When to Reverse Quarantine and Other COVID-19 Considerations

A lot of people in my social network have been trying to track news about the new coronavirus, COVID-19, which seems like a global pandemic that's going to kill a lot of people. I've found some of this overwhelming and difficult to figure out how to use, until I sat down with a few friends, over the phone, and worked out a simple analytic framework for thinking about some basic decisions. 

I figured I'd put this up, not so much because anyone should use my numbers as-is, but because maybe the simplicity of the reasoning might help others like me get over a sort of feeling of helplessness about how to think about this sort of thing.

I'm only counting selfish benefits here, not because that's all that matters, but to keep things simple. I encourage anyone who wants to, to extend this decision model elsewhere (or here in the comments).

At the end, some less structured thoughts and links to other info sources. Please double check facts yourself before relying on them, though of course I'll fix any errors I find.

Reverse Quarantine Length

The simplest, most reliable measure available to me, to prevent myself from being infected with COVID-19 is to hole up in my apartment and isolate myself for some length of time. But, it's costly to do that - and much more costly for people who are in the short run reliant on income sources that require them to show up somewhere. So, what length of reverse quarantine has benefits that outweigh the costs?

Costs vs Benefits

Since I'm in the young-and-in-good-health category, it looks like the consensus estimate is a 0.2% chance of death if I'm infected. The costs of avoiding all potentially deadly risks are prohibitively high, but a 1 in 500 chance of dying if infected, for something that seems like it's a global pandemic, is pretty high as far as these things go. If I faced one risk like that each day, I'd probably die within a year. But "pretty high" doesn't tell me what precautions are worth it. Can I use numbers?

Let's say that a reverse quarantine is worth it on any day that it saves me more time in expectation than it costs. So, on each day, I have some probability of getting infected if I interact with the outside world - let's call that daily_infection_rate. And each day of reverse quarantine costs me some fraction of a normal day's value - let's call that days_lost_per_day_isolated. And if I get infected with COVID-19, I lose some time that way as well - let's call that days_lost_per_infection. The equation that defines my break-even point is:

days_lost_per_day_isolated = days_lost_per_infection * daily_infection_rate

With about 45 years of remaining life expectancy, an infection costs me an expected = 0.2% (chance of dying if infected) * 45 (years life lost if I died today) * 365 (days per year) = 32 (days of life lost if infected)

In addition I'd be sick for a couple weeks. If I count those days as a total loss, then being infected would cost me 32 + 14 = 46 days. Let's round that up to days_lost_per_infection = 50 to make the next calculation simpler.

A day in strict reverse quarantine seems to me like it's probably about half as valuable as a normal day, so days_lost_per_day_isolated = 0.5.

This allows me to estimate the infection rate that would justify holing up:

daily_infection_rate = days_lost_per_day_isolated / days_lost_per_infection = 0.5 / 50 = 1%. So, on any day where going out and interacting with the world in a normal way would expose me to a 1% risk of infection, I should stay home.

How can I estimate my daily risk of infection? Well, in most places it seems to have something like a 3-day doubling rate. That means that if prevalence in my area is 3% today, it should be 6% in three days, meaning that on average, 1% of the population gets infected on each of the next three days. So, my break-even point looks like 3% prevalence.


Once 3% of people are infected, how long will it take for the outside to be safe-enough again? A crude way of estimating would be to ask how long it would take for everyone to get infected, and then recover. From 3% prevalence, it only takes 4 doublings, or 12 days, to reach half of the population. If we assume a symmetrical sigmoid curve, then the time to infect all but 3% of the rest should be about the same, for a total of 24 days until nearly everyone is infected. After that, it shouldn't take more than a couple months for the vast majority of cases to recover. So, a reasonably conservative estimate would be that a 3-month reverse quarantine would be adequate for my needs, if I time it right.

A friend suggested that where testing is more extensive (and therefore measured prevalence is a better estimate of actual prevalence), it looks like the doubling rate is more like 6 days. In that case, my threshold is more like 6% prevalence (though the linear extrapolation is less accurate), and it takes three doublings, or 21 days, to infect half the population, and (again assuming a sigmoid) another 21 days to infect the rest. With two more months to recover, that's again about 3 months' total reverse-quarantine time.

