I just did the math on the lives you can save by taking aggressive action against the #COVID19 #coronavirus today. In a growing epidemic like this, early action is so important that anything I (and you) can do this weekend to convince our local decision-makers to shut down large events and close schools as soon as possible is likely to save more lives than all the earning to give I've done over the last decade.
If anyone here sees any big errors in my math or assumptions that would change any of the conclusions, please LMK and I'll be happy to correct them.
By request, here is the full text as well:
As shown below, your personal risk, if you’re a young and healthy adult, of catching and dying of the COVID-19 coronavirus this week is fairly low: probably below or only slightly above your risk of accidental death from something else. The risk to older age groups and those with chronic diseases is somewhat higher, so they should indeed be doing everything they can to limit outside contact.
But your risk of inadvertently catching and passing along the coronavirus to someone else, and continuing a transmission chain that eventually results in a COVID-19 death, is much higher. It’s so high, in fact, that anything you can do as an individual to reduce that risk has a social value of at least $350/day (doubling every week), and canceling large gatherings presents an opportunity to save multiple lives, even for fairly small groups.
Is it really possible to know that?
It’s actually pretty straightforward to get a rough order-of-magnitude estimate of your baseline risk (if you continue to behave like most people around you) of contracting the COVID-19 coronavirus, depending on where you live and how many cases are likely circulating in your region. It’s similarly straightforward to calculate your risk of dying if you do contract the disease, based on your age and any pre-existing conditions you may have. It’s possible to estimate your risk of passing along the disease to others, and of them passing it along further, until eventually lots of people have it. And as a result, it’s possible to estimate how many lives you can save by taking certain actions today to limit your risk of contracting COVID-19 and passing it along to someone else. How? Let’s get started.
First, some ground rules. We’re doing rough order-of-magnitude estimations, so none of our inputs need to be precise. I’m going to use the best estimates I have, and not round things to a multiple of 10 unnecessarily, but I’m not going to use more than one significant figure of precision to avoid conveying any incorrect illusion of certainty.
Ok, show me: What’s my personal risk of catching the coronavirus?
To start, we need to know how many people in your region likely have been infected with the coronavirus to date, and are likely infectious. There are a few ways to calculate this. One is to rely on estimates from epidemiologists or other scientists. For the Seattle area, Trevor Bedford has estimated that there were 570 individuals infected as of March 1, and a mean epidemic doubling time of 6.1 days. That means we have almost double that many cases today, March 5, so let’s use 1000 cases as our starting point.
Next, we need to know how many people there are in our region. That requires deciding the region of interest (over which those 1000 cases likely extend): let’s use the numbers for the greater Seattle metro area, which has a population of 4M.
Now, we can simply calculate that 1000 / 4M, or 1 in 4000, individuals in our region are likely infected with the COVID-19 coronavirus, and mostly don’t know it yet as it just today became possible for any doctor to order a COVID-19 test, with a 3-4 day turnaround. (Previously, only the Washington Department of Health was running tests, and they have quite a backlog, so they were prioritizing cases already known to likely be infected.)
Next, we need to understand the reproductive number of the virus. That’s how many people are infected, on average, by each previous infection. The R0 for the COVID-19 coronavirus, which represents the baseline infectivity without intervention, is approximately 2.3. With interventions, it can be brought below 1, and the epidemic gradually brought to a halt, as is now happening in China. But we haven’t gotten quite that aggressive yet, so I’m going to assume that the R (effective reproductive number) is currently around 2, and will be brought down to (but not much below) 1 over the next month or so, and then will continue to be reduced until the local epidemic burns out.
So if 1 in 4000 people are infected today, and each of them will infect 2 people, that means your chance of catching COVID-19 over the next ~4 days (a single viral generation) is about 1 in 2000, assuming you and the people around you behave approximately the same way as everyone else in the community.
And what’s my risk of both catching it and dying?
