COVID-19 Scratch Models To Support Local Decisions: A Public Health Modeling Adventure

May 22, 2020

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Edward H. Kaplan, SM, MCP, PhD, NAM, NAE William N. and Marie A. Beach Professor of Operations Research Professor of Public Health Professor of Engineering

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00:00Like to introduce our next Speaker,
00:03Doctor Edward Kaplan.
00:04Doctor Kaplan is William N Andrea,
00:06a beach professor of operations
00:08research and as a professor of public
00:11health and a professor of engineering.
00:14He's an expert in operations research,
00:16mathematical modeling,
00:17and statistics, who studies problems
00:19in public policy and Management.
00:21Doctor Kaplan, thank you for being here.
00:25Thank you very much and
00:27Good afternoon everyone.
00:28I recognize I am the last thing
00:31between you and happy hour,
00:33but nonetheless I hope you will bear with me.
00:36I am taking a somewhat different Ave
00:39into this entire area of work because
00:41I came to this not as a researcher,
00:44but rather is a member of Yale's
00:46Public Health Kovid Advisory Committee.
00:48I think some of you have heard
00:50about the work of this committee.
00:53It's been meeting quite intensively
00:54since the very beginning.
00:56Of March originally charged by Paul Jenison,
00:59now chaired by Stephanie Spangler,
01:01polls the director of Yale Health and
01:04Stephanie is device focus for health fairs.
01:06You recognize many of the people
01:09who are on this panel.
01:11Basically,
01:11we were tasked to advise the L
01:14presidents and senior officials on
01:16public health aspects of this we started
01:19right into the middle of a crisis,
01:22literally just days before the first
01:24cases in Connecticut and at Yale.
01:27Or announced we are continuing
01:28to work to this day,
01:30typically in well they used
01:32to be morning phone calls.
01:34Now their morning zoom sessions every
01:36morning at 7:00 o'clock to try and
01:39work and support University decisions.
01:41Here are a number of different committee
01:43issues that have been addressed today.
01:45You can read them on the slide yourself
01:48so I won't go through them all,
01:51but I just want to mention that the
01:54issues that are highlighted here in orange.
01:57Are all issues are that involved
01:59what I would call scratch modeling?
02:02That is to say,
02:04mathematical models were essentially
02:06created in real time and on the fly
02:09to try and help answer questions
02:11as they occurred.
02:12So you'll remember for example receiving
02:15emails from the administration about
02:17the capping of University advance.
02:19Initially it size 100 then down to size
02:2220 and then eventually all events were
02:25effectively canceled that actually.
02:27Those recommendations Cam is the
02:29result of analysis that was conducted
02:32in a principled way trying to come up
02:34with appropriate crowd caps so that
02:37the probability that no transmission
02:39would occur in the event would be
02:42maintained at least 99% given the
02:44information that we had at the time.
02:47Again,
02:47this was done in the first week of March.
02:50Implications for the calendaring.
02:52Looking at the design of testing programs
02:54in a particular repeat screening
02:56and a number of other activities,
02:58some of which the committee didn't
03:00actually undertake but help to kick start,
03:02and they include the activities
03:05listed here so. Actually, it's been.
03:07It's been quite an experience to get
03:09to know the people on this committee
03:12from across the University and also
03:14to be involved in working on all
03:16of these issues in real time.
03:18Today I'd like to talk about two such
03:21projects and will start with a kick start,
03:23which actually has to do with this
03:26sludge sampling project that saw
03:27Domer mentioned when he spoke at the
03:29very beginning of the afternoon.
03:31And again, this is one of these ideas.
03:34It came about a couple of us.
03:36Were thinking what other
03:38ways could one manage?
03:40Uh, what could one gain information
03:42about the state of this outbreak,
03:44and the idea came up of
03:47environmental monitoring.
03:47The problem was is we didn't really know
03:50who in the University could do such a thing.
03:54The original proposal was actually to
03:56go to Union Station because of the
03:59frequent train travel between New
04:01Haven in New York and possibly study
04:04outflow into toilet swabs there anyway.
