Saturday, March 7, 2020

Pop Quiz

1) You have a lake that has a problem with lily pads. Every day the number of lily pads doubles. On Day 37, the lake is completely covered in lily pads. On what day was the lake half covered in lily pads?

Statistics is hard for a lot of people. That's why lotteries can exist. Research scientists, however, have to work in stats at a fairly high level to perform their jobs. Here's one, running some numbers. Her name is Liz Specht. She admits that some of her assumptions may be off, but points out that you can vary rates pretty significantly and it only changes the outcomes by a week or so in either direction.

  • We can expect that we’ll continue to see a doubling of cases every 6 days (this is a typical doubling time across several epidemiological studies). Here I mean *actual* cases. Confirmed cases may appear to rise faster in the short term due to new test kit rollouts.
  • We’re looking at about 1M US cases by the end of April, 2M by ~May 5, 4M by ~May 11, and so on. Exponentials are hard to grasp, but this is how they go.
  • As the healthcare system begins to saturate under this case load, it will become increasingly hard to detect, track, and contain new transmission chains. In absence of extreme interventions, this likely won’t slow significantly until hitting >>1% of susceptible population.
  • What does a case load of this size mean for healthcare system? We’ll examine just two factors — hospital beds and masks — among many, many other things that will be impacted.
  • The US has about 2.8 hospital beds per 1000 people. With a population of 330M, this is ~1M beds. At any given time, 65% of those beds are already occupied. That leaves about 330k beds available nationwide (perhaps a bit fewer this time of year with regular flu season, etc).
  • Let’s trust Italy’s numbers and assume that about 10% of cases are serious enough to require hospitalization. (Keep in mind that for many patients, hospitalization lasts for *weeks* — in other words, turnover will be *very* slow as beds fill with COVID19 patients).
  • By this estimate, by about May 8th, all open hospital beds in the US will be filled. (This says nothing, of course, about whether these beds are suitable for isolation of patients with a highly infectious virus.)
  • If we’re wrong by a factor of two regarding the fraction of severe cases, that only changes the timeline of bed saturation by 6 days in either direction. If 20% of cases require hospitalization, we run out of beds by ~May 2nd.
  • If only 5% of cases require it, we can make it until ~May 14th. 2.5% gets us to May 20th. This, of course, assumes that there is no uptick in demand for beds from *other* (non-COVID19) causes, which seems like a dubious assumption.
  • As healthcare system becomes increasingly burdened, Rx shortages, etc, people w/ chronic conditions that are normally well-managed may find themselves slipping into severe states of medical distress requiring intensive care & hospitalization. But let’s ignore that for now.
  • Alright, so that’s beds. Now masks. Feds say we have a national stockpile of 12M N95 masks and 30M surgical masks (which are not ideal, but better than nothing).
  • There are about 18M healthcare workers in the US. Let’s assume only 6M HCW are working on any given day. (This is likely an underestimate as most people work most days of the week, but again, I’m playing conservative at every turn.)
  • As COVID19 cases saturate virtually every state and county, which seems likely to happen any day now, it will soon be irresponsible for all HCWs to not wear a mask. These HCWs would burn through N95 stockpile in 2 days if each HCW only got ONE mask per day.
  • One per day would be neither sanitary nor pragmatic, though this is indeed what we saw in Wuhan, with HCWs collapsing on their shift from dehydration because they were trying to avoid changing their PPE suits as they cannot be reused.
  • How quickly could we ramp up production of new masks? Not very fast at all. The vast majority are manufactured overseas, almost all in China. Even when manufactured here in US, the raw materials are predominantly from overseas... again, predominantly from China.
  • Keep in mind that all countries globally will be going through the exact same crises and shortages simultaneously. We can’t force trade in our favor.
  • Now consider how these 2 factors – bed and mask shortages – compound each other’s severity. Full hospitals + few masks + HCWs running around between beds without proper PPE = very bad mix.
  • HCWs are already getting infected even w/ access to full PPE. In the face of PPE limitations this severe, it’s only a matter of time. HCWs will start dropping from the workforce for weeks at a time, leading to a shortage of HCWs that then further compounds both issues above.
  • We could go on and on about thousands of factors – # of ventilators, or even simple things like saline drip bags. You see where this is going.
  • Importantly, I cannot stress this enough: even if I’m wrong – even VERY wrong – about core assumptions like % of severe cases or current case #, it only changes the timeline by days or weeks. This is how exponential growth in an immunologically naïve population works.
  • Undeserved panic does no one any good. But neither does ill-informed complacency. It’s wrong to assuage the public by saying “only 2% will die.” People aren’t adequately grasping the national and global systemic burden wrought by this swift-moving of a disease.


michigan doug said...

