COVID models in support of selective quarantine

8 min readMar 20, 2020

Update: Tomas Pueyo has put together a compelling argument that we can go from suppression to containment without crippling the economy. If that appears to be possible as more data comes in, it is VASTLY superior to the strategy explored here. I’m leaving this piece online because all options are worth exploring, but with all my heart I hope he’s right.

Update: NYT has published an opinion piece pushing for the same strategy!

How long can a dynamical systems guy live in a COVID shutdown and not start building mathematical models of the spread? I made it about five days.

During that time, I was troubled by a lack of clear ideas about the long-term plan for dealing with the virus in the USA. I was (and am still) 100% on board with locking the country down hard for at least a few weeks to catch our breaths and get better data. But back-of-the-envelope calculations showed that if we tried to “flatten the curve” and let the virus sweep the population slowly enough to avoid overwhelming the hospitals, that process would need to be stretched out over a year or more of intense social distancing. I’m no economist, but that seemed pretty bad for business.

Then I had a thought. Based on everything I had read, there seemed to be fairly well-defined COVID risk categories with major differences in fatality rates among them. What if we tried to make a public health plan based on that reality?

tl;dr: Suppose we insist that the higher-risk population to stay in their homes for ~150 days while the virus sweeps the lower risk population. Can we achieve herd immunity while the high-riskers stay home, saving tons of high-risk lives while creating minimal economic disruption?

Spoiler: maybe! I would like your feedback!

Before we go further, a few disclaimers:

1. The data I’m basing my models on is very preliminary (more on that below), and comes mostly second-hand from news sources, which themselves seem to be getting it mostly from unreviewed papers and interviews with experts that are made to sound more confident than they probably are. Some of the sources I’ve incorporated into a holistic set of parameters and assumptions for my model:

2. The only reason I built my own models was in order to experiment with the details of quarantine and risk categories, which are not addressed by the otherwise awesome Epidemic Calculator (http://gabgoh.github.io/COVID/index.html). My model is simplified for speed-programming in ways that this calculator is not. I will provide links to spreadsheet versions of my models below, but unless there’s real interest I will not write up the details, so you’ll have to take them with a grain of salt. Please view these models as approximations designed to make an important point rather than exact forecasts. However, I was fairly careful to make sure my model agreed reasonably well with the predictions in the report from the Imperial College of London reported in Axios.

3. I’m a math guy. I can only guess at the feasibility of getting a whole big unruly country to mostly follow a specific set of rules more complex than “six-foot separation.”

4. In a sense, I’m exploring the herd-immunity strategy that Boris Johnson announced for the UK (and has since backpedaled on), but I’m focusing in on its potential to cut the death rate by protecting high-risk cases and its contrast against a general “flatten the curve” approach. So it’s not a new idea, just a reframed one.

First, as a reality check, here’s what happens if the initial fatality rate estimates are right and we do nothing — no huge increases in ventilator capacity, no social distancing or quarantine, nothing.

If the grim forecasts are right and we do nothing

My model is a little more optimistic than the 4 million deaths predicted in the Imperial College report — only a little over 3 million! Still, not awesome.

I didn’t bother to model the “wait for a vaccine” solution. This one is pretty clearly spelled out in the report: we socially distance really hard until July, then take a break for a month or two, then do it again for a while, and eventually the cavalry comes, maybe around day 500. Relatively few lives lost to the virus. Everyone has a really rough year, and the economic consequences are someone else’s guess. I think this is widely accepted as the best move, but there are some people questioning whether the ends justify the potentially huge impact on life in America.

Next, “flattening the curve.” This is what happens if we take measures to reduce the transmission rate just enough that we only barely exceed the country’s ventilator capacity. In my model, some people go to work but more than half stay home, particularly the high-risk cases, and people make a reasonable effort at social distancing. Then we stop the measures as soon as we can without vastly exceeding ventilator capacity AGAIN with the second wave of infection. This is different from “wait for a vaccine” — in that one, most of the country does NOT get the virus, so the death toll is much lower, but we have to be a lot more intense about the distancing measures we take and adapt quickly to any evidence of re-outbreak.

