10 ms·

Please poke holes in my Covid-19 math (SF Bay Area)

58 points by drodio 7y ago

andreyk 7y ago
"Multiply the number above by 1,024 (assumes a doubling of cases every 3 days) if you assume no social distancing measure are put in place: 2.1MM on the low end, mulitplying by a 10x ratio. " Poke -- lots of measures are already being put into place (Stanford is effectively shut down, the big tech companies are making everyone work from home) etc. Edit oh you have this right after: "Or, multiply it by less if you want to take into account various amounts of social distancing we're all doing. I'll cut that number above down by a huge amount – 90% – on the assumption that we all learn to stay home and self-isolate immediately, just to be super aggressive on my assumptions about how humanity will rise to the occasion" Still, kinda weird to start with assumption of no measures when there clearly are some already.
- freepor 7y ago
  Yep - the Bay Area actually has a great chance at curbing this because a larger fraction of workers than anywhere else can effectively work from home.
- cperciva 7y ago
  The 90% might be conservative. If the rate of spread can be reduced by 50%, it will reduce the number of cases after 30 days by 96%.
  - dmurray 7y ago
    And if it can be reduced by 60%, we will see exponential decay instead of exponential growth. (assuming R=2.4 is the average number of people each victim infects, which is a number I've seen used a lot). It seems plausible that social distancing can reduce human contact for the average person by 50%, and for people with some flu symptoms by 80%. All this is to agree, the growth rate is by far the biggest factor in getting an estimate of peak impact.
  - danenania 7y ago
    Does anyone have insight into how moderate/voluntary vs. strict social distancing impacts the rate of spread? Anecdotally, the streets in the SF Richmond District feel a lot emptier than usual when I go out for walks/runs (pretty much the only reason I'm going out anymore). Seems like it could be up to a 50% reduction. That should already be helping, but I wonder if spreading might follow a power law pattern where "super-spreaders" account for a vastly disproportionate share of transmissions. If that's the case, it might require a strict lockdown to meaningfully reduce the exponent?
- lkbm 7y ago
  > "Or, multiply it by less if you want to take into account various amounts of social distancing we're all doing. I'll cut that number above down by a huge amount – 90% – on the assumption that we all learn to stay home and self-isolate immediately, just to be super aggressive on my assumptions about how humanity will rise to the occasion" Dropping 90% is not a great way to calculate this. Look at the math for 61 days out (from March 8): https://youtu.be/Kas0tIxDvrg?t=465 https://youtu.be/Kas0tIxDvrg?t=465 I don't think our social distancing and hand washing will be near enough to prevent millions of deaths, but it's important to recognize that a small change in the growth rate does make a huge difference. Estimating how much we can affect the growth rate is hard, but I think models should be based on a iffy guess on that value rather than an iffy guess on the resulting count. (Expert models certainly are.)
- sneak 7y ago
  All the bars and restaurants are still open, and people are still allowed to visit friends and family. Most nCoV transmission is in small groups with close contact, not stadiums. Closing offices and schools is a good first step, but as long as bars and restaurants are still open and food delivery services are carrying it all over town, it’s a drop in a bucket.
  - edmundsauto 7y ago
    California just announced all bars are to close, and restaurants limited to half normal capacity.
creato 7y ago
> Multiply the number above by 1,024 (assumes a doubling of cases every 3 days) if you assume no social distancing measure are put in place: 2.1MM on the low end, mulitplying by a 10x ratio. (Just because if I multiply by a 50x ratio, it returns a number larger than the 7.8MM total residents in the Bay area.) This is why the spread of a virus like this is a logistic curve, not an exponential. An exponential is a good model at first, but extrapolating too far doesn't work like this.
- ignoramous 7y ago
  > This is why the spread of a virus like this is a logistic curve, not an exponential. More on this by 3Blue1Brown: https://www.youtube-nocookie.com/embed/Kas0tIxDvrg https://www.youtube-nocookie.com/embed/Kas0tIxDvrg
  - hef19898 7y ago
    Somewhere after, or around, thee 5 minute mark: "true exponentials are basically non-existent in real life"
- gbrown 7y ago
  The reality is even more complicated - sure, a logistic curve is a reasonable fit if we assume that the data is accurate and the population homogeneous and well mixed, but in practice things get more complicated quickly. There's a huge network of potential contacts, with a large degree of heterogeneity and important subcomponents at multiple geographic scales. In addition, the network is dynamic, not static, so that both highly granular and population scale phenomena can change the contact distribution. Two important questions are: 1. What can we actually measure with confidence to relate to a model of interest 2. At what level of sophistication is it feasible to actually model things Neither question is particularly straightforward in the face of ongoing epidemics.