04:06Dan Weinberg, who also spoke earlier today.
04:09Uh, suggested to me that the Magic
04:11figure on campus with professor Jordan
04:13Patcha and environmental engineering,
04:15which turns out to be a world
04:17expert in these kinds of studies.
04:19I got in touch with Jordan.
04:21We had a discussion that same
04:23day we're now talking March 11th,
04:25and that led to a March 16th meeting with
04:28other researchers who quickly joined
04:30in some who would be doing sample collection.
04:33Some who are experts in the
04:35actual laboratory testing.
04:36Some people contributing analysis.
04:38Jordan suggestion.
04:38Everyone agreed that the actual target
04:40should be to wastewater treatment plant.
04:43Be cause this is a plant which is served
04:46serving the populations of New Haven,
04:48Hamden, East Haven and Woodbridge,
04:50and that the collection and detection
04:52of pathogens in Seward Sludge is
04:54something which is longstanding practice.
04:57We put together the two cross campus
04:59team and the first samples were already
05:02being collected on March the 19th,
05:04so less than two weeks from when the idea
05:07was first raised until the action started.
05:10And here is just a cover
05:12sheet of the article.
05:14Coming out that sod again mentioned
05:16earlier and I just think it's it's nice
05:19to look both of course to acknowledge all
05:22of the people involved in medical students.
05:25Other researchers from across the University,
05:27and you can really see how people
05:30from across Yale have come together
05:32to try and tackle this problem.
05:35So this is the East shore water
05:37pollution facility.
05:3840,000,000 gallons per day capacity.
05:40As I mentioned,
05:41it serves these four towns and the idea
05:44here was to start gathering samples daily.
05:47And the analysis I'll share with you
05:50today is based on data collected from
05:52March 19th until May,
05:54the first.
05:55You can see the little tag here.
05:57It says Yale sample.
05:59So here's what happens.
06:01Actually,
06:01there are two different replicas
06:03with two different primers,
06:04and so here what we see are the
06:07actual raw measurements of viral
06:09RNA copies per milliliter here.
06:11From these different primary replica
06:13combinations viewed overtime and
06:15just looking at these raw data.
06:17You can see that they're very noisy,
06:19but you can see the shape actually
06:21of an epidemic
06:22outbreak pretty much from start to finish.
06:25So how does one analyze noisy data like this?
06:27Well, the first thing to do is to smooth it.
06:31To do it in a very simple way,
06:33we're using something called low as,
06:35which is just a locally weighted
06:37regression scatter plot smoothing.
06:38It's a very common technique
06:40used for problems like this,
06:41and what we have on this first figure here.
06:45Are raw data and smooths both
06:47for the average RNA measurements,
06:49which are the blue dots and also for daily
06:53admissions to the Yale New Haven Hospital.
06:56But we stricted to residents of
06:58the same for towns that is served
07:01by the sewage treatment plant.
07:03And if you do the smooth,
07:05it's possible to re scale and reposition
07:08and you actually see that these
07:10sludge RNA measurements were peaking.
07:12This is 3 days before the local
07:15admissions data were peeking.
07:17You might have thought that there would be
07:19a longer lead time than just three days.
07:22Certainly if you compare the RNA measurement
07:24in the sludge data had actual covert cases,
07:27you see much more of a displacement,
07:30but remember the kovid cases or following
07:32from testing delays and also many,
07:34many people who are hospitalized don't
07:36actually get diagnosed for Cove it until
07:38after they've been admitted to the hospital.
07:41So there are all sorts of reasons for
07:44why you would expect the longer lag here.
07:47But perhaps a more interesting way to look
07:50at this information is in this last figure.
07:54What we have here in this block
07:57curve is actually what I'll refer
07:59to as the transmission potential
08:01for a mathematical model,
08:04which is a SARS covariance
08:06transmission potential which explicitly
08:08takes into account the variation
08:10infectious infectiousness by time.
08:12Since infection an one thing I will
08:15mention is that this curve was not.
08:18Calibrated to the sludge.
