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COVID-19 projections for Connecticut

May 28, 2020
COVID-19 projections for Connecticut
  • 00:00- From a colleague
  • 00:05asking for help with planning for the intensive care unit
  • 00:10and floor bed capacity at the Yale New Haven Hospital
  • 00:14Health System and Yale New Haven in particular.
  • 00:18Margret and Sohei had previously, or around the same time,
  • 00:21been working with the statistics policy
  • 00:25modeling an epidemiology collective on a queuing model
  • 00:28or discussing the parameters of the queuing model
  • 00:32for the dynamics of Covid-19 patient flow through hospitals.
  • 00:37So we decided to use this model setup to make a concrete
  • 00:41software product in the form of a web application
  • 00:44that Yale New Haven Health System and other hospital systems
  • 00:47could use for capacity planning.
  • 00:50We wanted to respond to their very immediate need
  • 00:54to know how full the hospital would get if Covid patients
  • 01:00kept coming at the rates that they were seeing
  • 01:02and how they might expand capacity to accommodate
  • 01:06these new patients.
  • 01:09So we created a Slack channel,
  • 01:12a way of communicating directly in real time
  • 01:15with the team members, who created a GitHub repository.
  • 01:17Within, I think, only about two hours,
  • 01:20we had a web application written in R,
  • 01:22using Shiny framework,
  • 01:25where you could sort of dial in the
  • 01:30current bed capacity at a hospital system.
  • 01:32You could enter parameters that govern the length
  • 01:35of stay of Covid patients and how they move through
  • 01:37the hospital from the emergency department
  • 01:40to the floor to the ICU
  • 01:41and then toward discharge or possibly death.
  • 01:47So that product went live very, very quickly.
  • 01:53There are many other collaborators and contributors
  • 01:54to the application beyond just our group.
  • 01:59Our goal here was to produce
  • 02:03something very quickly and immediately useful.
  • 02:08The structure of this model is shown
  • 02:10in this very complicated diagram.
  • 02:12It's not as complicated as it looks.
  • 02:14The basic idea is that patients enter through
  • 02:18to the emergency department.
  • 02:21They move to the floor then to the ICU.
  • 02:27There are many things that could happen
  • 02:28if those places are full.
  • 02:31Each of those parts of the hospital is treated as a queue.
  • 02:34That is, it's essentially a pool of patients
  • 02:37who are waiting to exit.
  • 02:39One of the ways they can exit is to step up
  • 02:41from the floor to the ICU.
  • 02:43One of the ways they can exit is to die.
  • 02:45Another is to be discharged
  • 02:47if they are no longer acutely ill.
  • 02:50So sort of taking into account all of this schematic, this
  • 02:56stylized depiction of the way Covid patients
  • 03:00would flow through a hospital,
  • 03:02we wrote a system of ordinary differential equations,
  • 03:05which describe formally, the dynamics of this system.
  • 03:10It's a very simple type of modeling
  • 03:13that is very useful when the number of patients is large
  • 03:17and when you want sort of aggregate dynamics over time.
  • 03:21So we're not modeling, it's not an agent-based model.
  • 03:24We're not modeling individual patients trajectories
  • 03:26through the hospital.
  • 03:27Rather, this idea of patient flow through the hospital.
  • 03:31So this model, depicted schematically here,
  • 03:34is formalized in a system about ordinary differential
  • 03:37equations with many parameters.
  • 03:39Those parameters are calibrated to data that we have
  • 03:41from the Yale New Haven Health System
  • 03:46and to values from the literature.
  • 03:49We wrote this web application, which is now live
  • 03:53at the Shiny apps URL that you can see below.
  • 03:56You can interact with it if you like.
  • 04:01It basically allows the user to specify time horizon,
  • 04:04how quickly or slowly they think new Covid patients
  • 04:07will present to the emergency department
  • 04:10and then on subsequent tabs, you can dial in the current
  • 04:15hospital capacity at your institution.
  • 04:17You can dial in capacity increases that you anticipate
  • 04:20being able to implement into the future
  • 04:23to see how dynamics would change if say,
  • 04:25you could add 100 new ICU beds over the course of two weeks
  • 04:30a month from now, for example.
  • 04:32Then there are many, many input parameters.
  • 04:34Things like the age-specific rates
  • 04:39of death or of stepping up from the floor in the ICU,
  • 04:42to the average length of stay in each of those compartments
  • 04:47for patients who come to the hospital.
  • 04:50You can generate reports, downloadable PDF reports.
  • 04:54We sort of envisioned this tool being responsive
  • 04:57to the needs of hospital decision makers
  • 05:00who wanted to be able to add this planning capability
  • 05:04to their existing bed management software applications
  • 05:09and then to be able to generate reports for say,
  • 05:12supervisors and higher up decision makers
  • 05:14that would describe the scenario that the analysts
  • 05:17was most interested in.
  • 05:19The reports would also describe the consequences
  • 05:22of a capacity expansion strategy that might be implemented
  • 05:25by the system.
  • 05:27So I think this tool was very useful
  • 05:30to the Yale New Haven Health System.
  • 05:33It was publicized kind of broadly and we got some interest
  • 05:36from hospital systems throughout the U.S..
  • 05:39I had spoke to some of them about the ways
  • 05:41that they were making decisions, planning capacity increases
  • 05:45and using this application and others
  • 05:47that are also publicly available online,
  • 05:50to help guide their decision making.
  • 05:54This is an open source project.
  • 05:56You can get all of the source code for the Shiny application
  • 05:59on our GitHub repository here, shown below.
  • 06:07So what are the next steps for this project?
  • 06:10Fortunately, hospitalization in Connecticut is declining.
  • 06:15This figure that I've shown here is kind of compressed.
  • 06:17It's declining slowly.
  • 06:21But it has been declining for I think,
  • 06:23more than three weeks now.
  • 06:25Yale New Haven Health System, along with hospitals
  • 06:28heath systems throughout the state,
  • 06:30are doing much better than they were in mid-April.
  • 06:33They have enough bed capacity to accommodate
  • 06:35all the Covid patients and many more who may arrive
  • 06:39in the coming months.
  • 06:40So this is very good news for the hospitals
  • 06:42and for the state.
  • 06:43It's one of the reasons that the governor initiated
  • 06:48the first phase of the reopening plan on May 20 this week.
  • 06:53However, a lot of the projections and some that I'll show
  • 06:56in a few minutes, indicate a substantial risk of resurgence
  • 06:58of new cases, hospitalizations and deaths
  • 07:01following reopening the state.
  • 07:03This resurgence is anticipated to occur in July,
  • 07:06August, maybe September, depending on how things go
  • 07:09with reopening.
  • 07:11So I think that
  • 07:13the model, the web application,
  • 07:16and this work in general will unfortunately,
  • 07:20become useful again and very relevant again
  • 07:23later on in the summer if hospitalization
  • 07:25of Covid patients increases again.
  • 07:28So we want to maintain our capacity to continue developing
  • 07:31this model and responding to the needs
  • 07:34of decision makers within hospital systems.
  • 07:37We're taking this down time though,
  • 07:38to write a technical report and a lessons learned paper
  • 07:42about the way that we interact with health systems
  • 07:46and how we might improve the way
  • 07:48that we do that in the future.
  • 07:50This work is of course also gotten us very interested
  • 07:52in the ways that hospitals manage Covid patients.
  • 07:55We're very interested in comparative evaluation
  • 07:57and comparative effectiveness in the evaluation
  • 08:00of Covid-19 medical interventions.
  • 08:03That's something that Margret Erlensdottir
  • 08:06an MD PhD student in biostat is working on.
  • 08:09- Forrest? - Yes?
  • 08:10- Can you take a question?
  • 08:12- Yes, please go ahead.
  • 08:16- Have you only applied this to Yale New Haven?
  • 08:19- We have, the model itself is generic.
  • 08:22This is a good question, but we have calibrated many
  • 08:26of the length of stay and probability parameters
  • 08:30based on data that we received from Yale New Haven.
