The Jesús Fernández-Villaverde-Chad Jones epidemiological model

Here are the slides, definitely recommended.  Might this be my favorite epidemiological model so far?

I interpret the last few slides as being gloomy for some “star early performers,” including California, though you should not necessarily attribute that view to the authors.

Comments

In California the Y axis is much different than all the others.

Shhh. Don't tell anyone.

Tyler's comment about California
Also means that
Montana is in for
A lot of pain
Because
They will have no
Herd immunity.

If you can delay, like California, and you can change the rate of infection through testing and contact tracking, the infection rate declines, while waiting for a vaccine or better therapeutic strategies. And, you don't overwhelm the healthcare system which would otherwise have to ration and deny care.

Also FWIW, the gravity is different too

Don't most states look like California?

Outside of northeast, Louisiana, Michigan and maybe Washington, infections are low

But then Montana and Florida were never lauded as star performers

Meets,
It was a miracle,
Without human intervention,
That
California was spared.

At least he is candid enough to admit 'noisy and unreliable' for many of the future cases. It's a sign of confidence.

Tyler Cowen and credentialed epidemiologists:

Tyler Cowen was like a freshman thinking he was on a bus to Johns Hopkins, and instead found himself inside a Baltimore bunghole house.

Tyler Cowen: "You mean I publicly advocated implementing an economic catastrophe for this?"

Is there a parallel here? Well-meaning, persuasive intelligent public-health professionals will always sketch out the worst-case scenario, just like well-meaning, intelligent and persuasive defense-establishment professionals.

For a while, and sometimes for a long time, both groups have a monopoly on information and expertise. Then the results start to come in....intelligent laymen begin to suspect something is awry...

And we find we were not going to Johns Hopkins, but a Baltimore bunghole house...

Yes, the experts will have destroyed us all with their lockdown remedy.

I hope Trump listens to their advice and then acts on his instincts.

Prior to takeoff, the crew instructs the passengers to put their own masks on first in an emergency. Only then will the passengers be able to help others. You can't help anyone when you are unconscious.

Let's put our masks on first by unlocking the economy.

This lockdown is stupid.

I really don't see WA exploding any time soon as predicted here, unless they drastically reduce restrictions in the immediate future.

WA death totals for April 10-13 were much lower than the projection:16, 17, 8, 25. The projections appear to overestimate future deaths.

Which of the assumptions is most likely to be wrong?

Thinking about the Seattle area, I could see several major employers not getting a lot of people back into the workplace even if they can legally do so.

Amazon and Microsoft HQ's both have lots of jobs well-suited to work from home. IIRC, both of them moved to WFH before any legal requirement to do so.

Boeing's airplane factories hardly need to be cranking out many new aircraft now. They'd suspended 737 Max production even before coronavirus, and airlines are deferring orders left and right.

It is bizarre that on April 14, 2020, anyone is using spatially unstructured differential equation models and expecting them to be useful, rather than constructing models that account for the density or connectivity of particular regions. I can't understand why Tyler is impressed by this, but I'm sure there's a good reason. I'll try to elaborate later...

Because the more complex or "realistic" a model is, the less we are able to calibrate it with the very few and nosy data we have.

Yep, especially until recently we had few observations, and we probably still have data that are lacking in granularity, precision, and maybe reliability: are China's numbers accurate? Do we have decent estimates for the infection rate of any country yet? California just added 3,000 Covid deaths by re-classifying them based on their symptoms (evidently not enough resources are available to test those 3,000).

Looking at density is fine, but do we have good enough data to do that? I've seen plenty of county data available, but most counties have small samples sizes -- plus they are usually heterogeneous with high density areas and lower density areas in one county.

Even state-level data often suffers from small samples sizes, until the number of cases rises. And states are highly heterogeneous with regard to density; CA has tens of millions of people living in dense urban areas but it also has hundreds of thousands living in sparsely populated areas.

Elaboration hugely appreciated, if possible ...

I work at Google; my group does epidemiological models of coronavirus. We do (often) today still use spatially unstructured models. Finer-grained models that account for the density or connectivity of particular regions are useful for better pinning down R_0. This work just tries to guess R_0, and based on that, it's actually pretty reasonable.

I think the primary thing this work is missing is that they're overestimating residual R_0's in many areas. Compare slide 58 to death graphs from Italy or Spain; it seems clear that their post-lockdown R_0 was substantially less than 1. Combining this with data from China, one might take this as evidence that post-lockdown R0's are in general likely to be much less than 1.