Now, we can look at what risk of death that implies. That requires understanding the Infection Fatality Rate, the % chance of dying if infected (whether or not you become a case by showing up in the hospital or getting tested, or even have any symptoms at all). As with R0, the IFR depends on both the characteristics of the virus, but also on how overloaded your local healthcare system is, and therefore whether you can be properly treated with oxygen and ventilation in an ICU bed if you fall seriously ill. At the moment, the US healthcare system is not yet overloaded, so anyone catching COVID-19 will be well cared for. The relevant IFR is therefore that calculated based on similar non-overloaded cases, namely those outside Hubei province. The IFR itself is difficult to measure directly, but the CFR, case fatality rate, is more straightforward. This page has good info on CFR, from the WHO. To adjust from CFR to IFR, we can assume that half of the cases are detected, and divide all those numbers by 2. That gives us:
So if you’re a young adult who catches COVID-19 when the healthcare system is not overwhelmed, you have a 1 in 1000 chance of dying.
If you have a preexisting condition, you need to adjust your personal chances to reflect that. Dana wrote up an excellent tweet thread on how to do that. The takeaway is, if that for an average comorbidity, you’re at 2x risk of a healthy person your age. So if you have some preexisting condition that might make it hard to fight off a bad respiratory infection, double the risk for your age group.
So, back to our 1 in 2000 chance of catching COVID. What does that mean for your risk of dying from something you catch in the next few days? Well, just multiply. If you’re a young healthy adult: 1 in 2000 * 0.1% = 1 in 2,000,000. If you’re in your 50s with one preexisting condition, 1 in 2000 * 1.3% * 2 = ~ 1 in 80,000.
Ok, how does that compare to normal risks of accidental death?
Now, how do you compare 1 in 2M or 1 in 80k to something you can relate to in your daily life? In my opinion, the best comparison is to your average daily risk of acute death. That is, conveniently for calculations, about 1 in 1M, or what “The Norm Chronicles” calls a MicroMort.
So, if you’re young and healthy and living in Seattle, your chance of dying from a COVID-19 coronavirus infection you contract in the next 4 days (0.5 MicroMorts) is about 8x lower than the ~ 4 MicroMorts risk of accidental death you experience over that timeframe from all causes, like your daily commute. If you take better precautions than people have been taking on average, enough to bring your personal R value down well below 1, that risk is even lower.
But if you’re in your 50s with a pre-existing condition (as many people that age are), your risk is closer to 1 in 80k or about 10 MicroMorts. That means your risk of dying of COVID-19 contracted over the next 4 days is about double your risk of dying of another accident over that timeframe, or approximately equal to the risk of a single skydiving jump or riding a motorcycle for about 70 miles.
Wow. What about my risk of spreading COVID-19 to someone else?
Now that we understand how to calibrate our own personal risk, what about the risk of allowing someone else to die by inadvertently catching and passing on the COVID-19 coronavirus to someone else? Well, to figure that out, we need to make some assumptions about virus transmission, which I detailed above: an R of 2 right now, a serial interval of 4 days, and an R dropping linearly to 1 over the next month (7 generations), and continuing to drop after that. So if you catch the virus and behave on average, you’ll pass it to 2 people, who’ll pass it to 1.86, who’ll pass it to 1.7, etc., for a total of 21 people infected in the first month. That’s the peak, as we continue to get the R value lower each generation, until finally after 2 months the local epidemic is completely extinguished, with 139 people infected. Let’s round that to 100, as that calculation is highly dependent on how fast our local community manages to slow and stop the spread of the virus.
Now, those ~100 people who got your virus are likely to be a cross-section of the entire community, so we can use the average IFR of the entire population, or about 1%, to estimate that on average, a single transmission of COVID-19 will result in 1 extra death, most likely of the parent or grandparent of someone in our local community. And that’s assuming a best-case scenario like in China, where our interventions are sufficient to stop viral spread and contain the outbreak within 2 months. If infections continue indefinitely until therapeutic interventions like remdesivir or a vaccine can be brought to bear, the number of deaths from a single transmission could be much higher.
