The Imperial College Study: Part 2

[Links to the full series]

Part 1
Part 2
Part 3A
Part 3B

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Now I will start looking at the parameters that the Imperial College study used to characterize the coronavirus in its simulations. I'll start by looking at the basic reproduction number: the now-famous r(0) ("r naught").

1. What is r(0)?

R(0) is defined as the number of secondary infections a single instance of an infection will cause if exposed to a completely vulnerable population. It arises from a combination of multiple elements:

•   how naturally infective the particular virus is
•   how long an infected person is contagious *while* being still present in a population
•   how many people an infected person can be expected to contact during the infective period

Importantly, while the first two elements are virus dependent, the third is societally dependent. The more mobile and mixing a population is, the higher the r(0) will be. "Social distancing" is therefore a way of changing the r(0) of a particular disease by altering that third element.

From the perspective of a microsimulation, however, epidemiologists can just take the r(0) as a constant which determines the chance (on average) that any given non-infected individual coming into contact with an infected individual will become infected. This is because the microsimulation intrinsically accounts for degrees of social mixing by its rules that govern individual behaviors.

2. How is r(0) calculated in general?

This is an oversimplification, but I am aware of two methods of calculating an r(0).

First, an r(0) is said to be proportional to the early doubling rate of infections during an epidemic. During this early time period, there are so many more non-infected people compared to infected people that each instance of an infection will have essentially a "clean slate" of people to infect. Later on, an increasing percentage of infected individuals will come into contact with already-infected individuals, thus slowing the growth rate. Furthermore, in the earliest phases of an epidemic, the disease will be spreading without a lot of symptoms and without causing major alarm, so that social mixing will be normal as a whole. Later on, fear of the disease spreading through society will itself change mixing behavior and therefore the r(0) itself.

Second, you can examine a timeline of infection and death rates after the fact from a given epidemic event, and then run microsimulations for that population using different r(0) values until you reproduce the observed curve in the simulation.

3. How was the r(0) used in the Imperial College study calculated in particular?

The Imperial College simulation used the results from two different studies, each taking one of these approaches.

The first study was done by the China CDC (available here: https://www.nejm.org/doi/full/10.1056/NEJMoa2001316) looked at the first 425 cases reported in Wuhan and reconstructed an infection timeline by interviews which established when symptoms first occurred in each case. From this they saw an initial doubling time of the disease of about 7.5 days, which calculated out to an r(0) of 2.2, with a 95% confidence range of 1.4 to 3.9.

The second study was done by Julien Riou and Christian Althaus and funded by the Swiss National Science Foundation (available here: https://www.eurosurveillance.org/…/1560-7917.ES.2020.25.4.2…). They ran 2 million separate epidemic simulations with varying parameters and looked for those parameters that could reproduce the timeline of the infections as of January 29th, which at the time included 5,997 confirmed cases in China and 68 confirmed cases exported to other countries. Importantly, they allowed the number of cases *actually* in China in their simulations to vary substantially, in order to account for potential massive misreporting of the Chinese data. The results of this study was an r(0) of 2.2, with a 95% confidence range of 1.4 to 3.8.

4. How confident can we be in the results of these two studies?

Both studies that establish an r(0) of 2.2 for Covid-19 acknowledge the fact that they are operating on limited data, collected in a crisis situation. They both, therefore, should be treated as preliminary best estimates given the data that we had in mid February. Nevertheless, the fact that they agree very closely after taking very different approaches to the estimation does count for something.

Furthermore, I think there is good reason to believe that the true r(0) isn't lower than 2.2 given the newer European data that we have. If you look at infection growth rates for all of the European countries and for the United States since community spread started occurring in late February / early March, you can see a pretty consistent slope of the lines, yielding a doubling time of 3-4 days. This is significantly *faster* than the doubling time that was estimated for the Chinese outbreak. I believe that this makes an r(0) of significantly less than 2.2 very difficult to justify. I think the Imperial College agreed, because they used a base doubling time of 6.5 days (somewhere between current European numbers and the Chinese numbers) and a consequent r(0) value of 2.4. They did also explore values with a range from 2.0 to 2.6 to account for uncertainty.

So I think the calculations that the Imperial College did are a very reasonable interpretation of the best data that we have. I think newer studies taking the rapidly evolving new reports of infections given much greater worldwide testing would be good to do, but I very much doubt at the moment these studies would come to different conclusions right now. If anything, they would probably raise the estimated r(0), not lower it.