Several assumptions to keep in mind in the SIRD model

(1) that if once infected and you do survive, you do not get infected again. (necessary for "herd" immunity; and that also depends on transmissible the disease is, by the way). Do we have evidence of no re=infection? Might a person who was infected have a catastrophic response in reaction to being in contact with the virus? What is the rate of mutation of the virus and will the virus mutate so as to make current antibodies ineffective?

(2) SIRD is specific to a specific disease. So, if you get pneumonia and your lungs are damaged but you survive, and later die from a pneumococcal infection two years from now because your lungs were damage or your immune system was compromised, the SIRD model doesn't count that as a death from covid.

(3) The infection rate is not a given, and can be altered by testing and contact tracking to limit the infection rate. But, if there is community spread, the "natural" infection rate takes over as there is no intervention other than shut down.

That said, SIRD can give you guidance and affirms mitigation and contact tracking as a way to reduce infection rate and shows the sensitivity to infection rate.

Bill, you are making all the hypotheses you can think of which justify your prior approval for lock-down.

For instance you are making the hypothesis that a resolved infection may not result in immunity (or only in partial or short-term immunity), and a few posts above the other hypothesis that an efficient vaccine may be coming in relatively short term.

Not only are these hypotheses separately unlikely, but taken together they have a probability of almost 0. A vaccine works by simulating an infection or inoculating a real but weakened infection to the patient, to stimulate his immune system. If even the real thing don't stimulate enough or for long the immune system of the patient, it is very unlikely that an ersatz will do it.

The nature of an hypothesis is to pose the question and not to answer but to prove or disprove it.

You are a philosophy major. You should know that.

You seem to have knowledge that
(1) you cannot be reinfected and
(2) there will be a successful vaccine, and it will happen soon, making California's efforts wasteful.

So,
Please,
In the space below,
Post your proof and evidence.

Re: "Not only are these hypotheses separately unlikely, but taken together they have a probability of almost 0."

You are a philosophy major. I want to point out the false statement you made: that I argued a joint probability, and not an individual probability, and YOU claimed that I argued a joint probability.
Everyone can read the prior comment and see that I did not assert a joint probability.
You did.
Shame on you for asserting a claim to attack that was not made. You know better. And, I would expect better. Unless you didn't take a course in moral philosophy but instead took a course on sophistry.

Do we get to pick our favourite model do we? Or are we voting for how the virus works?

Or is this economics where the political ends justify the analytical means?

Please tell...

The models are only right when written by an economist, duh.

I think it does well with this model. The exposition is clearer with slides. Beta is modeled as an exponential decaying with two regimes using lambda from Heinsberg as the decay constant. It shows how different Ro can model the dynamics well at the beginning but will strongly diverge later. It shows gamma( recovery rate) is not critical.
The results make sense for California. It’s not much infected, so everything is up in the air as soon as it reopens.
Incidentally the latest results from Iceland show children and women get infected at a significantly lower rate
https://www.nejm.org/doi/full/10.1056/NEJMoa2006100?query=featured_home

Maybe the posited androgen connection we heard about the other day? Obesity is also associated with polycystic ovarian syndrome, which involves elevated androgen levels.

I kind of don't remember the androgen role but it sounded pretty persuasive at the time.

It could be. I am not much familiar with it. The other theories I have come across are:
Women: 2 X chromosomes mean women have better immunity since a lot of genes controlling immune function are on the X chromosome
https://www.nature.com/articles/nri2815?proof=true
Children: apart from a well functioning immune system that won’t generate “ cytokine storms” , have not much been exposed to the other 4 more benign Coronaviruses.
It is thought that to have antibodies who are similar to the real thing but somehow fall short ( slight mismatch) can be disadvantageous because they block the correct antibody from capturing the antigen.
They’re not good enough to stop the S protein to lock onto the ACE2 receptor, but gum up the process for the correct aB.

I forgot to mention that there’s a graph in the Iceland paper that caught my eye. ( Figure 4 Graph C).
Virus exposure from the family dominates the source of infections but from work it’s relatively small.
So much for our “ stay at home “ strategy lol

Also, Did you mention that Iceland has very good testing and tracking. Maybe if we had good testing and tracking we could have the same numbers.

Thank you!

What other models are in the running for your favorite?