08:19Data in the sense of any kind of
08:22a least squares point by point
08:23fit or something like that.
08:25Whether this is a model that was
08:27informed by early transmission dynamics
08:29that had been originally estimated in
08:31China but then updated for Connecticut,
08:33and I'm going to go through those
08:35details and roll them.
08:37And the only real calibration
08:38exercise involved was trying to figure
08:40out looking backwards.
08:41When did this local outbreak start?
08:43So basically,
08:44it's a matter of just sliding this
08:47curve to the left and to the right,
08:49but in terms of the peak in
08:51the timing and everything else.
08:53It actually just fits this curve
08:55almost obviously soft little bit here,
08:56but it fits it really quite well
08:59without the calibration.
08:59So that actually gives us reason to
09:02think that something is going on here.
09:04So what actually is going on with this curve?
09:06Where is it coming from and how could
09:09it perhaps help us understand why the
09:11separation between the RNA signal
09:13on the slides in the admissions to
09:15hospital is 3 days when some people
09:17might have expected that to be a
09:19much longer lead time?
09:21So to do this, we go back to
09:23the basics and Epidemiology.
09:25Jenny pets are earlier talked about
09:27how people estimate what it called
09:30generation times in exponential
09:31growth rates to try and put together
09:34estimates of the reproductive number.
09:36This is a graph which actually shows you
09:39what the details of that operation is,
09:42what you actually have here is
09:44a model of the age of infection
09:46dependent transmission rate.
09:48This is an age of infection dependent model.
09:51And the famous reproductive number
09:53are not that you've all heard about
09:55so many times today is actually
09:56the area under this curve.
09:58So a person who is infected at
10:00the beginning in a surrounded
10:01by susceptible individuals.
10:03The number of persons that initially
10:04infected person would in fact
10:06is actually found directly from
10:07the area under this curve.
10:09This turns out to be a very
10:11very important concept,
10:12and we're going to come back
10:14to it over and over again,
10:16both for this application for the
10:17one I'm going to describe next now.
10:20Originally in the very first paper
10:21that came out of Wuhan in the
10:24New England Journal of Madison.
10:25We are not was estimated at about 2.3
10:28but actually working with Connecticut data.
10:30Some of the same data that for us
10:33was talking about just moments ago.
10:36It turned out that in order to
10:38match the early rise in hospital
10:40admissions data in Connecticut,
10:42actually a larger are not was needed.
10:45It works out to be about 3.3 and you
10:48remember hearing from Nick Rousakis
10:50that that is in the neighborhood of
10:53where many of the more recent estimates?
10:55Of the reproductive number have have
10:57come in OK, so how do we get this thing?
11:01I call the transmission potential?
11:02That is to say,
11:04how is it that we figure out what
11:06this black curve is in the diagram?
11:09So here's how it works and we're
11:11going to follow what I call the
11:14scratch model in quotation mark.
11:15This has been published now
11:17in the amsam Journal,
11:19so the first step is we have
11:21this original time dependent.
11:22I should say age of infection
11:24dependent transmission rate.
11:25We call that. Lambda of eggs.
11:28The second ingredient we have to ask
11:30ourselves is what is the problems
11:32of infection at chronological time?
11:34Key.
11:34So the particular data I'm showing you
11:37here is actually from April the 9th,
11:39which is actually at the peak of
11:42the viral signal from the sludge.
11:44So at Time T,
11:46how many people in the population?
11:48What percentage have been
11:49infected for zero days?
11:51One days, two days, three days and so forth?
11:54And that's computed inside the model.
11:56It's given by this curve pie of 80.
11:59Notice at this point, by the way,
12:01that the epidemic is actually waning already.
12:04The reason is the maximum
12:06part of this curve is not.
12:08At Zero,
12:09which are people just becoming infected,
12:12time zero really correspond.
12:13Say incidence it to people
12:15who are infected about a week
12:18earlier and already you see
12:20a light coming in anyway.
12:21What you have is this fraction of people
12:25who are been infected for a duration a
12:28you have this as the age of infection,
12:31a dependent transmission.