The Imperial College Study: Part 1

[Links to the full series]

Part 1
Part 2
Part 3A
Part 3B

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A bit ago I posted a link to this study by the Imperial College of London, which is a projection of how the U.S. and Great Britain can expect the Covid-19 disease to progress in the next two years under various scenarios of different levels of social isolation: https://www.imperial.ac.uk/…/Imperial-College-COVID19-NPI-m…
I want now to do a series of posts explaining this study and the current research behind it, because I think this might be the most influential study currently informing government decisions. I encourage you to read the study yourself, but I won't assume this.

1. What is the nature of this study?

This study is the results of a series of computer simulations run by epidemiologists. Specifically, it is an application of pre-existing "microsimulation" (https://en.wikipedia.org/wiki/Microsimulation) software with parameters set to simulate Covid-19 on a virtual population. A "microsimulation" is a computer model in which the behavior of a population is modeled by creating millions of individual virtual people and having them move around in a virtual world according to a set of behavioral rules. If you've ever played any of the Sim City games or any of the Tycoon games, you've played with a simple, small-scale microsimulation. A lot of people at this point have seen an *extremely* crude microsimulation recently published in an article by the Washington Post: https://www.washingtonpost.com/…/20…/world/corona-simulator/.

In epidemiology, these things are incredibly useful because you can simulate the spread and effects of a disease much more accurately than by just talking in broad percentages. You setup your population according to the actual characteristics of the real world: children will congregate in schools during school days but stay home on the weekends, old people will live in nursing home clusters, working-age people will congregate in business and will travel a range of distances to work using public transportation according to actual percentages from real-life that you enter, and so forth. Your virtual population will be created with a range of ages and existing health conditions that you also enter, based on real-world numbers that are correct for the population and time period you are modeling.

Then you characterize your disease: how long is the incubation period? What is the range of severity of symptoms and does this vary on an age basis or by existence of co-morbidities? What is the range of infectiousness of the disease, and how does it alter over the timeline of the progression of symptoms? How close does one person need to be to another person to spread the disease? How much does having the disease itself limit the motion of an individual and therefore the likelihood that one person will continue contacting other people?

Then you introduce the disease into the virtual population and play the simulation forward a certain number of times with different random seeding, and it gives you a composite average result of what happens.

2. What are some advantages to this approach?

There are a number of great advantages to this approach in epidemiology. A lot of statements about how diseases spread are actually just abstractions of just this sort of real-life behavior. We say that diseases spread exponentially in the early phases of an epidemic, but this is just a rough mathematical approximation of the behavior of a self-replicating virus as it spreads through networks of people. A good microsimulation will take more exact accounting of real-world social distances and movement. There will be a real-world mix of dense urban centers and more spread-out suburban neighborhoods, there will be an age and health spread in the population you are simulating that matches the real world, sick people will slow down their movements, etc.

There have been some people who have doubted that Covid-19 will behave as badly in the U.S. as it has in China and in Italy. They've raised potential differences between us and them that could make a difference: different baseline health of the population, different population density, different levels of cultural contact, different standards of hygiene, different access to health care. If the microsimulation is a good match to a given population, none of these problems would apply to its projections.

Furthermore, the type of human and virus behavior that needs to be modeled in order to get a realistic simulation is not actually that complex. Basically, the only human behavior that needs to be about right is movement and proximity. Viruses also are pretty simple organisms and it doesn't take too much data to be able to get a pretty accurate knowledge on the average behavior of an infection in humans on aggregate. So I think the results of these simulations tend to be fairly robust.

Another advantage is that you can use the same model to test multiple scenarios. Not sure the exact R(0) of your virus? You can run your simulation with a range and see how it affects the outcome.

3. What are some disadvantages to this approach?

Not a lot, but I can think of a few. First, as with any computer simulation, the results are only as good as the underlying assumptions and the underlying programming. This can cause it to miss some things. For example, we are now in an absolutely unprecedented level of public awareness and discussion about the Covid-19 pandemic. This itself is likely to change societal behavior--has the model taken this sort of public awareness and consequent fear of spreading infection into account? I don't know. Also, if the underlying characteristics of the virus are not correctly understood, then you will have an example of "garbage in, garbage out". Yes, you can run the simulation on a range of inputs, but if you understanding of the parameters is very out of line from reality, the results won't be very helpful.