  • 08:34So in that sense, the dynamics that we present by default
  • 08:39are specific to Yale New Haven.
  • 08:41The user has the ability to change all of those parameters,
  • 08:45so we anticipate that this could be useful
  • 08:47for hospital systems of any size
  • 08:50with different patient demographics,
  • 08:51different age distributions for example.
  • 08:54So we want it to be as useful as possible,
  • 08:57but having said all this, the customer in this case,
  • 08:59was very clearly for us, Yale New Haven
  • 09:02and they had a very specific need and--
  • 09:04- Have you had a reaction?
  • 09:06Did you have an ongoing reaction with the people
  • 09:08at Yale New Haven who were using this product,
  • 09:10whether or not it was helping them or was it accurate
  • 09:13or did they have any complaints about it?
  • 09:16I'm sure they did.
  • 09:16Can you tell me about that interaction?
  • 09:19- Sure, sure.
  • 09:22I think that they made a few requests of us.
  • 09:25Some of them were very qualitative.
  • 09:27They wanted very early to be able to generate reports.
  • 09:30A lot of the requests were for additional functionality
  • 09:33rather than additional structure in the OD model
  • 09:37but they really,
  • 09:39I think many of the requests were about flexibility
  • 09:41and granularity in the predictions.
  • 09:44They wanted to be able to dial in the exact patient
  • 09:46demographics and the care parameters that were actually
  • 09:50being implemented at Yale New Haven.
  • 09:52So we tried to give them that ability and that control.
  • 09:58I think mostly, successfully.
  • 09:59We retained some of the generality of the model,
  • 10:02while allowing users to input the parameters
  • 10:05that they felt were right for their system.
  • 10:07In terms of the way it was used at Yale New Haven,
  • 10:11I think that by the time they asked us for help,
  • 10:15many of the actual capacity expansions
  • 10:18had already been implemented.
  • 10:19I'm talking about taking over high school gymnasia,
  • 10:22changing the configuration of parking lots
  • 10:25to provide drive through testing and turning,
  • 10:30I guess parts of the hospital into ICUs.
  • 10:33Many of those--
  • 10:36- You might say that they over expanded a little bit
  • 10:38since they quickly came not needed capacity.
  • 10:41So did you help them, saying hey,
  • 10:43you guys don't need to do that much?
  • 10:47- I think that based on the projections for population
  • 10:50level incidence that they were receiving in early
  • 10:52to mid-April, the capacity expansion was appropriate.
  • 10:59This model here did not provide
  • 11:03population level projections,
  • 11:05which I'll show in a few minutes.
  • 11:06So we were not telling them
  • 11:07that they had over expanded capacity.
  • 11:11I think that at the state level,
  • 11:13the total hospitalization in the state came very close
  • 11:17to the preexisting capacity, as it was in early March.
  • 11:22So I think that there was a big concern that it was unclear
  • 11:26what the doubling rate of new cases would be.
  • 11:29We had not yet seen some of the benefits of state lock down
  • 11:31and closure of schools.
  • 11:33So the hospital systems were expanding very aggressively,
  • 11:37I think for good reason.
  • 11:40- Okay, but they were just doing that by looking at
  • 11:44the daily or maybe the weekly case counts right,
  • 11:47and seeing what the doubling rate was and things like that.
  • 11:50They were doing anything more subtle than that?
  • 11:52- That is what they were doing when they called us on.
  • 11:55We tried to give them projections under their own
  • 12:00in-house assumed doubling rates.
  • 12:03So we were very interested in showing them when the hospital
  • 12:06would fill up and under what circumstance
  • 12:08and how different parts of the hospital would fill up.
  • 12:13- Okay.
  • 12:14I'll let you go on.
  • 12:16- In a few minutes I'll show state level projections
  • 12:18that might answer some of your questions.
  • 12:24All right.
  • 12:28- By the way, I'm John Hardigen, by the way.
  • 12:31Used to be in the statistics department.
  • 12:33- Yes, I know, good to see you.
  • 12:38All right, second project.
  • 12:40On April 14, so just as we
  • 12:47finished the most fundamental software development
  • 12:50on the application that I just showed you,
  • 12:52on April 14 we were asked to start producing projections
  • 12:55for the governor's Reopen Connecticut Advisory Panel,
  • 12:58which was charged with
  • 13:01making recommendations to the state, to the government,
  • 13:04to the Department of Public Health
  • 13:06on how reopening should proceed and what the timeline
  • 13:09should be and what business sectors could safely reopen
  • 13:12at which times.
  • 13:14The panel consisted of public health researchers,
  • 13:17including Albert Ko and several other people from Yale
  • 13:20and many business leaders in Connecticut.
  • 13:23It was a mixed group.
  • 13:27The panel needed projections at that time of Covid-19
  • 13:31incidence, hospitalizations and deaths
  • 13:33under future reopening scenarios, to plan testing expansion,
  • 13:37seroprevalence studies and most importantly,
  • 13:39to assess the risk of a second wave of infections.
  • 13:43So this was in mid-April,
  • 13:45around the time when hospitalization was peaking.
  • 13:48Of course, nobody knew exactly at that time
  • 13:51that the peak was occurring and there was a lot of concern
  • 13:55that things would continue to get much worse,
  • 13:58in terms of hospitalization in Connecticut.
  • 14:03The work of that committee
  • 14:07advised the governor in his reopening strategy,
  • 14:09which we've all probably heard about,
  • 14:11if you're following press releases from the state.
  • 14:14The state began reopening on May 20th and there's now,
  • 14:17I think, although the work
  • 14:19of the advisory panel may be wrapping up,
  • 14:22there's now an ongoing need for projections
  • 14:24to inform decision making and epidemiological study design,
  • 14:28that further informs decision making
  • 14:32for the Connecticut response and reopening.
  • 14:36This part that I'll talk about now is joint work
  • 14:37with Olga Morozova and Richard Li.
  • 14:42So at the beginning of this project, we had to explain
  • 14:46to decision makers and members of the advisory panel,
  • 14:50how data are different from model projections
  • 14:54and what sort of...
  • 14:59What the differences between these two products were.
  • 15:01But I think there is a recognition at that time
  • 15:03on the part of policy makers and committee members
  • 15:05that the policy makers have access
  • 15:07to a real-time data stream, which is very high quality.
  • 15:11They have access to all sorts of state dashboards
  • 15:14describing the current state of the Connecticut pandemic.
  • 15:18They know about hospitalization and bed capacity
  • 15:20information from the Connecticut Hospital Association.
  • 15:23They know about test counts and nearly real-time
  • 15:25case counts, number of tests positive at hospitals
  • 15:28and in the community.
  • 15:30They know how many deaths have occurred to attributable
  • 15:33to Covid-19 or that are suspicious,
  • 15:37that are possibly related.
  • 15:39They might have information about excess deaths
  • 15:42that are not attributed to Covid-19 but are above
  • 15:45and beyond what you might normally expect in a typical year.
  • 15:49They have access to all this information.
  • 15:51They have access to very responsive staff
  • 15:53and many very smart people working for the state
  • 15:57Department of Public Health and other state agencies.
  • 16:02So there might be a sense that policy makers have access
  • 16:04to all the information and the most timely information
  • 16:07they could possibly need to make good decisions
  • 16:08for the state.
  • 16:10We tried to argue that there was more information
  • 16:12that they might be able to use constructively
  • 16:16to guide reopening, and that was information that was not
  • 16:19directly derived from contemporaneous data streams,
  • 16:24but rather these would be projections from transmission
  • 16:27models about possible futures.
  • 16:30So projections here can tell us about what might
  • 16:33happen in the future, possible hypothetical
  • 16:34or counterfactual scenarios to be defined
  • 16:39by the governor and the outcomes that would occur
  • 16:42under those reopening scenarios.
  • 16:44So I'm talking about phases, business sectors,
  • 16:47reopening back-to-school, what might happen in late August,
  • 16:50early September, as children go back to school
  • 16:52or back to summer camp in June and July.