12:32So what you have to do is multiply
12:35these two curves together and that
12:38gives you this great curve down here.
12:41And a transmission potential is
12:43the area under the Gray curve,
12:45which is given by this interval.
12:48So that's actually where that
12:50transmission potential comes from.
12:51And now you go back and you say,
12:54Well, wait a minute,
12:56you showed us a curve of
12:58transmission potential.
12:59Overtime, that's right,
13:00that's exactly what I did.
13:02Every point on this curve corresponds to
13:05finding an area under the appropriate curve.
13:08The age of infection transmission
13:10isn't changing.
13:11What's changing is how many people
13:13have been infected for how long,
13:15so you'll notice here that we have many,
13:18many more people at the beginning
13:20here on the at the beginning,
13:22the first State of observation
13:24here was on March 19th.
13:25These are people who are
13:27infected just right around them,
13:28but of course they're not transmitting
13:30very much because it takes time
13:32until a person actually transmits the
13:34virus and this curve is going down.
13:36Here is the same curve I showed you earlier.
13:39This corresponds to the peak period
13:41now corresponding to the end.
13:42Here you'll notice it.
13:43Actually, the incidence of infection,
13:45which much higher three weeks ago here
13:47and currently it's already very low,
13:49so we get a smaller and we get
13:51a bigger are you get a smaller
13:54and that's how this model works.
13:56And that actually helps explain the mystery,
13:59because if you now put two curves
14:02on the same graph,
14:03both coming out of this model,
14:06the curve on the left which would be
14:08scared to the left axis is the actual
14:12incidence of SARS coronavirus two infraction,
14:14the curve to the right is
14:17the transmission potential.
14:19And the separation between the two
14:20curves is giving you the time lag
14:23from incidents to transmission
14:24potential to transmission potential.
14:26If you think about it is basically how
14:28much virus there isn't a community.
14:31It's sort of like a community viral load.
14:33If there was a way to actually measure
14:36that through viral testing in individuals,
14:38well effectively we're getting
14:39a signal of community viral load
14:42when we look at the sludge.
14:43So this is the answer to the mystery,
14:46because when we go back and say, Well,
14:49let's look at hospital admissions.
14:51Hospital admissions, of course,
14:52are also lag from incidents,
14:53but it turns out that there lag
14:55longer than the time from infection.
14:57Until this trans transmission
14:59potential moves they had.
15:00This is about a nine day lag.
15:02There's an extra 3 days here until you
15:04actually would see the admissions data,
15:06Peking, so that's an interesting story.
15:08It does tell you that you can understand
15:11what's going on in the sludge data,
15:13but it also answers the question
15:14as to why the lead time is perhaps
15:17not as large as people thought
15:19that it would be. Let's move on to
15:21a completely different problem.
15:22It's also related to some.
15:24Forest talked about an it has to
15:27do with repeat screening for the
15:29detection and control of this outbreak,
15:32and the emphasis here is really
15:34going to be on the detection
15:37and isolation of asymptomatic
15:39infections through viral testing.
15:41As we learn from Jenny Ann from
15:44others who spoke earlier today,
15:46most of the testing due date has
15:49been people who were symptomatic.
15:52As a consequence, you have cases.
15:54Driving tests as opposed to
15:56test discovering infections.
15:58With the advent of testing
16:00more more easily available,
16:02more frequent,
16:02the ability to test more frequently.
16:05We can turn that around and
16:07we can actually use testing to
16:10detect and isolate infections.
16:12The idea here is to gain actual
16:15control of transmission and
16:16to prevent local outbreaks.
16:18So it's not only about
16:20identifying individual patients.
16:22Most of these people actually would
16:24not have serious medical consequences.
16:26The issue is to block transmission
16:28and to do this in an efficient
16:31way requires intensive screening
16:33not once every six months,
16:35once every four months, once a month.
16:38It requires intensive screening,
16:39and so as I said,
16:41the focus here is to screen
16:43asymptomatic screen.
16:44For asymptomatic infections,
16:45the goal is to shorten the time
16:48from infection until the isolation
16:50of those people who test positive.