  - fsh 7y ago
    The data from China almost perfectly follows a logistic curve. Unfortunately, extrapolating such a smooth function is pretty much impossible before it starts saturating anyway.
trimbo 7y ago
> to get the actual number of confirmed cases today I think for this part you meant "actual number of cases"? Since the confirmed number was 1/10th of that.
olivierduval 7y ago
Something is missing: the average duration of covid patient in hospital. Hopefully, it is less than 30 days so some patient will go to hospital, stay a few days (then die or go home) and then leave their room in hospital... I don't think that it was accounted for in the calculation for number of beds in hospital
- coldcode 7y ago
  If you wind up in the ICU, it may be 2-4 weeks before you can be released, regular hospital beds don't count. You also have to assume how many assisted breathing systems (respirators/ventilators etc) are available. You can't simply assume the number of beds are available either since people may already have some other serious issue and be in one. In China they constructed massive hospitals out of large spaces on the fly, something I can't see happening in our for profit system, so the capacity is not likely to be very flexible at expanding quickly enough.
  - karlkatzke 7y ago
    The US does have the ability to set up large quarantine hospitals on the fly, but they are in tents. These are the same type of military tents that were/are used for migrant internment on the border. I'm struggling to find a name for the group that I participated in an exercise with, but in my volunteer Search and Rescue days I was a 'victim' for a practice exercise of deploying a tent hospital for a combined human and animal pandemic. The ability to set up these hospitals is there, what isn't there is the skilled nursing staff for ICU patients, or ventilators for patients who needed them. I'm really not sure how China handled that portion of caring for those that fell ill.
    - AstralStorm 7y ago
      The problem being required large number of ventilators which even US will have problems delivering in such case. Only China has the hardware on hand.
Spare_account 7y ago
>The Bay area currently has 204 confirmed cases (as of 3/15). Multiplying that by either 10x or 50x (Harvard's estimated ratio of confirmed:unconfirmed cases) to get the actual number of confirmed cases today: 2,040 - 10,200 actual current cases in the Bay area. >... >80% of those will be "mild" which means "possibly as bad as having pneumonia but not needing a hostpital stay." 14% will require a hospital bed. I have an issue with extrapolating the number of serious cases this way. I assume the 80% figure for non-serious cases is based on the number of formally tested patients. Therefore the 80% figure doesn't include all the community-spread undiagnosed cases that must also be non-serious (or they would have been in hospital). The percentage of serious cases amongst the true number of cases is presumably much smaller than 20%?
- rrss 7y ago
  The 80% figure comes from a study of 72k cases in Hubei. It may have the problem you suggest, but China was/is testing much more aggressively than the United States. http://weekly.chinacdc.cn/en/article/id/e53946e2-c6c4-41e9-9a9b-fea8db1a8f51 http://weekly.chinacdc.cn/en/article/id/e53946e2-c6c4-41e9-9...
- asdfasgasdgasdg 7y ago
  There is also the issue of assuming that social distancing only reduces the number of cases by 90%. Social distancing affects the exponent. Depending on how aggressive it is it could reduce the height of the peak by a lot more than 90%. I also have no idea the basis for the 10-50x assumption r.e. confirmed/unconfirmed cases.
  - nwallin 7y ago
    No, social distancing affects the base, not the exponent.