Sean,
The SIRD model is a standard epidemiological model. They were just applying data to the model and comparing different states or countries.

Sean, Just did a google search for you re various network diffusion and infection models: http://web.stanford.edu/~jacksonm/Jackson-Diffusion.pdf

Thanks Bill! This is very useful, educational.

I was also scanning for - hmm, given that IMHE seems to be struggling a bit ("observed percentage of death counts that lie outside the 95% PI to be in the range 49% - 73%, which is more than an order of magnitude above the expected percentage," via MR post from yesterday) I wondered if there were any OTHER IMHE-esque models that were ... better, somehow. Or more accurately predicting what was happening.

I don't know, but I am not surprised that it is difficult to predict when something grows exponentially and is associated with networks for transmission. But, I do know that when we plan electrical systems, or the internet, we plan to avoid disasters and system failures, so being slightly off early on one side of the tail is less damaging than to being more protected.

Looks neat, but I am not following exactly what they did. Still missing something. That said, I always find it suspicious when people hedge so much. Make a hard claim about tomorrow or the next day or at some point in the next 7 days. If you won’t, it means that you don’t believe your own model... that you are afraid of being wrong.

That is the biggest test of a good model. Make a hard prediction ahead of time so everyone can see if it’s right or not.

I agree that this is a very good models, quite clearly explained with the slide.

We want a model as simple as possible, with as few parameters as possible, so that we can hope to fit the parameters with the few and nosy data we have.

In this SIRD model, there are three parameter, beta, gamma, delta. The only simpler model is the SIR model, where you count together recovered and dead people (because from the dynamical point of view, they behave the same way - both can by assumption get infected again, nor infect other people). The SIR model has just two parameters, beta and gamma. But the SIR model is completely unadapted here, not only because the number of dead people there will be at the end is what we are most interested about, but even more because the most reliable series of data we have are about the number of deaths (and even them are pretty noisy and perhaps biased, but they are the best we have). So the SIRD is the best we have.

All models will have to deal with this ground reality:

"The number of coronavirus tests analyzed each day by commercial labs in the U.S. plummeted by more than 30 percent over the past week, even though new infections are still surging in many states and officials are desperately trying to ramp up testing so the country can reopen."
https://www.politico.com/news/2020/04/14/coronavirus-testing-delays-186883

Percentage of tests returning positive is falling. Testing isn't growing a ton but fewer people need tests (because fewer are sick).

If you're Tyler Cowen -- and thank God you are not -- you really only have three choices from here on out.

(1) Give credit to Trump that the USA did not have the 2 million dead that you were originally forecasting
(2) Admit that you have been an insane fearmonger since Day 1, along with all the other Dems, as this Flu is your last chance to crash the economy before November
(3) Come out with guns blazing against "The Modelers"

Guess which way Tyler is going?

Yep, pretty obvious. Gonna be a long, long five years for this boy.

Things to add to this model, that are likely to further widen the numerically unstable standard errors:
--Epidemic start date that varies in each measurement region
--Measurement model that varies according to testing resources of each measurement region
--Death rate that varies according to demographics and resources of each measurement region
--GRE scores of the modelers

I like the exposition- it lays out the variables very nicely, especially describing their effects on the outcomes.

Like they wrote near the end, what is really needed is more data on total infected- past and present.

R0 likely isn't the same across all of California. Actually it's likely that R0 would naturally decrease with time, both because of voluntary social distancing, and because "super spreaders" and communities with higher local R0 will be infected first.

Is there a model with two different reproduction rates, one for mainstream population and one for a small fraction of super-spreaders? Say, social distancing greatly reduces reproduction rate for mainstream but only reduces reproduction rate for super-spreaders negligibly. How large a fraction of the population can super-spreaders be before ever greater restrictions on mainstream stop having effect, i.e., where mainstream reproduction rate becomes small enough that overall reproduction rate is determined by super-spreaders?

Also, another variation would be "leakage" from mainstream to super-spreader population, i.e, more restrictive social distancing reduces reproduction rate of mainstream but non-compliance reduces fraction of population in mainstream.

What are the conditions under which these diminishing-returns-to-social-distancing models could still result in overall reproduction rate below 1?

The model in the Science paper that Bjorn Lomborg has been tweeting about seems to take the long view and takes into account wave dynamics in response to different levels of lockdown. See: https://mobile.twitter.com/BjornLomborg/status/1250114408723947521

The strongest lock down does not model as the best response. The jury will be out on lockdown policy until we can calculate excess mortality rates for the period up until mass vaccination is completed.