Hospital Overwhelm

Of course, if hospitals get overwhelmed, expected mortality probably goes up. At what prevalence should I expect that to occur? I've heard that hospitals in the US have a free bed per thousand people. So if 0.1% of the local population is hospitalized due to COVID-19, that eats up that spare capacity and new cases are much harder to treat. The true overwhelm point could be higher (due to emergency measures or triage) or lower (due to bottlenecks on specific equipment).

I hear that about 10% of cases end up hospitalized, so when 1% of the population is infected, 1% * 10% = 0.1% will be in the hospital. I don't have a good idea how much of this is already being averaged into the standard mortality estimates, so I'm not sure what to do with it - but (given the exponential nature of the disease) it's interesting that it's not many doublings away from my naive "time to hole up" threshold.

Another way of calculating it, possibly more reliable: there are about 60,000 ventilators in US hospitals, and 300 million people. So we use up all the ventilators when 0.02% of the population is hospitalized, or 0.2% contract COVID-19.

Interpreting Available Local Data

Unfortunately parts of the US government seem to be trying to cover up, or at least drag their feet on reporting, COVID-19 prevalence. And even if they weren't, testing efforts aren't properly scaled. CDC prevalence numbers are not to be taken literally. So how can we know when we hit that threshold?

Well, I'd expect to hear if the local hospitals are overwhelmed with COVID-19 cases, which would signify 1% prevalence based on the above calculations. But there's possibly an incubation period of up to a couple weeks. If the doubling time is three days, that's four doublings between infection and major symptoms; if six days, that's two doublings. So, by the time free hospital beds actually get used up, I'd expect between 1% * 2^2 = 4% (six-day doubling) and 1% *2^4 = 16% (three-day doubling) prevalence. One of those is after my bug-out time.

But if I look for news about ventilator shortages that should tell me when 0.2% of the local population has gotten sick. Again factoring incubation periods into account, 0.2% * 2^2 = 0.8% prevalence (for six-day doubling), and 0.2% * 2^4 = 3.5% (for 3-day doubling), which would give me advance warnings in both cases.

Anecdotally, I know of one cluster near my home in Pittsburgh of three suspiciously severe flu-and-pneumonia-like symptoms about a month ago, that a pulmonologist thinks in hindsight might have be COVID-19.

One has to use this kind of evidence when the powers that be are covering things up. I feel weird passing along on this sort of anecdotal data, but it really is the epistemically clean thing to do, given the behavior of the authorities, and it feels metaweird to undergo that sort of shift within my lifetime.

If these were the only cases, then a 6-day doubling time allows for about 5 doublings, or about a 32x growth rate, so I should expect around 96 cases locally. But this could be way off. None if these weren't COVID-19, way fewer for longer doubling times, and way more if there were (as I suspect) more cases not personally known to me. Pittsburgh has a population of 300,000, so 96 cases would be 0.032%, and only about 8 doublings or 1.5 months to go before I hole up. Probably I have less time than that.

But if the doubling rate is more like 3 days, then that's 10 doublings, or about a 1000x growth rate, amounting to 1000 cases locally, or 0.1% of the population, only five doublings or 15 days until I need to start reverse quarantine.

More information will of course become available between now and then (I'll know more in a couple weeks than I do now), and I have a month's worth of calories & other basic necessities stored in my apartment, so I don't expect to be caught totally off guard.

Other Information

Fever is a common early symptom, and runny nose is not. This might help with informal differential diagnosis.

Justin Shovelain's self-quarantine guesstimate model

The west coast of the US seems like there are probably enough cases out there that I'd be holed up quite soon if I still lived there. More broadly we should expect many more cases in the US than reported, because the US hasn't been testing, and we only know about the Seattle cases because the people there exploited a bureaucratic loophole. The CDC is an important info source here, but not a reliable interpreter of the facts.