16:52This is all PCR testing,
16:54not antibody testing. This is all.
16:56Based on PCR and so this is written
17:01recently been written about.
17:03I'm hopeful home with how we form
17:06in another doctor that many of you
17:08know at the medical school is also
17:10cross appointed with the management
17:13school in focusing on how to actually
17:15do this at a large level because
17:17the logistics of rapid screening
17:20can easily become overwhelming,
17:21but nonetheless it's a
17:23very important activity.
17:24If the idea is to try an really
17:27curtail the spread of infection.
17:29So how does this work?
17:31Well,
17:31I'm going to kind of break this up into
17:34100 level courses to 200 level course.
17:37New graduate course.
17:38So here's the 100 level.
17:40Of course,
17:40let's all pretend that in fact
17:42Christmas runs about 2 weeks.
17:44And let's assume that we have
17:46a perfectly sensitive test.
17:47And let's assume that we schedule
17:49everybody to get screened once a week.
17:51So Dan is going to be screened on Mondays,
17:53and forest is going to be screened
17:56on Wednesdays,
17:56and I'm going to be screened on
17:59Sundays and basically once a week
18:00we're each going to be tested.
18:02If this test was perfectly sensitive,
18:04what's going to happen well
18:06where the infection would fall
18:07if one of us became infected?
18:09The infection knows nothing
18:10about the screening process.
18:11It's totally independent
18:12of the screening process,
18:14so on average it's going
18:15to fall in the middle.
18:17It would distribute itself uniformly.
18:18So what that means is that you would
18:21be detecting infections on average 3.5
18:23days after the person was infected.
18:25Some people you detect only
18:26some people you detect later,
18:28but on average would be 3.5 days and
18:30at most Seven days after they occur.
18:32If you believe that there's a 14 day course
18:35of infectiousness into detecting people,
18:37on average after 3.5 days,
18:38that's one quarter of the way
18:40through the infectious period.
18:42Which means that you would be blocking
18:443/4 of 75% of potential transmission days.
18:46If you isolate people who you are
18:49finding testing positive alright,
18:50but we noted the screening tests
18:52are not perfectly Saturday.
18:53Suppose it's only 70% sensitive.
18:55What's going to happen while in
18:57the first week you would catch
18:5970% of people who are infected?
19:01But there's also a 21% chance it
19:04would catch someone who was infected
19:06in the first week in the second week
19:08because they could test negative in
19:10the first week but still test positive.
19:13In the second week,
19:14this is assuming that sensitivity
19:16is not dependent on an individual's
19:18biologies and a person who would
19:20test negative falsely would always
19:22test negative falsely.
19:24Rather the assumption here is that
19:26the real reason for imperfect testing
19:28an for less than perfect sensitivity
19:30here has more to do a sample
19:33collection and issues like that.
19:35So now it turns out that instead
19:37of blocking 75% of transmission,
19:39you block 58% of transmission.
19:41But that's still pretty effective.
19:43If you have a root productive number in
19:45the neighborhood of two, for example,
19:47and you're blocking 58% of the transmission,
19:49that would already get you below 1.
19:52So that's The Level 100 course
19:54rationalization for repeat screening.
19:55Now what I'd like to do is give
19:57you the level two, of course,
19:59so remember this graph.
20:01It's our friend from the earlier study.
20:03This is the transmissibility
20:04by age of infection,
20:06and suppose I detect an infected person
20:08by screening right here at the red line,
20:10all right and where that red line
20:12is going to fall is going to depend
20:15on how frequently I test if I'm
20:17testing quite frequently is going
20:19to push the red line to the left.
20:22If I'm not testing so frequently,
20:23it pushes the red line to the right,
20:26but wherever the Red Line Falls,
20:27if you isolate the person found infectious,
20:30the blue area to the right of
20:31the red line is blocked,
20:33its transmission that would
20:34have happened but doesn't.
20:35The new reproductive number you have as
20:37a result of the repeat screening program
20:39is still the area under the curve,
20:41but it's only the area of this part,
20:44right here.
