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.

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?

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).

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 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 curve) 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.

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.

Justin Shovelain's self-quarantine guesstimate model.

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

Johns Hopkins Plague Tracker

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, and sometimes you have to do the calculation for groups (e.g. whole 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 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 stores. Zinc 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.

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24 comments, sorted by Click to highlight new comments since: Today at 2:43 AM

Have you looked into whether cinchona is really an acceptable substitute for chloroquine?

I'm concerned for two reasons. First, the studies I saw were on chloroquine, and I don't know if quinine is the same as chloroquine for this purpose. They have slightly different antimalarial activity - some chloroquine-resistant malaria strains are still vulnerable to quinine - and I can't find any information about whether their antiviral activity is the same. They're two pretty different molecules and I don't think it's fair to say that anything that works for one will also work for the other. Even if they do work, I don't know how to convert doses. It looks like the usual quinine dose for malaria is about three times the usual chloroquine dose, but I have no idea how that translates to antiviral properties.

Second, I don't know how much actual quinine is in cinchona. Quinine is a pretty dangerous substance, so the fact that the FDA doesn't care if people sell cinchona makes me think there isn't much in it. This paper suggests 6 mg quinine per gram of bark, though it's using literal bark and not the purified bark product they sell in supplement stores. At that rate, using this as an example cinchona preparation and naively assuming that quinine dose = chloroquine dose, the dose corresponding to the Chinese studies would be 160 cinchona pills, twice a day, for ten days - a level at which some other alkaloid in cinchona bark could potentially kill you.

Also, reverse-quarantining doesn't just benefit you, it also benefits the people who you might infect if you get the disease, and the person whose hospital bed you might be taking if you get the disease. I don't know what these numbers are but they should probably figure into your calculation.

This is a relevant study I found on quinine's antiviral activity (albeit on a different virus):

A previous study reported that the antimalarial drug chloroquine, a drug that shares a similar chemical property with quinine (both are alkaline in nature), inhibits pH-dependent stages of Flavivirus replication (Randolph et al., 1990). This is a likely inhibitory mechanism of quinine in our experimental model.

Also, reverse-quarantining doesn't just benefit you, it also benefits the people who you might infect if you get the disease, and the person whose hospital bed you might be taking if you get the disease. I don't know what these numbers are but they should probably figure into your calculation.

I wanted to start with something very simple to avoid decision paralysis, but you're right that there are flow-through / flatten-the-curve benefits. I've added a note clarifying that while this consideration matters, I haven't counted it.

Have you looked into whether cinchona is really an acceptable substitute for chloroquine?

Nope! The epistemic status there is something like "rumor from a pretty sensible and curious friend." Definitely not a substitute for any other measure, and highly speculative. Edited to clarify (and link to your comment).

"Tonic water contains no more than 83 mg of quinine per liter," according to the FDA. I haven't found any tonic water brands that say how close they come to that threshold, but 3 2L bottles of tonic water per day could keep you well-hydrated *and* protected.

From what I can google, typical dosage of quinine for malaria would be at least 500mg every 8 hours. If you drink 6 liters of tonic water every 8 hours you'll have more to worry about than coronavirus. What I don't understand is why they haven't started treating Covid with chloroquine yet--it's cheap and plentiful and has minimal side effects. Are desperate doctors in overwhelmed ICUs really holding off just because it would be off-label?


In my estimates, also only counting personal benefit, but taking into account secondary long-term effects as well as the increased risk from overwhelmed hospitals, I got something closer to days_lost_per_infection=250, which is what I am currently planning with. Here is an abridged summary of that Fermi: 

  • Risk of dying in non-overwhelmed hospitals: 0.2%
  • Risk of dying in overwhelmed hospitals: 1.5%
  • Probability of being treated in overwhelmed hospital: ~50%
  • => Average risk of dying from getting it: ~0.8%
  • Remaining Life-Expectancy: ~50 years
  • => Expected life-months lost from death: ~5 months
  • Likelihood of secondary long-term effects when getting it: 5-15%
  • Average badness of secondary long-term effects: ~18 months
  • => Expected life-months lost from secondary-effects: ~2 months 
  • Primary negative effects from illness: ~1 month

Total negative effect: ~8 months = ~250 days

I think the effects on spreading the disease, infecting others, and increasing peak disease burden have a lot more variance, and I have a lot more uncertainty in them, but I think it seems reasonable to take the number above and multiply it by something between 1.1 and 3 to get the total cost.