  • 16:56What might happen under expanded testing
  • 17:00and contact tracing or continue to modified
  • 17:03social distancing guidelines.
  • 17:04Things like wearing masks or keeping six feet apart
  • 17:10and all of those things.
  • 17:11So we tried to explain how projections from these types
  • 17:15of models might be very different from simple plots
  • 17:19of the data streams that policy makers have access to.
  • 17:23This is a figure I showed them at the very beginning.
  • 17:26On the left, we have the number of death,
  • 17:28I think by early May, that had accumulated in Connecticut.
  • 17:33These are the red dots on the left hand side.
  • 17:36On the right hand side, we have a projection of what might
  • 17:38occur in the future on this day and I think it was
  • 17:40first week of May.
  • 17:42Right, and I think this may seem silly as a projection
  • 17:47exercise or it seems silly to
  • 17:52make a distinction between data and predictions,
  • 17:56but it may have useful in the setting to emphasize
  • 17:59that the real-time data that policy makers were using
  • 18:02was just the stuff on the left
  • 18:04and that if one believed the assumptions underlying
  • 18:07some of these dynamic transmission models,
  • 18:10that they could be provided with the stuff on the right,
  • 18:13which would be a projection
  • 18:14of what might happen in the future.
  • 18:16Here, I happen to have shown projections starting
  • 18:19on March 1, just to emphasize sort of how the line follows
  • 18:24the data points in the projection.
  • 18:27But the idea is that these projections would come
  • 18:29with some sort of uncertainty windows or sets
  • 18:34that would represent, in some sense,
  • 18:38the most likely possible futures under what we know today
  • 18:41and what we believe may happen about the future.
  • 18:44So the-- - May I stop you for a second?
  • 18:47- Of course. - Forrest.
  • 18:50First of all, I think you'll agree that the points
  • 18:53on the line at the left are extremely highly correlated
  • 18:55with each other, since they're just cumulatives.
  • 18:59And that's not a good way to show what's happening,
  • 19:01is to look at cumulatives.
  • 19:02You have to kind of guess what the derivatives are
  • 19:06and people aren't so good at that.
  • 19:07You would be much better off trying to project
  • 19:10and look at say, the weekly values.
  • 19:13Certainly can't look at daily values because God knows
  • 19:15what the daily values goes from,
  • 19:17but you know, you see in a week they kind of catch up
  • 19:19with the truth.
  • 19:20So if you looked at weekly values, you would tell on
  • 19:22what the present situation was.
  • 19:24Surely, that's what the hospitals need to know.
  • 19:27They don't need to know how many people they had
  • 19:29a long time ago or what the total was.
  • 19:31They want to know that the present charge is.
  • 19:33So I would just suggest that the thing you should be
  • 19:36working on is something closer.
  • 19:38Can't use daily values, it's too small,
  • 19:40but a weekly value and then that's what really matters.
  • 19:43That's the present situation.
  • 19:46- Certainly and have access to all that information.
  • 19:48The State Department of Public Health produces
  • 19:50weekly smoothed and unsmoothed count.
  • 19:54In fact, daily counts as well.
  • 19:56They're very volatile.
  • 19:58They jump up--
  • 19:59- The daily counts have a huge weekly effect.
  • 20:02You just don't want to rely on them at all.
  • 20:05The docs aren't bothered to do things on the weekends
  • 20:07is my interpretation of it.
  • 20:08But maybe it's someone not bothering, but whatever it is,
  • 20:11it's a big weekly effect.
  • 20:12It's something you don't want to have.
  • 20:14But if you take a weekly value, that's always averaged out.
  • 20:17I just think that projecting the future
  • 20:20and I think you would find there's quite a lot
  • 20:22more error in that.
  • 20:23You're getting the benefit of the fact that all this
  • 20:26is highly correlated but if you were trying to project
  • 20:28the future, these things would be whoa, of stuff.
  • 20:32- Yes, totally agree.
  • 20:33This figure was generated in response to a very specific
  • 20:36question, which is how many deaths will the state expect
  • 20:39to have accumulated on a future date.
  • 20:42- Okay.
  • 20:45Thanks.
  • 20:48- Okay, so I wanted to answer this question
  • 20:50because I hope that you're all wondering about it.
  • 20:54Does the world need another Covid-19 projection model?
  • 20:58There are lots of them out there.
  • 21:00Vary in quality, some from very experienced research groups
  • 21:05and experienced epidemiologists, some from
  • 21:09Silicon Valley software developers
  • 21:11who just learned about regression.
  • 21:13I don't think that the world needs another Covid-19 model
  • 21:17at the national or international level.
  • 21:19But I think Connecticut does for several reasons
  • 21:23that I wanted to describe briefly here.
  • 21:27We wanted to develop a scenario analysis tool
  • 21:29that was responsive to specific questions
  • 21:31from the Connecticut leadership,
  • 21:33who were planning to reopen the state.
  • 21:38We thought there were several reasons that we could add
  • 21:39some value here, beyond what is provided by some of the more
  • 21:42generic models that are available
  • 21:47for national, state and also local projections.
  • 21:50The first thing is access to epidemiologists
  • 21:53at the School of Public Health
  • 21:54and in the Public Health Modeling Unit.
  • 21:57We have pretty unique access to data
  • 21:59from the Connecticut Hospital Association
  • 22:01on the bed capacity and bed occupancy throughout the state.
  • 22:06We can use information on individual patient trajectories
  • 22:10through the healthcare system from using data
  • 22:12from Yale New Haven.
  • 22:14We have access to empirical epidemiological studies
  • 22:18from Yale emerging infections program and data streams
  • 22:21from the Department of Public Health through Yale EIP.
  • 22:25We have connection to the people who are running
  • 22:28the testing and seroprevalence studies
  • 22:30to be conducted in the future and the model projections
  • 22:34that we produce will be very closely tied
  • 22:38to the conduct of those studies.
  • 22:39Some of them can give information that we can use
  • 22:42for calibrating the model, and in turn,
  • 22:44we can use model projections
  • 22:48to provide preliminary estimates of say,
  • 22:51cumulative incidence of Covid-19 for study planning,
  • 22:56in order to do sample size calculations.
  • 23:00And of course, we are hoping to be able to help
  • 23:04with the Department of Public Health's
  • 23:07implementation of optimal testing and sampling strategies
  • 23:10as they look for new cases and try to control outbreaks
  • 23:13that may occur in the future in Connecticut.
  • 23:20So the modeling principle here,
  • 23:22this is an infections disease model that I'm gonna show you.
  • 23:25It's not a model for hospital
  • 23:29patient flow through hospitals.
  • 23:31But I think in introducing this to people who have not seen
  • 23:35these models before, the operating principle
  • 23:38is that of mass action.
  • 23:41I think if mathematical infectious disease epidemiology
  • 23:44has a central dogma or a single principle that governs
  • 23:47the structure of quantitative models for infections,
  • 23:51it's something like the Law of Mass Action,
  • 23:54that in a small time interval, the number of new cases
  • 23:57that accrue is proportional to the number of ways
  • 24:01that susceptible individuals and infectious individuals
  • 24:05can come together.
  • 24:07This means that new cases or incidences
  • 24:09is driven by the product of--
  • 24:11Or sorry, I should have said the product of susceptibles
  • 24:14and infectives or the number of ways that people
  • 24:18susceptible individual can come into contact
  • 24:20with an infected person.
  • 24:23This general principle is what underlies all transmission
  • 24:27models and many transmission models are compartmentalized
  • 24:29or they are separated in space and geography
  • 24:33or by age group or by different risk categories,
  • 24:36but this is the essential principle.
  • 24:38That new cases of a certain type and a certain place
  • 24:41arise at a rate that is proportional to the product
  • 24:45of the number of susceptibles and infectives.
  • 24:47The number of ways that disease can be transmitted.
  • 24:53So we have divided the population of Connecticut
  • 24:56into many compartments.