Now, to bring it all together: if you have a 1 in 2000 chance of catching COVID with an R of 2, you have a 1 in 1000 chance of passing it along, and since doing so will on average result in 1 death, a 1 in 1000 chance of someone dying. Conversely, if you take aggressive action for the next 4 days to avoid catching and transmitting the coronavirus, you have a 1 in 1000 chance of saving a life, a 1 in 200 chance of avoiding one ICU visit, and a 1 in 50 chance of avoiding one hospitalization. To put that into MicroMort terms, you can avoid 1000 community MicroMorts. If we value such life at more than $1M, in terms of what we’d pay to reduce the risk of accidental death of an elderly relative, that means your actions to eliminate the risk of COVID-19 transmission over 4 days are worth about $1000 to your community, or $250/day. If we also look at the probabilities of avoiding the $10k cost of one hospitalization and the $40k cost of an ICU visit, that's another $100/day.
What about canceling gatherings to prevent COVID-19 spread?
So that’s for what you, personally, can do. What about for larger gatherings? Well, if each person has a 1 in 1000 chance of inadvertently causing a death today, then bringing together 100,000 people to the Emerald City Comic Con, starting March 12, after the infected population grows another 2x to ~2000, and the chance of a death from 4 days of average behavior increases to 2 in 1000, then we could have expected Comic Con to result in 200 deaths in the attendees’ communities, plus or minus any adjustments for how likely an average comic con attendee is to transmit the virus. As I was posting this, ECCC just announced they are canceling: by doing so, they likely just saved those 200 lives. That choice comes at great cost for them and all the exhibitors and attendees who would have attended, and they all deserve a lot of respect and thanks for doing what's best for the larger community.
And shutting down schools to save lives?
What about the decision about whether or not to shut down a school? We can assume for our calculations that the risks of severe outcomes to the kids are basically zero. And kids are probably a bit less likely than adults to transmit the virus since their symptoms tend to be very mild. So let’s assume they’re 2x less likely to transmit, and therefore a given kid, engaging in average behaviors, has a 1 in 2000 chance of inadvertently causing a death today. If we further assume that kids are harder to keep away from others than adults are, and that it’s only possible to cut kids’ risk of transmitting the virus in half by keeping them home from school and forcing them to sit still for a full day of online learning, then today’s closure of all schools in the 22,000 student Northshore School District likely saves about 10 lives each week the schools are closed. Michelle Reid deserves a ton of kudos for being the first public school superintendent in the area to shut down all schools in the district and start saving lives.
How about workplaces?
Most adults spend about half their waking hours at work. If work therefore represents half of their average risk of catching and transmitting the coronavirus, then asking 100 employees to work from home for 4 days is expected to save about 5 lives over the course of a 2-month outbreak. All employees should work from home if you can, and anyone who has to go to work should be especially careful to wash and sanitize hands frequently, avoid touching their face, and remain further than arms’ reach apart from coworkers at all times.
This is why shutting down schools, canceling conferences and church services, and having employees work from home is so essential to do promptly: each conference, church, or office we shut down directly saves multiple lives over the next few months. If you’re a healthy young adult looking only at your personal risk of contracting COVID-19 this week and dying as a result, the risks are actually fairly low: less than the risk of the driving you’d do to get to all those places. But if you instead look at the bigger picture, the actions you can take today to implement aggressive social distancing will save so many lives that it’s unconscionable not to implement them once we understand the lives that can be saved by doing so.
If you have any contacts with local elected officials on your local school board, city or county council, or similar, or if you know anyone at your local school district, city or county administration, or anyone involved in public health, we also have a shorter version of this document available here for public health officials and decision-makers with scientific backgrounds who are already familiar with COVID-19 epidemiology. Feel share either this article and/or that document with them and make sure they're fully considering all the public health implications as they decide whether to close schools, cancel events, and give guidance to local employers.
This is my first time posting here, so not sure of all the protocols: if it'd be better to duplicate the content here rather than linking to the LinkedIn post, I'm happy to move it over.
Yeah I’d love to see it copied over here, looks like an interesting analysis
If you do, I suggest mentioning explicitly it's been cross-posted
I just went ahead and edited this post to include the full text.
Thanks for writing this and sharing!
On the $250/day figure, if you want to make the cost-effectiveness of reducing the probability you spread the disease more comparable to GiveWell-recommended charities by valuing lives equally, the cost to save a life through AMF is about $2,000*, so you would use that instead of $1 million, reducing the impact about 500 times to about $0.50/day or about $15/month. This means that if it costs you > $15/month (directly or through opportunity costs) to avoid the risk, you can do more good by donating that to AMF instead.