If your math is right,starting around Dec1 in China.
Every one on the planet has it now.
Either they stopped counting or it stopped spreading over there.

Miguel GFZ said...

I think Epidemics are being confused with endemics. Epidemics come with an expiration date which we don't know but exist Flu-Type sicknesses eventually subside.
stuff like yellow fever and the whole parade of tropical diseases are Endemics. those suckers do not die but they can be controlled easier. .

edutcher said...

The woman needs a good man and some time in the sack.

It's the flu.

Notice it's the Lefty sanctuaries that have most of the cases.

LSP said...

Good analysis. See the Epsilon graph for N Italy.


I was talking with a friend about the spread of this, particularly in countries that do not have as advanced a health care system. Specifically, India, but really any country that has very densely packed cities.

A couple of years ago I was in China on business. I remember seeing the factory workers cheek-to-jowl (and was told there's less emphasis on "personal space" which I'd already known). One company we visited, specifically, had apartments for rural workers with 6-8 people in one apartment. I didn't get to see them, of course, but I can only imagine.

My first thought was that any disease of any communicability would cut through that whole city like a hot knife through butter.

And... call me vicious, but the places in the US where this will really affect the population are the same: densely packed cities which are mostly liberal.

Aesop said...

Pop Quiz A.: Day 36. Duh.

Re: Specht.
Some of her assumptions are okay, but many, many of them aren't just wrong, they're ridiculous.
In a nominal 300-bed hospital, fewer than 10 (on average) are suitable for Kung Flu isolation in a negative airflow room.
1) Kung Flu will never flood all hospital beds.
2) Kung Flu will soak up all available isolation rooms, and all possible ICU beds, body-slamming an always scarce resource.
3) For 80% of Kung Flu victims, they will be told to go home and self-quarantine, and treat the symptoms, and they'll be fine.
4) in fact, some 20% of the total number of victims may not have any notable symptoms.
5) The problem then, is the 20% at the other end of the bell curve.
15% will need hospitalization, and it won't be available. But not by the date specified; she's probably a month or more early.
6) The 5% of the little end will be the ones who die, soaking all ICU beds up, and all available ventilators, and then swamping mortuary services, crematoriums, and graveyards, and leading to a pretty good shot at mass burials and/or corpse bonfires.
7) Overall, we'll be turning Kung Fu patients away, in droves (because if we didn't, health care would totally collapse for everything, which would be asinine), and sending them to whatever slapdash FEMA-camp hellholes FedGov comes up with. Because we're not going to infect the staff, and all public spaces in the hospital, to waste resources on 1-3% of the population that's going to die anyways, and simultaneously dropping the ball on heart attacks, strokes, trauma, and other easily-treatable medical conditions for which we can save lives.
8) Masks are similarly important overall, but pointless in the short term, as are all other supplies, because eventually, TPTB will have a come-to-Jesus epiphany, and realize than anyone that gets Kung Flu needs to go - in all cases - to a kung Flu treatment Center, not to the Friendly Local Big Medical center, because if we see them there, they'll die anyways, and kill all healthcare for everyone else, which keeps most hospitals running around 90+% of capacity 24/7/365/forever even without Kung Flu.

That's why I've been telling people not to get the virus: because if you're in the sick-or-dying 20%, you're going to get shunted into ghetto care, far below typical first-world standards of care, because it's all there can be, and all there will be.

Aesop said...

American health care is not going to fling itself on the pandemic live grenade in a futile bid to try and save everyone.
It's going to necessarily throw Kung Flu victims, en masse, under the bus. It's Lifeboat Ethics 101: when you can't save everyone, you save the moistest with what you can, and let the sea of disease take the rest.

When faced with losing everyone, or letting the sickest victims of Kung Flu die, the adage will be the old Russian saying:"toughski shitskiy, Comrade."

Something Ms. Specht never even considered, but which makes exquisitely logical sense, with virtually irrefutable logic.

Jeff said...

Very impressive, but if this were true, why aren't we seeing these numbers in South Korea or Japan, which are weeks ahead of us in the flu's progress?