  • 24:59Those who have not had the disease,
  • 25:01those who are susceptible,
  • 25:03those who have been infected,
  • 25:06they are exposed but not yet infectious.
  • 25:08So they don't have symptoms.
  • 25:11Those who are infectious but remain asymptomatic,
  • 25:14those with mild symptoms.
  • 25:16They know they're sick
  • 25:17but they do not require hospitalization.
  • 25:19Those with severe symptoms who do require hospitalization.
  • 25:24Those who have mild symptoms but are successfully isolated
  • 25:28because they realized they have symptoms or they got
  • 25:33a viral test that told them that they are infected.
  • 25:36So they successful isolate themselves.
  • 25:38Those people with severe disease who are hospitalized,
  • 25:42those who have severe disease but remain unhospitalized
  • 25:45because there's no space for them.
  • 25:47This is very important in projecting deaths in the future
  • 25:50scenario, in which we run out of hospital capacity.
  • 25:55Then we have severe institutionalized populations,
  • 25:58who are not in the hospital,
  • 25:59such as people in nursing homes, correctional institutions
  • 26:03and other long-term care facilities.
  • 26:06Those who have been infected but did not die
  • 26:09and are now recovered or successfully isolated
  • 26:12and recovering and those who have died.
  • 26:15So the idea here is to divide up the population
  • 26:18of Connecticut into a number of people
  • 26:22in each of these compartments.
  • 26:28The model that we put together is a variation
  • 26:30on the susceptible exposed infected and removed model.
  • 26:38We divide up the infectious individuals into three
  • 26:42categories that I told you about, severe, mild
  • 26:44and asymptomatic infections.
  • 26:47We have two different types of patients
  • 26:49who need hospitalization.
  • 26:51We have unhospitalized patients.
  • 26:55We can remove patients by isolating them
  • 26:57and they can recover after some amount of time,
  • 27:01if they do not die.
  • 27:04This is the basic structure of the SEIR model.
  • 27:09The usual model structure is just this linear part,
  • 27:12SEI and then R.
  • 27:15We divided up into these additional components,
  • 27:19not because we believed that these components
  • 27:21cover every possible scenario or every possible type
  • 27:25of illness or state of the world or state of patients,
  • 27:28but because this is the most parsimonious model
  • 27:31that we can think of that captures the dynamics
  • 27:34of infection that are most likely to lead to the outcomes
  • 27:38that a state government cares most about.
  • 27:40Those are state-level hospitalizations and deaths
  • 27:44and possibly cumulative incidents.
  • 27:48Right, so this model is not intended to capture
  • 27:51every biological or epidemiological feature of Covid-19
  • 27:55transmission in Connecticut.
  • 27:57Rather, it is the simplest model that captures the features
  • 28:00that policy makers care most about.
  • 28:06It's also structured by geography.
  • 28:10We found that the...
  • 28:14We looked at information about travel and commuting patterns
  • 28:17throughout the state to look at where people
  • 28:18might be mixing, where they live, where they work,
  • 28:21others things like that.
  • 28:22But we found that that information did not give us
  • 28:26much more information than simple adjacency matrix
  • 28:28of counties in the state.
  • 28:33We're well aware that many people in Connecticut
  • 28:38work or commute or travel often to New York City area.
  • 28:41We'll try to accommodate that in the model
  • 28:45or in our interpretation of the model.
  • 28:48Rather, the adjacency matrix of counties in Connecticut
  • 28:54gives us much of the information that we use
  • 28:55for the geographically dependent nature of transmission.
  • 29:04Basic idea--
  • 29:05- Rhode Island and Massachusetts
  • 29:07aren't doing too good either.
  • 29:09- They're not doing well, I agree.
  • 29:12To avoid turning this into a very granular or national model
  • 29:19we are going to treat the exogenous force of infection
  • 29:22experience by Connecticut residents as something else.
  • 29:28So we sort of imagined that it is
  • 29:31subsumed into the force of infection experience
  • 29:33by everyone in Connecticut.
  • 29:35I agree, both a lot of infections
  • 29:38and a lot of heterogeneity outside of Connecticut
  • 29:42in bordering states.
  • 29:45So most of this we don't specifically take into account.
  • 29:50The basic idea here, I'm just showing two compartments
  • 29:54of the ODE system, the basic idea is that in county I,
  • 29:59the number of susceptibles or the rate of new infections
  • 30:02is governed by the number of infectious individuals
  • 30:07in that county and the number of infectious individuals
  • 30:10in neighboring counties.
  • 30:13Here in beta is the transmission rate of infection.
  • 30:17So individuals who are susceptible transition to the exposed
  • 30:22infectious state and then to other states down the road.
  • 30:25But these are sort of the mass action equations
  • 30:28for a heterogeneous population in which the force
  • 30:30of infection is coming from outside and within
  • 30:34individual counties.
  • 30:39I'm not going to go into a great deal of detail
  • 30:42about the system of ODs that is most useful here.
  • 30:48I'll just say that we solve in numerically.
  • 30:50It's a system of 11 differential equations
  • 30:53given the parameters, which I'm just gonna bundle into
  • 30:56a vector theta.
  • 30:58Let Y of T given theta, be the solution to the OD system
  • 31:01at time T with parameters theta.
  • 31:03You can solve this system with pretty good accuracy
  • 31:07using modern OD solvers.
  • 31:10This solution--
  • 31:11- They're just linear equations, are they?
  • 31:13Linear right?
  • 31:15- They're non-linear in the right hand side
  • 31:18is non-linear in the other model compartments.
  • 31:21Right, that's what mass action is.
  • 31:24It's proportional to the product.
  • 31:26So OD is proportional to the product of S and I.
  • 31:31So it's--
  • 31:33- On the other hand, you agree that S doesn't change much
  • 31:35because unless you've got a very fully infected population,
  • 31:39S doesn't change that much.
  • 31:41You've got--
  • 31:42- S is most quickly when infections are increasing
  • 31:45most quickly and Connecticut right now,
  • 31:48S is still pretty large.
  • 31:50I think cumulative incidence is between 5% and 15%.
  • 31:55So S has not changed.
  • 31:57- S is 85% and is gonna change.
  • 31:59I'm just making it linear for myself, that's all.
  • 32:02- Sure, yeah.
  • 32:04So right now S has not decreased that much.
  • 32:08You know, between, it's still at 95% to maybe 85%,
  • 32:13something like that.
  • 32:15As the pandemic progresses and into the fall,
  • 32:17if there's another resurgence of infections,
  • 32:19we will expect S to change quite a lot more.
  • 32:22If it changes a lot, then we'll be in herd immunity
  • 32:25territory where depletion of susceptibles
  • 32:28plays a prominent role in altering the dynamics
  • 32:32of the pandemic, but we're not there yet.
  • 32:34- But I am right in thinking that this is linear,
  • 32:36it's really just a matrix problem isn't it,
  • 32:38that we have to solve.
  • 32:39- If it were linear it would be a matrix problem.
  • 32:41- Yeah, okay.
  • 32:44- Right. - Yeah.
  • 32:47- So this system is a deterministic system.
  • 32:52Engineers, mostly and some epidemiologists,
  • 32:55have been thinking for a very long time about principled
  • 32:58ways of estimating parameters for deterministic system.
  • 33:02Unfortunately, for models of this type,
  • 33:04which is generally the case in infectious disease
  • 33:06epidemiology, there are some serious
  • 33:11identifiability problems.
  • 33:11Not all parameters can be uniquely estimated from the data
  • 33:16or infinitely many combinations of parameters
  • 33:18that appear to fit equally well.
  • 33:23We only observe in this case,
  • 33:25the hospitalization and death compartments.
  • 33:27There's some information from PCR testing
  • 33:30about the prevalence of infection at different times,
  • 33:34but because the testing strategy in Connecticut
  • 33:36and elsewhere has varied so dramatically
  • 33:40over the last few months, we didn't feel like we could use
  • 33:42any information from testing alone to inform the sizes
  • 33:47of the currently infected compartments.
