# COVID-19 projections for Connecticut

May 28, 2020## Information

Associate Professor of Biostatistics, Statistics & Data Science, Operation, and Ecology & Evolutionary Biology

5.25.2020 Biostatistics Seminar

ID5250

To CiteDCA Citation Guide

- 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.