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

May 22, 2020

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

Information

ID: 5237
To Cite: DCA Citation Guide

Download Transcript

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.