  • 33:51So basically, we're trying to estimate many parameters
  • 33:54for a system with 11 components using only the time series
  • 33:59of hospitalizations and deaths.
  • 34:02So it's quite challenging and in practice,
  • 34:04this necessitates taking parameter values
  • 34:08from the literature, from clinical studies,
  • 34:10from our knowledge of how hospitals treat patients
  • 34:14and also using a statistical estimation scheme
  • 34:18to learn about elements of theta, of the unknown parameters.
  • 34:22I wish that I could give you a more coherent statistical
  • 34:26inference strategy in which all of the parameters
  • 34:31were learned from the data and I could tell you
  • 34:34that they were being consistently estimated
  • 34:36and that as the epidemic went on, we would get more and more
  • 34:39precise estimates of each of those parameters.
  • 34:41Unfortunately, it's just not true.
  • 34:43That the model structure that we need here to be able
  • 34:46to accommodate
  • 34:51the structure of the pandemic is more complicated
  • 34:54than the model structure that we could possibly identify
  • 34:59non-parametrically or semi-parametrically
  • 35:01or even in this parametric model.
  • 35:05So I just wanted to give you some examples
  • 35:06of how people do this in practice.
  • 35:08These are not exactly endorsements
  • 35:10of statistical frameworks.
  • 35:12The basic idea is that given theta,
  • 35:14we can solve the ODE system, it gives us deterministic
  • 35:17solutions at time points where we have an observation
  • 35:21and then calibration or statistical inference
  • 35:23essentially amounts to minimizing a loss criteria
  • 35:26and are comparing the observed values to model predictions.
  • 35:31The two frameworks that are most frequently used here
  • 35:34are imposing a normal errors or gaussian errors,
  • 35:37almost normal gaussian errors
  • 35:41or equivalently minimizing at least squares type
  • 35:44of loss function or doing this plus on maximum likelihood
  • 35:49estimation for elements of theta
  • 35:51that you can identify in this way.
  • 35:53I think in this project we used
  • 35:58the Poisson maximum likelihood.
  • 36:01There are many things about this, one of which is that
  • 36:03a Poisson random variable could take values
  • 36:06that are larger than the size of the population.
  • 36:08In practice here, that's not what occurs
  • 36:12because the number of infections here is small,
  • 36:15but this is basically a framework for doing a type
  • 36:18of statistical inference or learning about
  • 36:22a posterior distribution on parameters
  • 36:25from a model, which gives deterministic predictions
  • 36:27and which doesn't have any inherent stochasticity.
  • 36:31The procedure that we used here, which I'm not gonna
  • 36:33talk about in great detail here, was developed
  • 36:36by postdoc Olga, is a hybrid approach that fixes
  • 36:39some parameters and imposes uncertainty distributions
  • 36:42on them from our prior knowledge and the literature
  • 36:46and conducts Bayesian posterior inference
  • 36:49on known parameters and initial conditions.
  • 36:51So we try to learn jointly about parameter--
  • 36:55Yes go.
  • 36:56- Forrest, there's a question people always ask of this
  • 36:58whenever I give a talk like this,
  • 37:00how do you determine your prior distribution?
  • 37:03- In this case, I would say we're in a very good position
  • 37:06to interpret priors as literally being prior beliefs.
  • 37:11We have for example, point estimates and confidence
  • 37:14intervals from published studies.
  • 37:19We also have parameters which are intrinsic to the model
  • 37:22but for which we have very little information.
  • 37:24So we assign to them, what we believe qualitatively,
  • 37:27to be an appropriate representation of our uncertainty
  • 37:31or ignorance about those parameters
  • 37:33under the parametrization.
  • 37:36But to your question--
  • 37:38- What you believe to be true then, is that right?
  • 37:42- Oh certainly.
  • 37:43It is a mixture of what other people believe to be true
  • 37:46and what we believe to be true as well.
  • 37:48So I would take a subject of interpretation
  • 37:49to the priors here.
  • 37:52They are subjective in the sense that we believe
  • 37:56these uncertainty distributions.
  • 37:59They are quantitative in the sense in that
  • 38:02some of them come from published studies.
  • 38:06- Okay, I'm sorry, I do just a little bit longer.
  • 38:11You know, I know you've got a lot of parameters in here,
  • 38:13many of which I don't know anything about,
  • 38:15but I suspect the very important one is parameter
  • 38:18which says what is the ratio of new cases,
  • 38:24assuming that susceptibility isn't changing
  • 38:26to the infection rate, right.
  • 38:28What's the...
  • 38:30That's the number,
  • 38:32that ratio is an important ratio.
  • 38:34New cases against the number that are infected
  • 38:38and that number out to extract is an important number
  • 38:42because it changes a lot, according to the conditions
  • 38:44that the government sets.
  • 38:46Changes all the time because you're trying to reduce
  • 38:48contacts and effectively reducing that contacts
  • 38:50is to change that ratio.
  • 38:52I assume that that's built into the model somehow,
  • 38:55but I would think you probably don't know very much
  • 38:57about how the government's policies and whatever
  • 39:00are gonna change that ratio.
  • 39:02So if you said you know, I know it's gonna be a month
  • 39:04from now, I'd say no you don't.
  • 39:06- Oh sure. - Yeah.
  • 39:08So how do you handle it?
  • 39:10- We certainly do parametrize that rate,
  • 39:14that is the transmission rate that you were talking about.
  • 39:16It's the parameter that multiples the product
  • 39:19of the number of susceptibles
  • 39:20and the number of infectious individuals.
  • 39:23That's called beta in the model.
  • 39:25Beta does change over time.
  • 39:27It's parametrized as a sum of step functions.
  • 39:33Those step functions change in their value
  • 39:36around when the governor closes schools, which happened,
  • 39:42I think on March 25th and when the governor--
  • 39:45Or sorry, a little bit earlier, maybe March 20th,
  • 39:48I can't remember.
  • 39:49Then when the governor issued the stay at home order,
  • 39:52the stay safe stay at home order,
  • 39:56which I think took effect on the 23rd.
  • 39:59So those step functions are in the model for historical
  • 40:02interventions that were implemented by the state.
  • 40:04For future interventions which are implemented by the state,
  • 40:07we are guessing.
  • 40:09Fortunately, we are guessing using information
  • 40:11from the people who will actually make those decisions.
  • 40:14So I will show how we assume that that transmission rate
  • 40:20or contact rate might change in the future
  • 40:23under guidelines expressed by the governor
  • 40:26and policy makers.
  • 40:28Right, so in the future of course,
  • 40:29I don't know what going to actually occur.
  • 40:31The best I can do is ask the people
  • 40:33who will implement the change.
  • 40:35- All right, well.
  • 40:37I'm sorry, this is my last remark.
  • 40:39I won't keep on doing this, but I would think that
  • 40:42these rates that we're talking about,
  • 40:43which seems to be are really critical to what happens
  • 40:45in the model, that you and find invasion inferency
  • 40:49you have to give a plausible, defensible probability
  • 40:52for them, which I would find hard to do,
  • 40:55and I also find it hard to do because I know that those
  • 40:58rates differ huge amount in Connecticut
  • 41:00between the different counties, that you can just see
  • 41:03if you look at what's happening in different counties.
  • 41:05Those rates are different because different
  • 41:10amount of separation and different amount
  • 41:12of personal contact.
  • 41:13- Sure.
  • 41:14- I think so kind of do that on an average way
  • 41:16of all the counties, seven or eight of them,
  • 41:19you'd think you at least got a vary among the counties
  • 41:23and have some number among the counties.
  • 41:25Then if there's a change of policy from the governor,
  • 41:27there'd be a change in sum or expected you need
  • 41:29to have that built in somehow here.
  • 41:31- Certainly.
  • 41:32In this work, I guess in all policy-relevant work,
  • 41:37there is a constant tension between the need
  • 41:41for parsimony and parametrization
  • 41:45and the need for these rich ways
  • 41:48of accommodating heterogeneity.
