rate

254
00:13:16,060 --> 00:13:17,740
that is going
through the filter,

255
00:13:17,740 --> 00:13:19,840
there's still lots of
other air in the room

256
00:13:19,840 --> 00:13:22,180
and it's not all being removed.

257
00:13:22,180 --> 00:13:24,280
So unfortunately, you
don't get such a benefit

258
00:13:24,280 --> 00:13:25,870
from that, unless
you could completely

259
00:13:25,870 --> 00:13:28,600
choke off the outdoor air
and just keep recirculating

260
00:13:28,600 --> 00:13:30,000
until you remove all the virus.

261
00:13:30,000 --> 00:13:32,080
But then a problem is, you
also run out of oxygen,

262
00:13:32,080 --> 00:13:34,360
and you don't have very
good air in the room.

263
00:13:34,360 --> 00:13:36,100
So that's not really
a solution either.

264
00:13:36,100 --> 00:13:38,890
So basically, air
filtration is helpful,

265
00:13:38,890 --> 00:13:41,270
but I would say it's
not super helpful.

266
00:13:41,270 --> 00:13:43,600
A factor of 10 is good,
we like factors of 10.

267
00:13:43,600 --> 00:13:45,460
But it's not a factor of 100.

268
00:13:45,460 --> 00:13:48,430
And we might actually
rather have a factor of 100.

269
00:13:48,430 --> 00:13:57,510
So then we can ask ourselves,
well, what do we get from masks

270
00:13:57,510 --> 00:14:00,290
And by this, I mean
everybody's wearing a mask.

271
00:14:00,290 --> 00:14:02,360
So keep in mind,
we never know who's

272
00:14:02,360 --> 00:14:04,590
the infected person
ahead of time.

273
00:14:04,590 --> 00:14:06,170
So we want to
consider a case where

274
00:14:06,170 --> 00:14:07,550
everybody's wearing a mask.

275
00:14:07,550 --> 00:14:09,650
And so then by assumption,
the infected person

276
00:14:09,650 --> 00:14:11,780
is wearing a mask, and
any susceptible person

277
00:14:11,780 --> 00:14:12,980
is also wearing a mask.

278
00:14:12,980 --> 00:14:14,600
So that's our assumption here.

279
00:14:14,600 --> 00:14:18,100
OK, so this is good
mask compliance here.

280
00:14:18,100 --> 00:14:19,520
And so we can ask
ourselves again,

281
00:14:19,520 --> 00:14:22,490
what is the transmission
rate with mask

282
00:14:22,490 --> 00:14:27,740
compared to the transmission
rate when there are no masks?

283
00:14:27,740 --> 00:14:29,630
And the way my
notation works here,

284
00:14:29,630 --> 00:14:32,320
Pm is the mask
penetration factor.

285
00:14:32,320 --> 00:14:33,320
So that would actually--

286
00:14:33,320 --> 00:14:34,700
Pm equals 1, actually.

287
00:14:34,700 --> 00:14:37,500
That would be the case where,
basically, there is no mask,

288
00:14:37,500 --> 00:14:40,040
because all the airflow
goes in and out of the mouth

289
00:14:40,040 --> 00:14:43,260
without any kind of filtration.

290
00:14:43,260 --> 00:14:44,740
So this is just Pm squared.

291
00:14:48,360 --> 00:14:51,220
And the important thing
is that it's squared.

292
00:14:51,220 --> 00:14:55,500
So one argument you will hear,
which even influenced the World

293
00:14:55,500 --> 00:14:57,240
Health Organization
back in January

294
00:14:57,240 --> 00:14:59,250
at the beginning
of the pandemic,

295
00:14:59,250 --> 00:15:02,920
is that the virus is so small,
as we've already discussed,

296
00:15:02,920 --> 00:15:07,080
and probably is going to be
carried in very small droplets.

297
00:15:07,080 --> 00:15:10,320
And therefore, any
filtration, even a mask,

298
00:15:10,320 --> 00:15:12,420
is not really that helpful,
because masks are not

299
00:15:12,420 --> 00:15:14,940
going to be filtering at the
scale of 120 nanometers, which

300
00:15:14,940 --> 00:15:16,070
is a virus.

301
00:15:16,070 --> 00:15:18,240
And even the smallest aerosol
droplets, many of them

302
00:15:18,240 --> 00:15:19,500
do get through.