20:45Now of course,
20:46the timing which this is interrupted
20:48is itself random,
20:49because while you might be
20:51screening on schedule,
20:52the infection isn't infecting
20:53people on the same schedule,
20:55so you have to take into account the
20:58distribution of where this lies,
21:00but mathematically,
21:01that is not difficult to do.
21:03So now will go to the graduate course
21:05and just to make life interesting,
21:08let's imagine that we're considering
21:09a residential campus,
21:11and maybe that residential campus has
21:1310,000 students who are living on site.
21:15And here are the kinds of parameter
21:18variations that we consider here at
21:20the beginning of the school year,
21:22everyone is susceptible or perhaps
21:24looking at some of forest projections,
21:26maybe 15% or more have already
21:28become infected, and so maybe only
21:3080% of the students are susceptible.
21:33Suppose the tests are only 70% sensitive.
21:35These are all variables which
21:37can be changed in the analysis.
21:39Suppose we test weekly.
21:40Suppose we test bye week was suppose
21:43we don't bother testing at all.
21:45Suppose we account not only for
21:47internally generated outbreaks
21:48where you start with your RO,
21:50an initial person comes in,
21:51or a couple of people come in infected and
21:54the whole thing just generates from there,
21:56but you also include the possibility
21:58it we have a residential campus.
22:00People are going to go off campus,
22:02don't be infected in the community,
22:04and bring infections back that it
22:06campus or visitors from off campus could
22:08come in and infect students as well.
22:10We take a look at a number of
22:12different reproductive numbers,
22:13not just one which is the same thing as
22:15we can get a number of different age
22:18dependent transmission curves, land of A.
22:20And let's do a Sprint.
22:22Let's ask what happens if we try and
22:24pack the whole fall semester between
22:26September 1st and November 20th,
22:27which happens to be the Friday before
22:30Thanksgiving. What happens, OK?
22:32Let's find out what happens,
22:34so I'm going to show you graphs
22:36of the cumulative incidence of
22:38infection just for a few scenarios.
22:40So you get an idea of how this works.
22:43Let's start with a relatively low
22:46reproductive number of only one and a half.
22:48That would suggest that social distancing
22:51procedures taken on the campus actually
22:53are affective and its students are,
22:55by and large,
22:56going along with them,
22:57but on the other hand,
22:59we still will have imported infections
23:01coming from the outside.
23:03And suppose that are coming in at
23:05a rate of one per day,
23:07which means if we're looking at 80 days,
23:10there would be 80 infections
23:12imported just because of people
23:13going around town or visitors coming
23:15to school here on the left axis is
23:18the cumulative incidence infection.
23:19If you took this situation,
23:21it did no testing whatsoever and
23:23basically just let the outbreak
23:24run unmitigated.
23:25Here is what happens on the right axis,
23:28if indeed you do screening.
23:30And if you disquieting biweekly every
23:32other week, or if you do screening.
23:34Weekly and what happens?
23:35What would happen here?
23:37Is that over this run of 80 days
23:40you would end up with 20% of
23:42the students or the residents.
23:44I should say on campus students
23:46and graduates to interpret.
23:47Perhaps also some workers who are
23:49resident and in any event you would
23:52have about 20% being infected.
23:53But if you screen everybody biweekly in this,
23:56see which situation following the
23:58theory that I showed you earlier,
24:00you're going to have about 3 1/2%
24:02look at the difference 20% for
24:043 1/2% from biweekly screening.
24:06Only one and 1/2% of the
24:08screen on a weekly basis.
24:10This is an example of a scenario that
24:12could be controlled by weekly screening.
24:14Let's make the scenario more challenging.
24:16Suppose it turns out that the behavior
24:18on campus is more or less like what was
24:21going on in Mujan at the beginning.
24:23So we gotta reproductive number
24:24more like 2.3 instead of 1.5. Well,
24:27now what happens if you don't do anything?
24:29And if you basically let this go unmitigated,
24:32you're in real trouble,
24:33because 80% or so will become infected.