  • 41:52What we have found in this setting is that we lacked
  • 41:55the information or data to be able to separately
  • 41:58parametrize transmission rates at the county level
  • 42:04but that we can capture the aggregate number of cases,
  • 42:07hospitalizations and other relevant outcomes
  • 42:09at the state level by averaging over them.
  • 42:13The reason is because the counties themselves
  • 42:15have very different incidence, which actually does explain
  • 42:19quite a lot in the differing trajectories
  • 42:22of case counts and hospitalizations and deaths
  • 42:25within the counties.
  • 42:30- Hi Forrest thank you, this is very interesting.
  • 42:32This is Donna.
  • 42:33I have a question.
  • 42:35Do you have, the para--
  • 42:37Hi.
  • 42:38Are the parameters identifiable without Bayesian priors
  • 42:41or just from the data that we have or do you need
  • 42:46the priors in order to estimate the parameters?
  • 42:49- A subset of parameters is uniquely identifiable
  • 42:52by maximum likelihood or is point identified.
  • 42:55But really speaking, the answer to your question is no.
  • 42:59There are infinitely many combinations of parameters,
  • 43:04which fit any given loss function criteria equally well.
  • 43:07So we do need parameters here.
  • 43:09It is unfortunate and I think--
  • 43:12Yeah, go ahead.
  • 43:15- Priors you mean.
  • 43:17Do you know like what's the simplest possible model
  • 43:21that's just identifiable from the data
  • 43:23and is that model useful at all or is it so simple
  • 43:26that it's not even helpful?
  • 43:29- Two parts to that question, the simplest model
  • 43:31that is identifiable from the data is probably one in which
  • 43:34there is no heterogeneity in types of infection,
  • 43:39no asymptomatic infection.
  • 43:40We just lump all those people together
  • 43:42and there's only one kind of hospitalization
  • 43:45and people just transition, a certain proportion
  • 43:47of people transition to hospitalization.
  • 43:49That model is probably, has all the parameters identified.
  • 43:56And no, it's not useful.
  • 44:00That seems to be what we have found.
  • 44:03But I would say, I think there are two kinds
  • 44:05of usefulness, right.
  • 44:06One is answering the questions that policy makers have
  • 44:09and the other one is what Charles Manski calls credibility,
  • 44:12that there is a need to take into account
  • 44:16known heterogeneity and known mechanisms
  • 44:20when we construct these models.
  • 44:21So if I produce a useful projection that a policy maker
  • 44:24likes but I have not separated out asymptomatic infections,
  • 44:28then the numbers that I'm producing may become less,
  • 44:32regarded as less credible, right.
  • 44:34There's always this rhetorical function of modeling
  • 44:38beyond the numbers that are being produced,
  • 44:40to being able to accommodate or capture known mechanisms
  • 44:44by which data are generated
  • 44:48is one way that we can produce more believable
  • 44:50and actionable projections, right.
  • 44:53So I think there's this balance right,
  • 44:55between parsimony and richness and also this balance between
  • 45:03simplicity and believability of the assumptions.
  • 45:07So here we tried to you know, strike that balance.
  • 45:09If you think we've done it wrong, then please let us know.
  • 45:14- No, I definitely don't think you did it wrong,
  • 45:16but it would be interesting to see how much you lose
  • 45:20and sort of,
  • 45:22sort of cross validated predictability
  • 45:26by adding in priors, as opposed to just using the data
  • 45:30itself in a very simple model.
  • 45:32- Right, so--
  • 45:33- I don't know if you know the answer to that or not
  • 45:34but you should probably go on and I know other people
  • 45:37are wanting you to go on and not spend time answering
  • 45:40a lot of individual questions and we can always
  • 45:42talk another time.
  • 45:44- Okay, sounds good.
  • 45:46The model fits pretty well, fits observe data pretty well.
  • 45:49Here, I'm showing projections that start on March 1st,
  • 45:51rather than at the current day or any intermediate day,
  • 45:54just to emphasize that
  • 45:58model projections and uncertainty intervals here,
  • 46:00which are point-wise 95%, I call it--
  • 46:04They are not proper confidence intervals.
  • 46:07They're point-wise projections from draws,
  • 46:10using draws of parameters and initial conditions
  • 46:12from the posterior distribution over those quantities.
  • 46:15They're not confidence intervals in the strict sense.
  • 46:19But they do appear to
  • 46:22match observed data quite well.
  • 46:26So I think we're capturing dynamics that govern
  • 46:29what has occurred already.
  • 46:30We can learn quite a lot about the transmission rate
  • 46:34and under historical circumstances because we know
  • 46:37when those circumstances changed.
  • 46:39So we can estimate for example,
  • 46:41the percent decrease in transmission in Connecticut
  • 46:45following closure of schools and implementation
  • 46:48of the stay at home order.
  • 46:50That is what causes actually,
  • 46:51this downturn in hospitalizations and flattening
  • 46:54of cumulative deaths in the state.
  • 46:58So here, just to get a little bit more concrete,
  • 47:01on the upper left-hand corner, we see what we call
  • 47:05the contact intervention.
  • 47:06This is a function that multiples that transmission rate
  • 47:10parameter that we were discussing.
  • 47:12So in early March, schools are closed,
  • 47:15people start staying home
  • 47:16and so this intervention drops down.
  • 47:19The level to which it drops is a little more,
  • 47:23it drops more than 85%, I think, or somewhere around 85%.
  • 47:28That is an estimated quantity.
  • 47:30So the drops in historical contact are estimated
  • 47:35based on the changes in hospitalizations and deaths
  • 47:39and the implied changes in new infections.
  • 47:42Then what happens after the dotted line,
  • 47:44that is after May 20th, this is just a scenario
  • 47:49in which the amount of contact between individuals
  • 47:53increases at, I think here, monthly intervals by 10%
  • 47:57of the suppressed latent contact.
  • 48:00Under this historical and hypothetical future scenario,
  • 48:07we see cumulative incidence in the upper right-hand corner,
  • 48:11projected from March 1st onward.
  • 48:14Hospitalizations, with the dashed line,
  • 48:17showing expanded hospital capacity in Connecticut.
  • 48:27We see projections of deaths under this scenario,
  • 48:31cumulative incidence as a proportion of the population size
  • 48:34among people who are alive.
  • 48:35So this is what you would get if you conducted
  • 48:37a seroprevalence study in the future.
  • 48:39We hope this is useful for planning those types of studies,
  • 48:42and estimates of the affective reproduction number
  • 48:46in Connecticut over time.
  • 48:48There are two scenarios in particular that we want to show
  • 48:54policy makers that correspond to slow and fast reopening.
  • 48:57Really, this is not reopening scenarios.
  • 48:59I'm not sure what happened with this green annotation.
  • 49:03I don't know if you can see it.
  • 49:04If I did that or somebody else did, but just ignore that.
  • 49:09I'm not sure where it came from.
  • 49:11Under slow reopening, we imagine that people
  • 49:16release 10% of their latent suppressed contact
  • 49:19every month and under a scenario like this,
  • 49:22where everybody keeps distancing and everything goes
  • 49:24very well in the state, new infections continue their drop
  • 49:29and rise very slowly into the late summer and fall,
  • 49:32hospitalization stays low throughout the summer.
  • 49:39Deaths sort of begin to plateau and do not rise above
  • 49:4310,000 by the end of the summer.
  • 49:48Right, so this is the scenario that the state
  • 49:50is really hoping for.
  • 49:51It's a slow reopening that does not substantially increase
  • 49:55new infections with very slow rise
  • 49:59in new infections as the state reopens.
  • 50:02In contrast, a more pessimistic scenario,
  • 50:05which I think corresponds more to
  • 50:12a fast reopening, is one in which contact increases by 10%
  • 50:17or 10% of suppressed contact is released every two weeks.
  • 50:22This results in a very fast resurgence of new cases,
  • 50:26new hospitalizations and deaths by the end of the summer.
  • 50:29This is what the governor would like to avoid
  • 50:33when school children are scheduled
  • 50:34to go back to school in the fall.