Slate Star Codex estimate of COVID-19 danger, with links to other info

Johns Hopkins Plague Tracker

Modeling COVID spread vs health care capacity

Some complications in my model: Infections by mail are nonlocal, and complicate the "when to reverse-quarantine" question. Intermediate sanitation measures may cost a lot less less than reverse quarantine and it would be good to have estimates for those. Other people may have something closer to a budget constraint than a smooth preference curve. Sometimes you have to do the calculation for whole groups (e.g. families) rather than individuals. None of this includes flow-through benefits to others or taking oneself out of circulation, OR (if you're doing critical work) cost to others of staying in.

Some things I'm doing:

Stocking up on high-quality hand sanitizer for the duration. Zylast antiseptic seems like the best option currently commercially available. Handwashing, of course, and not touching my face when I'm out. Moisturizing my hands after washing when feasible, to avoid cracked skin. Getting plenty of sleep & moderate exercise.

Avoiding places where lots of people will be in close proximity or touching the same things, except in high value cases (I'm probably gonna still keep going to yoga classes for now since there are zero confirmed cases anywhere near Pittsburgh, but be much more careful to sanitize my mat before & after).

Unsure how to think about sequestering my mail, especially since I live in an apartment, so space is limited, but I should spend a few hours on that.

Copper tape has antimicrobial properties. I ordered some on Amazon and have been putting it on commonly touched surfaces my home like sink water tap handles, car door handles, and the back of my phone. (Had to be careful to avoid covering the antenna, though.) Be careful when applying, since the edge of a copper sheet can cut you.

Chloroquine seems promising as a treatment or prophylactic, quinine is similar to chloroquine (with caveats), and cinchona bark, which contains quinine, is available at many herb storesZinc acetate lozenges work on colds, many of which are coronaviruses, and seem likely to reduce the severity and duration of COVID-19.

We should expect shortages of masks, ventilators, and oxygen concentrators, and if you have relevant skills you might want to look for and contribute to efforts to produce them.

11 thoughts on “When to Reverse Quarantine and Other COVID-19 Considerations

  1. Guy Srinivasan

    > A day in strict reverse quarantine seems to me like it's probably about half as valuable as a normal day

    A big bold disclaimer there would have been helpful to me, I think this number changes radically per-person, which radically changes the heuristic. All the rest didn't seem to change a ton for me. days_lost_per_infection is possibly higher if you are paycheck-to-paycheck; possibly much lower if you already work from home, have companion(s) who are observing the same discipline, etc (me).

    1. Benquo Post author

      days_lost_per_infection would change a lot for someone older or (especially) a young person with a preexisting respiratory ailment or immune dysfunction.

  2. Romeo Stevens

    FWIW I covered the whole back of my phone case in copper tape and it seems to be receiving data and wifi just fine. Might be different if applying tape directly to phone.

  3. Emma B

    > With about 45 years of remaining life expectancy, an infection costs me an expected = 0.2% (chance of dying if infected) * 45 (years life lost if I died today) * 365 (days per year) = 32 (days of life lost if infected)

    I don't care about maximizing my number of days left under the assumption I lead a finite lifespan.

    Care about children, care about altruism / the ultimate outcome of our world, care about your own immortality, but I don't see any reason to care about the integral of your future experiences / time left.

  4. Ivan

    As people decide to self-isolate, the doubling rate declines, affecting this threshold.

    I don't know how to carry that observation forward myself.

    Other contagion-reduction measures will also reduce doubling, so maybe we'll isolate for a bit and then replace isolation with more livable measures that still keep R0 below 1, like large gathering bans and temperature checking and ongoing handwashing religion, the type of stuff that's keeping things muted in China as people reemerge.

  5. walter white

    The United States is a huge landmass, so using stats on the country level is misleading and not as useful. If you get sick on the West Coast, you're going to your local hospital not some place in the Mid-West or East Coast. You have to dig deeper to really get at meaningful answers.

    Some people have been shitting on the Italian health care system, but if you normalize the infection and death rate, you'd see they higher concentration of the elderly.

    I personally may not be at high risk category, but if my community is due to age, population density, number of hospital beds per population, etc these are all factors to consider.

  6. Pingback: Estimating COVID-19 Mortality Rates | Compass Rose

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