If the grim forecasts are right and we “flatten the curve” with ~200 days of social distancing

Huge drop in productivity relative to doing nothing (though I guess a bunch of the people staying home could keep working on their laptops), saves ~1.4 million lives. Note that if I choose numbers to make the social distancing more effective, but go with the same general strategy of letting the infection run its full course at a slow enough rate for the hospitals to handle, I can cut the death rate a bit, but it takes even longer. At that point, maybe we should have just waited for a vaccine?

Finally, I made the key assumption was that we can split the country into two groups:

The group of people age 65 and over plus those with other health risk factors, constituting about 1/6 of the population, who have, on average, a 5% chance of a COVID infection becoming life-threatening.
The group of everyone else, who have about a 0.5% chance of a COVID infection becoming life-threatening.

Of course, subtler approaches could break the population down further, but this seemed like somewhere to start.

What happens if we insist that the high-risk group stay in their homes for ~150 days?

If the grim forecasts are right and we quarantine the high-risk population for ~150 days

Note the following:

A much smaller drop in productivity than the “flattened curve.”
~1.7 million lives saved, even better than flattening the curve. Why? Because when the low-riskers were having their infection party, the population as a whole reached herd immunity. Note that I did not model re-infection — not enough is known about the immunity or partial immunity gained by infection yet. But if the population does not achieve herd immunity and the infection spreads again, we could let the high-riskers out of their solitude gradually from lowest- to highest-risk gradually (first the 65–70 year olds, and then two weeks later the 70–75 year olds, etc.), avoiding overwhelming the ventilator supply AND possibly hitting herd immunity at some point along the way. The worst-case death toll wouldn’t be too much worse than the flatten-the-curve one, though more of the deaths would have been low-risk cases.
I had to assume a pretty darn effective quarantine. This may be the hole in the argument — if the quarantine isn’t effective enough to keep the high-riskers safe, there will be a lot more deaths. However, I imagine a quarantine will be more effective when it’s about self-protection and not herd protection. Plus, this is not a critical-mass-participates-or-it-fails quarantine, it’s a participate-or-you-risk-your-life quarantine.

So I think this policy merits some attention. Separating low- and high-riskers, many of whom will share families and/or homes, would obviously be very difficult— some low-riskers would probably need to join the high-riskers for part or all of the duration. The whole thing might go down a little easier with a bill to financially support the high riskers during their hibernation, and with a charge to the low-riskers to take care of the high-riskers however they can without physical proximity.

To end on an even brighter (?) note, I decided to scope out the situation if the new reports of many undetected asymptomatic infections covered in this STAT article turn out to hold for the US population. True, that means lots of people are currently infectious and don’t know it. But on the whole, this is great news. It means that the fatality rate for the virus is only half what we thought. Here’s what the model looks like for doing nothing:

If the optimistic data is right and we do nothing

Note that the beginning of the infection looks just the same — the hospitals are overwhelmed, and the death toll starts mounting — but in the end, the fatality rate is just half what was forecast. With a suitable mitigation strategy in place, we could probably knock it down by half again.

It feels weird to speak so cavalierly about a million deaths, but these are strange times. I’m afraid of what’s ahead — there will certainly be a lot of suffering for a lot of people. I do not envy our leaders the decisions they are going to have to make (and, ideally, take responsibility for). I just hope they do it with their eyes open to the data and the range of possible strategies, which should include segmenting the population by risk category. In the meantime, let’s talk about this. I would love your feedback on these ideas, and I’d love other modelers or public health thinkers to step up and tell me where I’ve gone wrong.

MODEL DETAILS:

I’m using an SIR model (SEIR models are important for capturing the short-time-scale dynamics, but less so for the long time-scale). Each population is split into L and H risk categories, and S and I are split into Free and Quarantined. Different fractions of L and H infections go straight to “severely infected” status, where those below the hospital capacity get a 50% chance of survival and those above die. Parameters are listed in the spreadsheets below.

LINKS TO MODELS (Google Sheets simulation):

COVID models in support of selective quarantine

Written by Jonathan Cannon