SEIR Modeling

You may notice mentions of SEIR models in forecasting COVID-19. The initialization stands for Susceptible Exposed Infected Resistant. These are a form of time series models that are common in viral epidemiology. A new one was released yesterday as a white paper† through the Institute for Health Metrics and Evaluation at the University of Washington in Seattle's site for COVID-19 projections.

† White paper is a good phrase for a student interested in research or policy to learn. It does not have a firm definition. Generally speaking, it means that the paper lists no authors. So who the heck wrote it? Instead of authors it usually has the name of some institution that published it listed as the author (or the name of the directors of the institution, even though they may not have done the research themselves). Employees of that institution wrote it, usually under executive direction. White papers are often produced by government or quasi-governmental policy advocacy organizations to support the policy position of the institution with something that looks like (and don't get me wrong, it usually is) serious research.

The paper is reviewed by Carl Bergstrom in this tweet storm. Here's the money quotes "The authors find that health care capacity will be overrun [in] the US, badly, ..." and "... this is a model of successful suppression of the epidemic with no second wave."

Nationwide, they expect the epidemic to peak in 2 weeks, and to subside somewhat more slowly than it built up. Their forecast range is that at peak on April 10-11, the U.S. will need 18-74K ICU beds. They say we have about 20K of those, but this dashboard says we have 64K. I don't know who to believe. Hospital bed needs peak a little later on around April 13-14 when we will fill 118-467K beds. They say we have 183K, but according to that dashboard we have over 800 K of those that are "staffed". Oh ... and we'll be short 19K ventilators too.

What's going on here??? I think "Staffed" is a polite way of saying that they're not all all in hospitals. Where else could they be? Nursing homes. Rehab facilities. Hospice. I dunno ... elementary school nurse's offices??

They also do state level projections. Consistent with where we are now, Utah will be running late on this. Our ICU use will peak around April 20th at just over 300 beds (they're range is roughly 220 to 380). According to them, this is a shortfall of about 120 statewide. According to the dashboard we have 513 of those. We should be OK on hospital beds, where we peak out at needing 1,600-2,400, and we have 2,800 of them (5,600 according to that dashboard). Utah is also going to be short 157 ventilators ...

And some states, like New York are going to get wrecked. I am not sure when they ran the simulations posted on their website (or how often they're updated). I'm pretty sure what they show for today is a projection. Anyway, they have New York state already at capacity for ICU and hospital beds. This is consistent with news reports out of New York City, but not for the whole state (a lot of that inconsistency just points to the model not being fine-grained enough). The model predicts that in about 10 days, New York state will need 20,000 ICU beds; they have 718 (or 3,100 according to the always more optimistic dashboard cited above).

It gets worse. Total deaths nationwide should be done by mid-June at 80K. Their interval estimate is 40-160K. For perspective, Katrina was 1,300, 9/11 was 3,000, annually car accidents have been hanging around 40K for a couple of decades. Do note that the 80K number is in the ballpark of what influenza claims every year. But keep in mind that this SEIR model is claiming that because we've done all these drastic things so far, and if we keep them up, we might be able to limit it to what the flu does. For Utah, it's a little later, with 300-1000 deaths in total by early July. That works out to 3-10 in Cedar City.

These are based on an SEIR model. To an economist these make little sense: they model growth of an epidemic by assuming the spread is characterized by increasing returns to scale. Gee ... no wonder they find they always get worse. They're not impossible to parse out though, if you think of the 4 parts as columns in a spreadsheet. The basic mechanism is that the susceptible come into contact with the infected, and so a fraction of the susceptible shift into the exposed column. Some of the exposed eventually shift into the infected column. Some of the infected column shift into the resistant column who can no longer be or spread infection (unfortunately that can also include fatalities, which aren't usually modeled directly).

************************************

Take your mind back to late January? Do you remember when I pointed out that a large scale quarantine of the well has never been tried? China was the first, but of course everyone's doing this now, right?

It turns out that there's no model in epidemiology that supports this. That doesn't mean it's a bad idea. What it does mean is that it was a command-and-control political response to the epidemic that was never envisioned by people who work in public health.

Instead, in public health, they worry about quarantining the sick. This makes sense. Think of any movie or TV show you've seen about an outbreak of anything. They always quarantine the sick. Heck, that's what you do when you get a cold in the winter. No one every quarantines the well. Except China in 2020 ... and a lot of other places.

In fact there aren't many SEIQR modeling papers out there. The Q stands for Quarantine, and note from the order that it is the infected who are quarantined until they become resistant. The idea is that you reduce interactions of the susceptible and infected by quarantining some of the latter. The approach in China, and now elsewhere, was to quarantine both.

Tooting my own horn here ... and who actually found an obscure paper, read it, and put it into a spreadsheet? Yours truly. I mentioned this after class one day to TL, with the intention of showing you guys, and now I'm finally catching up with that. Their model was intended for modeling the first SARS epidemic in 2002-3, when only the infected were quarantined. Anyway, I'll email you a copy of the spreadsheet model to look over (it's kind'of innovative, and it's an unfortunate fact of modern academics that if I upload it to Canvas for you, it actually becomes property of SUU).

Here's the thing: business students always whine that they don't like math or aren't very good at math. Then they get into business majors and find out that it's the second mathiest college on campus, and mathier than a lot of science departments. You're not alone; this happens at all schools. Anyway, business students often say they can't understand the math, but then they turn around and do very sophisticated math in their spreadsheets. So while you may look at the math in the paper and honestly have no idea what it's all about, I code the stuff into a spreadsheet, and I betcha' some of you will be able to figure out what's going on.