*and it has other benefits and other GiveWell-recommended charities are estimated to be even better; this doesn't take into account how many years of life are gained or quality of life. GiveWell suggests not to take these estimates literally.
Even if you want to eliminate the economic value of life and only consider their moral value, you still need to consider the economic value of avoiding hospitalization, which is about $100/day. It's highly unlikely that buying malaria nets is higher value than actions you can take that will meaningfully contribute to overwhelming an expensive hospital system.
I don't think it's unlikely at all; I don't think that $100/day would be used for something nearly as cost-effective as bednets if it weren't being spent on healthcare. Hospitals and governments will spend what it takes to handle the coronavirus in patients, up to a pretty high limit per patient.
I think a more important concern might be limited medical resources and triaging, but that should go into the cost-effectiveness analysis model, and it's not something I should speculate about without expertise.
Thanks for doing the math, I think this is valuable even with a basic model.
I think this analysis undercounts the impact of spreading the virus. You only model local community transmission, but if the epidemic doesn't burn out in the Seattle area, it'll cause additional community spread elsewhere, which leaves room for another lg(8B/4M) = 11 doublings.
A linear reduction in R also might be too optimistic. In the plausible worst case, R is nearly constant until the final few generations when it saturates and starts to burn out.
I agree that it is useful to make simple models. The consensus appears to be that there will be a global spread, so then it appears that short-term actions could have very high impact. However, one could also argue that then the end state is going to be the same, so that would mean short-term actions would have no impact. It is true if social distancing (physical distance, handwashing, gloves, masks, etc.) is maintained for the entire pandemic, then R0 falls below one sooner, so fewer people get the disease. You can see a model of this here. On the 80,000 Hours podcast, they say that reducing travel out of the place of origin by 90% in the beginning only delays the outbreak 3 weeks, likely not enough time to get a vaccine. So which one is right, a huge impact due to short-term actions or basically nothing?
Presumably the benefit comes from flattening the curve. I.e. if we don't introduce control measures, the demands on the healthcare system will be unmanageable, whereas if we spread them out, then the healthcare system can cope with the demand.
I don't know how to add images in comments, so here's a link to a relevant image: https://imgur.com/ckt0ujv
And this is the article the image came from: https://www.vox.com/science-and-health/2020/3/6/21161234/coronavirus-covid-19-science-outbreak-ends-endemic-vaccine
This version that has been making the rounds on twitter makes the point even plainer: source
The syntax for embedding images is
![alt text](url). For this and other forum formatting issues, try googling along the lines of "markdown insert image" or "markdown cheatsheet" (still what I do despite using markdown regularly)
I agree that if we have sustained protective measures, it would not only lower the peak but also reduce the total number of people exposed. However, I am defining a short-term action as doing something we would not normally do in the next few weeks, like canceling a conference or early travel bans. I think this would delay the peak, but it's not clear to me that the peak would be appreciably lower. Furthermore, this says there are about 60,000 full function ventilators and 160,000 total ventilators. If 10% percent of people are infected at the peak and 3% of those require ventilation, that would be 1 million requiring ventilation. So even in the US, and with moderate protective measures, it looks like most people would not be getting the ventilation they need (though lowering the peak will still help somewhat). Of course if the protective measures actually stopped the spread early, then that would be a big benefit.
I don't expect the outbreak to continue indefinitely in the US, Europe, or East Asia. As noted at https://www.linkedin.com/pulse/bending-curve-covid-19-how-avoid-being-wuhan-lombardy-scott-leibrand/ , we are likely to need to implement 50-75% social distancing in order to avoid overloading ICU capacity, and at that point we've also basically stopped growth in new cases, making it comparatively easy to keep doing more of the same until new cases start to noticeably shrink, as they did in China, Singapore, and now Korea. The real question to me is how long it takes us to bring R down to and below 1. As lunis did, I originally thought that 1 month was optimistic, but Washington State has surprised me, and seems to have implemented the necessary social distancing after about 2 weeks (mostly in the last 2 days). As a result, my estimates of the value of individual actions may have been slightly overestimated. But this is one area where I'm happy to have been wrong, as it means people were listening and finally did the right thing. :-)