How did you estimate "Likelihood of secondary long-term effects when getting it" and "Average badness of secondary long-term effects"?

Likelihood of secondary long-term effects when getting it

I estimated this primarily on the basis of hospitalization rates and cases that are classified as "severe" which are around 10%-20% from what I've seen so far. 

Average badness of secondary long-term effects

I mostly just read a bunch of papers on Pneumonia and looked up some related reading on secondary effects from other diseases. Here is an answer that goes into detail on this: 


Should read "~8 months = ~250 days"

Oops, thanks, fixed!

Very dangerous assumption here that death is the only adverse outcome. Survivors of some other Corona virus infections have had lasting debilitating effects. We just have no data on this for the current pandemic.

As OP mentioned this was a purely "from my self-interest perspective". Even extending this to the risk of infecting family members would change the equation markedly I think.

How dangerous is that assumption? What multiple of the impact from death is the impact from disability? How different a decision would that imply?

In my personal Fermi Estimates, I multiplied the cost from death by about 2.5 to account for secondary long-term effects, mostly because the number of young people being hospitalized and needing major medical attention is in the 10% range (i.e. 50x higher than the default death rate), and a significant fraction of those are hooked up to mechanical ventilators, and my medical intuition says that if you are hooked up to a mechanical ventilator enough stuff has gone wrong that you will probably walk away with some long-term effects.

My calculated doubling time of 2-3 days is only really trustworthy for the first 2 or 3 doublings in a given country after the virus breaks containment.

I anticipate it increasing after that (and we see that in multiple countries) as government measures and personal behavioural changes kick in. If it follows a Sigmoid curve, as China appeared to after quarantine, then the length of time required to allow the virus to work its way through the population will go up dramatically.

(Edited to remove some errors)

"Be careful when applying, since the edge of a copper sheet can cut you."

Did you discover this independently, or was this from my, uh, case report on Facebook?

Fwiw I discovered it independently. :P

Heard it from someone I can't remember on Twitter, and then gave myself a (minor) copper cut.

Wow, heh, we're at N=4 at least then, counting Ray above. Probably future advice about copper tape should clearly document this hazard (I'm not even joking...)

I added this to the google doc.

Could your quarantine length calculation take into account that if you're infected today and recovered 14 days later you're in a significantly better position than if you quarantine for 14 days? Possibly this is overwhelmed by other factors in this case, but I think ignoring it could lead to some absurd results like quarantining for 10 years.

By the time even just 2% of the population will be infected, hospitals will already be overstrained and governments won't want to risk things getting tremendously worse, so very strong recommendations on social distancing will be given out. (They might still be weaker than in China or South Korea, but probably enough to halt the spread.) So, at some point soon you have something between 0.5% and 4% of the population infected, but everyone is at home isolated. The question is what happens next. I don't really know because it seems like as soon as containment measures are lifted, the whole thing starts again. Maybe with summer temperatures it can be kept in check somewhat well with less drastic measures than "never leaving the house," but I could imagine that socializing will be affected throughout the rest of the year.

Not sure where to put this in terms of your thinking. Vox had a report from CDC (USA) talking about flattening the curve. The relevant aspect, perhaps, is that from CDC's perspective, social distancing, self-quarantine, work from home and similar actions was not actually expect to reduce the number of infection. The goal was to shift the peak right and bring the peak down to, or below, medical capacity.