303
00:15:19,500 --> 00:15:22,770
In fact, when you get to
about 1/10 of a micron,

304
00:15:22,770 --> 00:15:27,000
or 100 nanometers,
most mask materials

305
00:15:27,000 --> 00:15:28,320
don't have good filtration.

306
00:15:28,320 --> 00:15:29,850
The very simple
reason is they also

307
00:15:29,850 --> 00:15:31,320
have to allow good airflow.

308
00:15:31,320 --> 00:15:33,780
So if you have such tiny pores
that you're catching things

309
00:15:33,780 --> 00:15:36,280
at that scale, the problem is
there's a very high resistance

310
00:15:36,280 --> 00:15:37,650
to flow and you can't breathe.

311
00:15:37,650 --> 00:15:39,150
In fact, you've
probably experienced

312
00:15:39,150 --> 00:15:41,860
that if you're wearing a good
mask that you can't wear it

313
00:15:41,860 --> 00:15:43,320
for too long,
because after a while

314
00:15:43,320 --> 00:15:44,740
you can't breathe anymore.

315
00:15:44,740 --> 00:15:47,680
So you need to have some big
enough pores to allow flow.

316
00:15:47,680 --> 00:15:50,310
And that makes it really hard to
filter the smallest particles.

317
00:15:50,310 --> 00:15:53,950
But the interesting thing is
this thing comes in squared.

318
00:15:53,950 --> 00:15:57,420
So we can ask ourselves, well,
what about different qualities

319
00:15:57,420 --> 00:15:58,170
of masks?

320
00:15:58,170 --> 00:16:01,650
So a really good mask material
that is perfectly fitting,

321
00:16:01,650 --> 00:16:05,040
so like a high quality
surgical or N95 mask,

322
00:16:05,040 --> 00:16:06,710
if you don't have
any leakage of air,

323
00:16:06,710 --> 00:16:08,430
you have a really good fit,
and you're just going right

324
00:16:08,430 --> 00:16:10,170
through the material,
this could be

325
00:16:10,170 --> 00:16:15,940
as high as 99% filtration for
aerosols, for the aerosols

326
00:16:15,940 --> 00:16:16,740
that we care about.

327
00:16:20,290 --> 00:16:23,220
And this would be like a high
quality surgical mask material,

328
00:16:23,220 --> 00:16:26,040
like not even
factoring for the fit.

329
00:16:26,040 --> 00:16:31,860
So if it's 99% filtration,
what that means is Pm is 0.01,

330
00:16:31,860 --> 00:16:33,100
but it comes in squared.

331
00:16:33,100 --> 00:16:37,890
And so this factor is
actually 10 to the minus 4.

332
00:16:37,890 --> 00:16:39,420
Four orders of
magnitude compared

333
00:16:39,420 --> 00:16:41,500
to one order of magnitude
you get from the filter.

334
00:16:41,500 --> 00:16:45,140
Now, that's for perfect
masks, really good masks.

335
00:16:45,140 --> 00:16:46,480
What if our mask is not so good?

336
00:16:46,480 --> 00:16:49,300
So actually, we have an N95.

337
00:16:49,300 --> 00:16:53,590
N95 actually is guaranteed
to filter about 95%

338
00:16:53,590 --> 00:16:54,950
of the aerosols.

339
00:16:54,950 --> 00:16:58,900
And so if you take
0.05 and square it,

340
00:16:58,900 --> 00:17:01,270
you're getting a number
of order 10 to the minus 3

341
00:17:01,270 --> 00:17:03,480
for Pm squared.

342
00:17:03,480 --> 00:17:05,210
And what about cloth masks?

343
00:17:05,210 --> 00:17:08,270
So this is where
the debate comes in,

344
00:17:08,270 --> 00:17:12,349
because these days people are
wearing cloth masks, which

345
00:17:12,349 --> 00:17:13,310
makes a lot of sense.

346
00:17:13,310 --> 00:17:16,290
It's way better than nothing,
as we'll see in a moment.

347
00:17:16,290 --> 00:17:18,960
But yeah, one could argue,
well, a lot of the cloth masks

348
00:17:18,960 --> 00:17:20,960
might be letting through
these aerosol droplets.

349
00:17:20,960 --> 00:17:22,210
They're not really that great.