24:35And, of course, that would never happen.
24:37I'm just showing you what the
24:39power of screening is.
24:40Suppose you screw. In this situation,
24:42once every other week biweekly screening,
24:44you still end up with 12.5% of
24:46the students being infected.
24:47By the way, as I say,
24:49These things just think what this implies
24:52about isolation capacity that you would
24:54need in order to put people getting sick.
24:56But weekly screening in this
24:58scenario still is infecting less
24:59than 2 1/2% of the students overall.
25:01And finally,
25:02let's really try and challenge
25:03us a little bit more.
25:05Here's what reproductive number of
25:073.3 this is closer to what we saw
25:09in Connecticut at the beginning,
25:11based on the initial rising hospitalization.
25:13Or smiles have similarly rapid
25:14increase at the very beginning.
25:15We're still keeping up by one
25:17imported infection everyday.
25:18Now, of course, if you didn't screen,
25:20you would have a complete disaster
25:22because almost everyone would
25:23be infected in this scenario.
25:24But again, we would not let that happen.
25:27On the other hand,
25:28look what happens if we scream.
25:30BI weekly screening doesn't really
25:32get you enough.
25:33It would tell you that you go from
25:35like 100% to 46% or something,
25:37so you cut it in half.
25:39But who would accept half of the
25:41students almost getting infected
25:43and yet weekly screening in this
25:45very same scenario gives you a
25:47cumulative incidence of four percent.
25:484% of 10,000 is still a sizable
25:51number of students,
25:52but it's not an uncontrollable number.
25:54So this,
25:54this again is an example of what
25:56happens with weekly screening.
25:58Now.
25:58It's possible that even weekly screening.
26:00Could be overrun and here, for example,
26:02just again to give you a sense of
26:05the kinds of analysis one can do.
26:06We have no imported infections,
26:08one per week, one per day.
26:105 today we have our different
26:11reproductive numbers.
26:12We have weekly screening.
26:13We have biweekly screening and here
26:15we see the numbers of infections that
26:17would occur over the same 80 day run.
26:19The first thing to do if you
26:20want to compare by we've got the
26:22weekly screening is just look
26:24at the difference in this scale.
26:26We're talking thousands.
26:26Here were up at that level only
26:29in the very very worst case.
26:30But this.
26:31This has a pretty important lesson to it,
26:33which is if you're into the weekly
26:36screening world I hope I've convinced
26:38you that we should be there if
26:41for it down in this region were OK.
26:44Up here we have one imported infection for
26:47day an we have a reproductive number of
26:50say 2.26 which is doing well number well,
26:53you know we're still going to have 200
26:56infected students at the end of the 80 days.
26:59Anything out here of course
27:01these are disastrous scenarios.
27:03So weekly screening isn't the panacea.
27:05It doesn't always work.
27:06It really depends on what the
27:08underlying parameters are here,
27:10which suggests to me that if you're going to.
27:14Rely on a screening program to get
27:16you through a residential program.
27:18You have got to be very, very,
27:21very confident that your epidemiological
27:23scenario really is gonna land you
27:25in this part of the parameter space.
27:27'cause if you move over here,
27:30it becomes lights out pretty fast.
27:32So to summarize,
27:33modeling can help understand transmission
27:35dynamics that has a lot of applicability
27:37and I hope I've illustrated that with
27:40the sludge data modeling can help
27:42understand intervention proposals.
27:43I've gone into detail on repeat screening.
27:46But of course there are many
27:48other interventions that one
27:49can study in the same way.
27:51Epidemic modeling in general
27:52is not about curve fitting.
27:54It is not like election polling.
27:56It's not like trying to make a guess and
27:58see if you kind of hit the hit the target.
28:02Rather,
28:02it's more like trying to navigate
28:04a car through the fog.
28:05Want to understand transmission dynamics?
28:07And you want to use that understanding
28:09to assess alternative decisions or
28:10interventions to support decision-making?
28:12And that's my story,
28:13and I'm sticking with it.
28:15Thank you very much.
28:19Thank you very much.