  • 50:40There is a lot of interest right now in seroprevalence
  • 50:42because of competing claims about herd immunity
  • 50:45and how many people have been already infected
  • 50:47and have evidence of prior infection.
  • 50:50Under these scenarios, we can produce projections
  • 50:53of the proportion of people in a random sample
  • 50:56in the state, who might have evidence of prior infection.
  • 51:01So this is very important for designing seroprevalence
  • 51:04studies that we can use to further calibrate these models
  • 51:07and that can be used to guide policy.
  • 51:14I'm going to try to finish up very quickly here.
  • 51:17There are a couple of key messages from this work
  • 51:19that we tried to convey to policy makers.
  • 51:21The first is that the state is doing pretty well,
  • 51:23in terms of suppression of contact, closure of schools
  • 51:26and the stay at home order have effectively reduce
  • 51:28transmission and hospitalizations in Connecticut.
  • 51:32If contact increases quickly, the state's at serious risk
  • 51:37of big resurgence by later summer 2020.
  • 51:40Real time metrics that policy makers have access to
  • 51:42are really not going to serve as an early warning system
  • 51:46for that resurgence.
  • 51:49The state probably needs to be evaluating future projections
  • 51:53under realistic contact scenarios for the state.
  • 51:57We still have a lot of uncertainty that we tried to capture
  • 52:01in model projections about cumulative incidence,
  • 52:04asymptomatic fraction,
  • 52:06how things are going to go with children,
  • 52:10the effects of enhanced testing and contact tracing
  • 52:13and how contact patterns may change following reopening.
  • 52:18So we are issuing a series of reports, which you can read
  • 52:22online and we will be updating them in real time
  • 52:27as the summer goes on.
  • 52:28You can find them at this URL.
  • 52:29You can also email me and I'll point you to them.
  • 52:34These are sort of continuously updated research products
  • 52:36and I hope that they will represent
  • 52:38the latest information from Connecticut
  • 52:40and our latest predictions for the state as it reopens.
  • 52:45Also, there's a document here which summarizes
  • 52:47much more detail about the transmission model
  • 52:50that I have given here in this presentation.
  • 52:53I'm gonna skip over this stuff about our workflow.
  • 52:56We can talk about it later, if anybody is interested,
  • 52:59but this is just how we transition from regular research
  • 53:03to doing this type of very active software development.
  • 53:07I will end here.
  • 53:08I want to thank all of the people in the group
  • 53:11and beyond, who have been working on this tirelessly
  • 53:13over the last couple of months.
  • 53:15All of the products that I've told you about
  • 53:17are publicly available.
  • 53:18You can find the source code on Git
  • 53:21on our Git repositories and you can find the web application
  • 53:24and the reports online as well.
  • 53:27So I'd be happy to take any questions.
  • 53:29- Thanks, thanks Forrest for the last part.
  • 53:32I think some people have some questions using the chat box.
  • 53:39Ken asked, "Is the model used at currently proposing
  • 53:43"used at hospital or by your medical group?"
  • 53:50- The ICU planning app
  • 53:53has been used, we know, and possibly is being used
  • 53:56at Yale New Haven Hospital.
  • 53:58The projections for Connecticut are not intended for use
  • 54:01in any particular hospital systems,
  • 54:03though I think they will be of interest
  • 54:05to leaders of systems who are planning to accommodate
  • 54:10a potential second wave of infections
  • 54:12as it might occur later in the summer.
  • 54:15I hope that as we get farther in the summer,
  • 54:18if there is a second wave that appears to be coming,
  • 54:21that the projections will be useful in planning
  • 54:23capacity expansion efforts, possibly at or beyond levels
  • 54:27that we already saw in April.
  • 54:31So we will be generating any information
  • 54:33that decision makers at those hospital systems
  • 54:37think would be useful as they plan their response.
  • 54:40That's a great question.
  • 54:42- Thanks.
  • 54:43And...
  • 54:49Let me see and Sherry asked,
  • 54:55"In the first reopening model, what amount was the reopening
  • 54:58"assumed to start in?"
  • 55:01- Exactly on May 20th,
  • 55:03which is when the governor began the process of reopening.
  • 55:08It is also true that the governor has been
  • 55:13giving information about potential reopening plans
  • 55:15for a very long time
  • 55:17and that there is some change in contact as people
  • 55:19begin to anticipate those changes in policy.
  • 55:23I think that if you are looking at human mobility data
  • 55:28from cell phones and other sources,
  • 55:31you will see that people have been moving around
  • 55:33for a while, increasing their level of activity
  • 55:36outside of the home, even before May 20th in Connecticut.
  • 55:41Whether that has actually resulted
  • 55:46in a substantial increase in transmission remains to be seen
  • 55:50but I don't think we should assume that just because
  • 55:52people are moving around and possibly returning
  • 55:54to some types of work that there will be a corresponding
  • 55:58increase in transmission.
  • 56:02- Okay thanks.
  • 56:03Daniel asks, "Is the increase in incidence starting
  • 56:07"in September a cumulative effect of prolonged increase
  • 56:14"in contact."
  • 56:15- Can I just ask the question directly?
  • 56:16So I'm wondering, in the parts where you're showing
  • 56:18the two reopening models, it looked like the curve
  • 56:21starts to go back up around August,
  • 56:23September in the slow one.
  • 56:25I'm wondering if that's because you reach a threshold
  • 56:28above a certain percentage of contact
  • 56:30or if it's a cumulative effect?
  • 56:32Like, if we were to keep contact at .2 for example,
  • 56:36throughout all of this time and it weren't to increase
  • 56:39above a threshold, is there a situation which you don't see
  • 56:42that tail come up again?
  • 56:45- Yes, great question.
  • 56:47If you like to think in terms of the effective
  • 56:49reproduction number, this increase just corresponds
  • 56:52to a time about three weeks after
  • 56:55that number goes above one.
  • 56:58So there is a threshold effect and to answer your question,
  • 57:00if contact were to remain below a level
  • 57:06that would give that value of one,
  • 57:08then you would not see this type of resurgence.
  • 57:11I think as a practical matter, it is very unlikely
  • 57:14that the state can avoid a situation where the effective
  • 57:17reproduction number does above one.
  • 57:21I think this is not the stated strategy of anyone
  • 57:24and it's probably not, but I think it is the realistic
  • 57:29expectation about what will happen in reality.
  • 57:32The reality is that the state is going to try very hard
  • 57:35to increase a level of contact just about to that level,
  • 57:39where they would see some local outbreaks
  • 57:41that can be extinguished but they will try to maximize
  • 57:45the level of contact, meaning economic activity
  • 57:49and social mobility
  • 57:53that the state can achieve.
  • 57:54So they'll try to get as much economic productivity
  • 57:57and contact as they can without causing resurgence
  • 58:03or large outbreak or an overrun of hospital capacity.
  • 58:08- Thank you.
  • 58:09- Thanks.
  • 58:12- Akil here have two questions.
  • 58:15So the first one is are there any assumptions
  • 58:17of the proposed population who have Covid-19
  • 58:20but have not been tested?
  • 58:24- There are implicit and explicit assumptions
  • 58:26about that proportion.
  • 58:28I think we can produce predictions
  • 58:31for the current prevalence and also cumulative incidence
  • 58:37but those predictions depend quite a lot on our prior
  • 58:39assumptions about the asymptomatic faction.
  • 58:44We don't have very precise information about how many
  • 58:48or what proportion of infections are totally asymptomatic
  • 58:51and would go undetected by the healthcare system
  • 58:54because people don't seek testing or seek care of any kind
  • 58:58when they're not feeling sick.
  • 59:02So certainly, we can try to learn about those things.
  • 59:03There's some information in the available case counts
  • 59:07and in hospitalizations and deaths about that stuff,
  • 59:12but we still have a lot of uncertainty about current
  • 59:15cumulative incidence.
  • 59:17I think it's fair to say that currently prevalence
  • 59:18is quite low in Connecticut.