350
00:17:22,210 --> 00:17:24,200
In fact, if you look
at the cloth masks,

351
00:17:24,200 --> 00:17:27,500
they could give you a range,
but it might be anywhere from--

352
00:17:27,500 --> 00:17:30,020
I mean a really bad
cloth mask is 10%.

353
00:17:30,020 --> 00:17:33,820
That'd be like just a single,
thin, cotton, very loose weave,

354
00:17:33,820 --> 00:17:35,350
like on a bandana.

355
00:17:35,350 --> 00:17:36,800
That's pretty bad.

356
00:17:36,800 --> 00:17:39,920
But most of the multi-layer
cloth masks, or the silk masks,

357
00:17:39,920 --> 00:17:41,320
they can actually
do pretty well.

358
00:17:41,320 --> 00:17:45,050
They can even get as high as
90%, which is pretty high,

359
00:17:45,050 --> 00:17:46,160
but it's possible.

360
00:17:46,160 --> 00:17:47,990
And maybe a lot of
them, depending on maybe

361
00:17:47,990 --> 00:17:50,190
they're not fitting so well,
they might be more like,

362
00:17:50,190 --> 00:17:51,800
let's say, 50%.

363
00:17:51,800 --> 00:17:54,800
But the thing is,
this comes in squared.

364
00:17:54,800 --> 00:18:00,350
And interestingly, even
the 90% case, that's 10%

365
00:18:00,350 --> 00:18:03,170
get through, so Pm is 10%.

366
00:18:03,170 --> 00:18:07,580
But when you square 10%,
it's still 10 to the minus 2.

367
00:18:07,580 --> 00:18:10,280
And if you take these lower
numbers and square them,

368
00:18:10,280 --> 00:18:11,780
you're still talking
about something

369
00:18:11,780 --> 00:18:15,410
which is on the order
of 10 to the minus 1.

370
00:18:15,410 --> 00:18:17,600
So what this calculation
tells you is that even

371
00:18:17,600 --> 00:18:20,320
like some of the worst
masks you can wear,

372
00:18:20,320 --> 00:18:22,320
as long as there's good
compliance and everybody

373
00:18:22,320 --> 00:18:25,010
is actually wearing
those masks indoors,

374
00:18:25,010 --> 00:18:27,080
then the fact that
this comes in squared

375
00:18:27,080 --> 00:18:29,600
means that you get
at least a factor

376
00:18:29,600 --> 00:18:31,520
of 10 reduction in
the transmission

377
00:18:31,520 --> 00:18:34,520
compared to having no
masks in a well-mixed room.

378
00:18:34,520 --> 00:18:37,700
And in fact, decent
masks will do way better.

379
00:18:37,700 --> 00:18:42,020
You could get a factor of 100,
1,000, or potentially 10,000

380
00:18:42,020 --> 00:18:44,720
in reducing the transmission
rate by wearing masks,

381
00:18:44,720 --> 00:18:46,670
whereas with filtration,
even with the most

382
00:18:46,670 --> 00:18:48,260
expensive and highest
quality filters,

383
00:18:48,260 --> 00:18:50,700
you can barely get better
than a factor of 10.

384
00:18:50,700 --> 00:18:53,100
So this is a really important
concept to keep in mind.

385
00:18:53,100 --> 00:18:55,950
And it comes out of a
really simple calculation.

386
00:18:55,950 --> 00:18:58,880
And the simple reason
that I mentioned before

387
00:18:58,880 --> 00:19:01,730
is that air filtration is only
filtering part of the air,

388
00:19:01,730 --> 00:19:04,280
and the rest is just out
there for you to breathe.

389
00:19:04,280 --> 00:19:10,820
But masks are much better
because they capture the source

390
00:19:10,820 --> 00:19:13,040
and they also block the target.

391
00:19:13,040 --> 00:19:15,440
So that basically,
every droplet has

392
00:19:15,440 --> 00:19:16,850
to go through the
mask on one end

393
00:19:16,850 --> 00:19:19,220
and it has to go through
it again on the other end.

394
00:19:19,220 --> 00:19:21,470
Whereas the filter is
missing most of the droplets.

395
00:19:21,470 --> 00:19:22,850
They're floating
around the room.

396
00:19:22,850 --> 00:19:24,440
They're not going
through the filter.

397
00:19:24,440 --> 00:19:28,480
Unless you choke off the outdoor
air, and you can't do that.