Second, the results these types of simulation provide are very specific and realistic. But "realistic" is not the same thing as "real" and I think these simulations tend to produce a bit of over-confidence in their results because it looks like you're observing reality when you are just roughly simulating it.

4. How good a fit to reality is the model that was used in this study?

That, I am not sure of. However, I think there is good reason to trust it's a fairly good fit. With epidemiology, we have an opportunity to run such models and test their output every year because we use them things to predict the movements of seasonal flu. We've used them to model known outbreaks from the past to see if the results they produce match historical known results.

I'll stop my first post here. In a subsequent post, I'll get into the assumptions which this particular study used: how it characterized the virus and how it justified those characterizations.

Archived Facebook Coronavirus Posts: March 18th

[I'm transitioning a bunch of Facebook posts I made on the Coronavirus to my blog.  This was from March 18th]

A lot of people are now asking, what's the end game here? How long is extreme social distancing going to need to be applied?

I think there are two answers here. One would be a *final* answer, and I don't think anyone knows the this yet because we're not sure about how effective our chosen isolation tactics will be yet. But I don't think this means we have to decide, right away, on extreme *and* long term isolation. I believe there are some very concrete goals we can aim for during an *initial* extreme social distancing period. This would give us, not an end game per se, but an end game for the first period of this event, after which we can re-evaluate and adjust. So the following are my suggested goals for the first month of our semi-quarantined life in Europe and the United States.

1. More data. The most up-to-date data and the best analyses of this data has been painting a very grim picture of the upcoming year. However, many people aren't satisfied with this data and disagree with or outright disbelieve the interpretations of this data. But even with rather extreme social isolation for a month, we're going to continue to get a lot more data on the behavior of this virus around the world. I think a month of social isolation will provide the time for a lot more data to roll in. So we can believe the experts for a month and act as if the very dire predictions are correct, but then call for a re-examination of the data at the end of this period.

2. More testing. So far, the best model for reducing spread of covid-19 with the least amount of social and economic impact has been South Korea, and their strategy centers around extremely aggressive testing. The President should use whatever emergency powers are necessary to cut through whatever bureaucratic red tape still exists around getting massive amounts of tests available to the public. Further, we ought to do whatever we can to develop a good *antibody* test, as opposed to the current antigen test. When we are able to support easy testing for whomever wants it, up to a reasonable percentage of the entire population, then we will better equipped to deal with hunting and destroying this infection without needing as extreme an amount of social isolation.

3. A social media app for tracing infections developed by a trusted source. Part of South Korea's strategy is aggressive *tracking* of people, so that when one develops an infection, they can go ahead an warn a bunch of other people who have been in the same area to get tested. This sort of big-brother overseeing isn't likely to fly well in the States, so I think we need an op-in, anonymized version for the liberty lovers of the West. If not an app, then instead we need some other policies to enable us to track and contain the virus in the wild.

4. A lot more ICU resources. We should engage in a WWII, "build an airforce from scratch" style emergency manufacturing campaign to dramatically increase our ICU capacity: buildings (modular structures, temporarily commandeered hotels, etc.), PPE, ventillators, etc. Similarly, we should recruit heavily from the medical field and train up massive amounts of new people in the specific techniques required to care for ARDS while in an infectious environment.

The primary justification for extreme social distancing is that we don't have the ICU capacity to treat all the sick people we expect in a short period of time if this disease acts as expected. So, let's increase that capacity. We need to do that by a rather insane number (maybe 50 times existing capacity?)--but that sounds cheaper to me than shutting down the entire economy for 18 months while we wait for a vaccine. So let's get on this!

5. Research progress on non-vaccine medicines. It will take 12-18 months to develop a vaccine, we're told. However, a standard shortcut to finding working medicines without such a lengthy set of trial periods is to search for existing medications that have already been FDA approved and to see if they have some effectiveness against the disease you are fighting. We already have a number of interesting candidates in various stages of testing, the most interesting one to me being the combination of zinc and chloraquine. There are also some antivirals from the HIV world that might show up.

I don't know if it's reasonable to hope for results on this front in just a month, but whatever we can do to accelerate this process would be great. It's possible we could find a set of medications that have a real impact on the disease severity in just a month.

So those are my ideas. Anyone else have something they'd like to add?