Is there a reason we don't use moving averages (probably weighted) for this sort of thing?

Using daily averages, it seems like we could get a situation where something might cause deaths to move forward from the future (like maybe a cold spell or doctors were over-worked on a particular day), and suddenly we see a spike and then a decrease in the daily number of deaths for a week.

Early predictions (i.e., before the peak) underestimate the impact, while later predictions (i.e., after the peak) overestimate the impact. Is that an accurate summary of the graphs? I'm reminded of the hurricane spaghetti models, or what might be called the buffet model: something for everyone.

For one willing to think about my point, one will conclude that the project of infection rate and deaths will depend on when we reach the peak. The more optimistic believe the peak will occur tomorrow (April 16). The less optimistic believe the peak will occur mid-summer. Where one is positioned at the peak will determine one's projections. Duh.

I find it hard to put much stock in any policy predictions from a model that doesn't build in heterogeneity in the spread rate. We know that there are super-spreaders and that they are important; given exponential growth, the top of the distribution may be contributing nearly all of the cases. Without getting a handle on the variance and how it is explained by demographic and observable characteristics, it doesn't really let us explore any of the alternatives between "let it rip" and "total lockdown". For example, we know that large events create super-spreading opportunities. But as far as I can tell, we have no idea how barring large events shifts the distribution. Same for barring interstate and international travel without being screened, masks, etc.

And there seems to be zero empirical data on demographic observables and spread rate, e.g., kids don't seem to get very sick, do they just tolerate it better (in which case opening schools might be a disaster) or do they shed a lot less virus (in which case it may opening schools might not change anything materially). Sure wish someone would round up some kids, find out which are positive, and see how much virus is coming out of them, it is a very knowable thing. Same with positive people with and without a fever -- sure, you might be positive and asympotmatic, but how much virus are you shedding versus someone who has an elevated but detectable fever and no other symptoms (and so might not realize he was sick unless he bothered to take his temperature)? If there is a big difference, then maybe we can ask everyone to take their temperature every day and check it before entering places with a lot of people, that might be enough. Again, seems like not too difficult of a thing to measure, zero suggestion it is actually happening.

Similarly, assuming that the spread rate per case is independent of the number of infections also seems very likely to be wrong and to highly interact with heterogeneity. If I am on a bus with 30 people and 5 people are infected, the probability seems much higher than the cumulated spread from 1 person. (And the difference between 25 and 28 people has to be negligible.) That seems reasonably important, because once cases are again at a very low level, then measures that reduce the spread rate at the top of the distribution might be enough.

As a thought experiment, consider ten clusters where only a single person from each leaves the cluster and visits all the others each period. If hardly anyone is infected, then I might be able to stop the spread rather dramatically by cutting that person from visiting all ten to just one each period. But if a good number of people are infected, then the probability those super-spreaders encounter it is too high, and clamping their travel rate alone may not be enough to push the spread rate below 1.

Applying widespread travel restrictions, prohibitions on significant gatherings, and temperature checks before entering high-traffic areas when cases are low seems underrated.

"elevated but detectable fever" => "not too elevated but detectable fever"

Dan,
You make a good point. However, These models can be adjusted based on heterogeneous network structures. And they are.

Go up and look at the link I posted in response to Sean.

One of the issues you might consider is that clusters get connected over time. So, ask yourself, do people from NYC travel to Florida; and how did Colorado have some hot spots.

I agree it is bothersome that things that appear simple to measure have not been measured yet, like whether kids are immune or infected but asymtomatic. Also what is the temperature sensitivity - can't someone put some virus on pieces of metal, warm them up to different temperatures and see if they survive? We still have no idea if it is temperature sensitive. I suppose it'll just have to become obvious over time. Or not. How will we tell if social distancing is working, or if it is just spring?

A very similar model for the UK with time varying parameters that evolve with distancing measure is here:
https://www.kaggle.com/kiwiakos/covid19-uk-model

It's not clear if future predictions of fatality rates are taking into consideration a learning curve or medical personnel in treating the disease. They should. If there is even a small improvement in treatment success over time, we should assume a declining fatality rate if all other variables remain constant.

You're right. It should be reflected in the Infection Rate in the SIRD model. So, actions to reduce "I" have an effect on SIRD rate.

Tyler going all Julie Andrews here.

Comments for this post are closed