  • 59:22- Okay thanks.
  • 59:22I guess I saw something new saying they test the people
  • 59:26(unclear speaking).
  • 59:29Because they can test other people that have the ability
  • 59:32and then they have some estimate of the asymptomatic case,
  • 59:37the rate of them?
  • 59:38- Yes, that's true.
  • 59:41In some very specific settings, like institutional settings
  • 59:44like nursing homes and correctional institutions,
  • 59:47you can test everybody and then you can learn how many
  • 59:51infections are asymptomatic.
  • 59:53The question then becomes of how representative
  • 59:57those samples are compared to the rest of the state.
  • 01:00:01Is it safe to take situations where people
  • 01:00:05are living in very close proximity
  • 01:00:08and possibly poor health conditions and to generalize
  • 01:00:13all of that information to the state?
  • 01:00:15I think there is some very good anecdotal evidence
  • 01:00:17from prisons, from nursing homes
  • 01:00:18and also testing systematic testing of healthcare workers
  • 01:00:23that we can try to take into account,
  • 01:00:26but it remains unclear how generalizable
  • 01:00:29that information is.
  • 01:00:30For example, healthcare workers may be immunologically
  • 01:00:33somewhat unlike members of the general population
  • 01:00:36who are not continuously exposed to different types
  • 01:00:40of illness and to coronaviruses in particular.
  • 01:00:43So I would hesitate to take large screening studies
  • 01:00:45of nurses for example, and apply the asymptomatic fraction
  • 01:00:51or prevalence or incidence in that sample
  • 01:00:53to the general population.
  • 01:00:56- Thanks.
  • 01:00:58And the second question of Akil is can Covid-19 models
  • 01:01:03from different states learn from each other?
  • 01:01:06I have relay the question is because currently your model
  • 01:01:10is most about stating the data
  • 01:01:11and you can validate how good the model is.
  • 01:01:15Because states, maybe they have their reopening plan
  • 01:01:18at different times, can this provide useful information
  • 01:01:21about how good the model is by learning
  • 01:01:24from different states.
  • 01:01:25- Yes, great question.
  • 01:01:27It is always true that information from other contexts
  • 01:01:30can be very useful if you know what is different
  • 01:01:33in those other contexts.
  • 01:01:35I would love to be able to use more granular information
  • 01:01:37from neighboring states throughout the northeast
  • 01:01:40to inform projections from Connecticut,
  • 01:01:42'cause as we know, Connecticut is not an island
  • 01:01:45and as soon as New York opens up and people start working
  • 01:01:47in New York, then everything will change quite a lot,
  • 01:01:50quite quickly in Connecticut.
  • 01:01:53So I would like to share information.
  • 01:01:56We have focused on Connecticut here because we have very
  • 01:01:58detailed information about Connecticut but no special access
  • 01:02:02in Massachusetts, Rhode Island and New York.
  • 01:02:07So that's why we've done it, but I think it will become
  • 01:02:09very important and I always thought
  • 01:02:13it would be the job of the CDC and the US
  • 01:02:16to synthesize a national and local projections
  • 01:02:18and to gather all the granular local information
  • 01:02:21and to put it all together.
  • 01:02:22That has not happened in this particular pandemic.
  • 01:02:26So I think everyone else is trying to scramble
  • 01:02:31to aggregate information at the right levels
  • 01:02:33to produce predictions that are actionable locally.
  • 01:02:37But there's not coordination right now
  • 01:02:39between groups that are doing state-specific
  • 01:02:42reopening plans, unfortunately.
  • 01:02:44As for whether the differences or staggered reopening
  • 01:02:48can be used as a kind of instrument to identify
  • 01:02:50the causal effects of reopening, I assume that's the subtext
  • 01:02:54of the question, the answer is yes.
  • 01:02:57I think people are very interested in doing that.
  • 01:02:59The problem is that reopening is somewhat endogenous.
  • 01:03:03The states to reopening as a function of the conditions
  • 01:03:06currently in the states and also obviously,
  • 01:03:09as a function of the political considerations
  • 01:03:12of the leadership and of the population.
  • 01:03:16Right now I don't think it's safe to say that reopening
  • 01:03:19occurs randomly in some time interval
  • 01:03:22and that we can exploit that randomness in a simple way
  • 01:03:24to assess the effect of reopening.
  • 01:03:27Certainly, some of the states that we observe
  • 01:03:29reopening quickly, take Georgia for example.
  • 01:03:34Those states are likely to see at least local
  • 01:03:36and possibly very broad resurgences and outbreaks
  • 01:03:42that may result in reversion to more restrictive movement
  • 01:03:45conditions in those states.
  • 01:03:48So I think really, there's this going to be a long,
  • 01:03:50longitudinal sequence of treatments,
  • 01:03:53meaning changes in state regulations and then outcomes,
  • 01:03:57which the regulators will observe
  • 01:04:00and then this kink of cat and mouse game,
  • 01:04:01where decision makers try to tamp down on local outbreaks
  • 01:04:06and then respond to ones that occur in the future.
  • 01:04:11So we will try to learn about the effects of all those
  • 01:04:13interventions and changes in policies
  • 01:04:16but I think that there is cause for some skepticism
  • 01:04:20in really learning a generalizable causable effects
  • 01:04:24just from the time series.
  • 01:04:27- Thanks.
  • 01:04:29I guess one last very specific question about a talk.
  • 01:04:33So Paul asked, "Have you considered how real time data
  • 01:04:36"metrics, such as oxygen sensors from fitness trackers
  • 01:04:39"could effect your predictions?"
  • 01:04:41- Very interested in distributed measurements
  • 01:04:44at the population level that could be helpful
  • 01:04:46to inform some of these things.
  • 01:04:49I think that we have not yet seen widespread adoption
  • 01:04:53of mobile apps
  • 01:04:58for self monitoring for contact tracing.
  • 01:05:04There is some adoption of thermometers and oxygen sensors
  • 01:05:10but as far as I know, there are no data streams
  • 01:05:12that are publicly available.
  • 01:05:14- This is Paul Forcher, I asked the question.
  • 01:05:18There are some, there's--
  • 01:05:20I'm participating in two studies.
  • 01:05:22One that's run out of by Mike Snider,
  • 01:05:26who use to be at Yale who's head of Stanford Genomics.
  • 01:05:31The other one's institute
  • 01:05:34and any of you can sign up for these things
  • 01:05:37and if you have a fitness tracker that's tracking
  • 01:05:41oxygen levels, there's emerging evidence that changing
  • 01:05:46oxygen levels can be predictive of Covid infection
  • 01:05:49before the patients are symptomatic and there's some...
  • 01:05:54So I would, those are two studies that you could
  • 01:05:57connect with and I wouldn't be surprised at all
  • 01:05:59if they would share all of their realtime data
  • 01:06:01that they're collecting with you.
  • 01:06:02- Yeah, that is a great idea, thank you.
  • 01:06:04With these--
  • 01:06:05- Mike Snider's a former Yale person,
  • 01:06:08so you already have an inroad with that guy.
  • 01:06:12- Yeah, thank you, that's a great idea.
  • 01:06:15- Okay thanks, I guess that's all questions for the talk.
  • 01:06:20If you have any questions, I guess they can talk to you.
  • 01:06:24Like the audience can talk to Forrest offline.
  • 01:06:28- Please feel free to email me, anybody who has questions.
  • 01:06:30- Some people want to hear more about the talks,
  • 01:06:34like you didn't have time to cover,
  • 01:06:35that I guess the interest you can talk to Forrest offline.
  • 01:06:40Also, this talk will be recorded
  • 01:06:41and will be publicly available.
  • 01:06:44Also, on the previous talk are also recorded.
  • 01:06:47I'll also send out a link to everyone
  • 01:06:51in the School of Public Health,
  • 01:06:54so if you want you can access it.
  • 01:06:56Okay thank, thanks Forrest.
  • 01:06:58- Thanks everyone.
  • 01:06:59- And thanks for everyone. - Thanks everyone.