Archived Facebook Coronavirus Posts: March 17th

[I'm transitioning a bunch of Facebook posts I made on the Coronavirus to my blog.  This was from March 17th]

As you may have heard, one potential vaccine for the coronavirus has already begun early human trials. Nevertheless, it is still thought that widespread availability of a vaccine is still 12-18 months away at minimum.

That may *seem* like a long time, but as someone who spent the last three years thinking my son had a very rare disease and following very intently the development of new potential treatments for that disease, I can assure you that this is *lightning* fast for a new treatment to get FDA approval.

So the question should be asked, why is it so slow to move from the scientific development of a potential cure or vaccine to the actual rollout to the public? Some of this has to do with proving efficacy of the treatment outside of the lab, and some of it has to do with proving the safety of the treatment. But a lot of it also has to do with medical research ethical rules that have been setup to avoid past abuses wherein humans were used as "guinea pigs" in order to drive scientific understanding.

Some of these rules are good and proper in ordinary situations, but are nevertheless not *intrinsically* necessary to medical ethics. That is, there are maybe other ways we could safeguard respect for human life that don't follow these rules strictly.

Given the *massive* economic and societal costs entailed in the prolonged quarantining of huge sectors of society, I think it is the right thing to do to review those ethical rules which are dictating a 12-18 month minimum path to the release of a vaccine. We *might* find some potential shortcuts.

Archived Facebook Coronavirus Posts: March 13th (post 2)

[I'm transitioning a bunch of Facebook posts I made on the Coronavirus to my blog.  This was from March 13th]

I thought it would be worth posting this video, which is of someone who has (mostly) recovered from the coronavirus describing what the early symptoms were like. https://www.youtube.com/watch?v=H2E1t3yMXgE&t=1800s

Of importance, I thought, were how mild the initial symptoms were: just a cough, really. The fever was tentative and barely registered at first.

The implication of this is that self-quarantining does need to happen quite aggressively, as soon as even mild symptoms arise. The *further* implication of this is that it would be really great if we had reliable and very easily accessible testing, because the stage at which you want to self-isolate with the coronavirus is the same stage at which it looks just like the cold or allergies or something. It would be really nice to be able to tell the difference very early on.

Archived Facebook Coronavirus Posts: March 13th

[I'm transitioning a bunch of Facebook posts I made on the Coronavirus to my blog.  This was from March 13th]

Some new information (to me) on COVID-19 coming out of the UK that has some specific implications for self-isolation: https://www.youtube.com/watch?v=BYTFk34nhoI

Key new information:

* Infectiousness of the disease starts before any symptoms show, but peaks around the time symptoms first show up. Then once symptoms begin, infectiousness goes way down after around 7 days.

* The most characteristic elements of COVID-19 are still a fever and/or a *dry* cough. The fever, however, is often not high--the UK criteria is only 100 degrees Fahrenheit.

* It is now confirmed that children do get the infection and spread it; it's just that they very frequently get an extremely mild form of the disease. While this is good news in the sense that most children are safer than everyone else, it does kind of make children our "plague rats" in this outbreak.

So, what are the self-isolation implications of these facts?

1. We need to have a high level of suspicion and self-quarantine *right away* as soon as even mild symptoms show up.

2. We especially need to pay attention to *dry* coughs and/or any level of fever.

3. We should probably quarantine our children if they are sick *at all*. Note that the UK is not recommending shutting down schools, though.

4. Seven days of self-quarantine should be enough unless you continue to get sicker.

Archived Facebook Coronavirus Posts: March 10th (post 2)

[I'm transitioning a bunch of Facebook posts I made on the Coronavirus to my blog.  This was from March 10th]

I'm annoyed by the persistent "coronavirus crisis is just being hyped by the liberal media!" theory people seem to be clinging to. I've been following this story very closely and I just do not see that as being the case.

If you still think the worry here is just caused by media overreaction, I would encourage you to watch and compare these two YouTube videos:

First, here is video about the new coronavirus from the early days of the outbreak in China by Dr. Eric Strong, a medical professor at Stanford and a practicing hospitalist: https://www.youtube.com/watch?v=AajszIH2ahs

Main takeaway (paraphrasing): "It's early yet, there's a lot we don't know, but don't worry, this could be no big deal at all and you're much more likely to get the flu than this new thing."

And this is the latest video on the situation he posted today:
https://www.youtube.com/watch?v=qsJ7LYZhUlQ

Main takeaway (exact quote): "For the country as a whole, including its health care system: I think things are going to get bad . . . like, really bad."