- YZF 7y ago
  It's the nature of all these figures that you can calculate them relatively easily for known cases but are somewhat more illusive for all infections. That said I think you can put an upper bound on the number of undiagnosed cases out there by looking at deaths and hospitalizations (in places where that data is reasonably accurate). There's at least a few ways of getting ballpark figures: - https://cmmid.github.io/topics/covid19/severity/diamond_cruise_cfr_estimates.html https://cmmid.github.io/topics/covid19/severity/diamond_crui... (EDIT: this gives some estimates by age correcting the data from the diamond princess cruise which I think is one of the best data sets we have since most passengers got quarantined/tested/monitored). - looking at data from countries with reasonably strong testing regimes and responses. E.g. Israel or Canada are two I'm following. In Canada 12% of the cases so far required hospitalization (EDIT: https://torontosun.com/news/provincial/ontario-sees-spike-of-39-new-cases-of-coronavirus https://torontosun.com/news/provincial/ontario-sees-spike-of... ) - Surveillance test data for countries that do that. 20% does sound on the high side from what I've seen read. My mental ballpark is 5%-10%. I'm sure there are local variations (smokers, air pollution, age distribution, general health...) EDIT: The US has 62 reported deaths. Just estimating based on 0.5% ifr that gives 12,400 cases. Then you have to back-adjust this. Let's say by 2 weeks? That's maybe on the order of 100k+. Obviously this will have a very large error bar but it gives us some intuition. Feel free to poke holes at my math ;)
mokus 7y ago
Why start today? There were 5 cases confirmed in the US as of Jan 25, 50 days ago, at least some of which appeared to be community transmission. Applying this math for the US as a whole with the 10x initial factor gives 5 * 10 * 2^(50/3) ~= 5.2 million cases TODAY. If we don’t believe that number (or do we? Hell, I have no idea at this point), why do we believe the same math with today as initial conditions?
- jessriedel 7y ago
  I don't think the OP math is sensible. (At the absolute most basic, if you're trying to be "conservative" about modeling the effects of social distancing on exponential growth, you should cut the growth rate rather than cutting the absolute number by some percentage.) However, that said: it makes more sense to model growth as exponential once you've documented community transmission as the primary driver. When the US had 5 cases, they were all imported from China and basically contained.
  - mokus 7y ago
    I had recently seen a claim that among the first 5 US cases, some had been apparent community spread, but searching back now I can’t find any substantiation for that claim. So yeah, looks like my assumptions here were wrong. Sorry. Using the same math from feb 26 instead, which is the date I saw a CDC article published about first suspected community transmission, the figures are instead 15 * 10 * 2^(18/3) = 9600, which is more plausible. In any case, the calculations are extremely sensitive to the growth rate which, as you say, is also a thing we can control by modulating behavior. The extent to which we will actually do so is debatable, of course. As far as I’m aware I’m still expected to show up on site for work tomorrow.
    - Izkata 7y ago
      Using the "Total Cases" graph (logarithmic view) here [0], it looks like Mar 1 is when the US's reported cases became exponential, and is probably a better baseline. [0] https://www.worldometers.info/coronavirus/country/us/ https://www.worldometers.info/coronavirus/country/us/
dnautics 7y ago
The exponential growth-to-the-whole-population makes a major assumption: everyone is susceptible. Given the virulence of COVID-19, and the surprising lack of total population penetration in Hubei (now that we know just how late the quarantining efforts were given the apparent latency between carrier status and symptoms) one wonders if there isn't, say, a genetic factor which makes one more susceptible than others, for starters, and if COVID-19 simply has/will burn itself out in many places.
- hef19898 7y ago
  Plus, everyone who got at the beginning, and went through it, will be immune for a certain time. So these interactions have to be taken into account as well. Plus everyone being immune from the beginning. So no, no exponential function. But as the math guy said, "indistinguishable from an exponential in the beginning". Edit: The math guy being 3Blue1Brown in his video linked elsewhere in this thread.
- codingslave 7y ago
  I personally believe that there is a genetic susceptibility to the virus, but unfortunately, any kind of academic study regarding this is mostly suppressed/shamed. But if you go back an read studies of SARS, many will straight out say that specific genetic pools within China were more susceptible than others.
whatsmyusername 7y ago
"Some people cannot, or will not, practice social distancing for a variety of reasons and will continue to spread the virus to many people. So everyone else must start today." I.E. Trumpettes who believe this is all just a conspiracy against the president.
kragen 7y ago
The biggest hole is that the doubling time is usually closer to 7 days (10% growth in cases per day) than to 3 days (41% growth in cases per day). We do see 41% daily growth in reported cases in times where the testing is catching up to a much larger population of undetected cases, but overall 7 days is a more reasonable doubling time. On that assumption, 2040 × 2⁴·⁴ = 43068 actual cases in the Bay Area in a month. When you're modeling exponential growth, most of your possible errors are just an additive time shift, a small one if the growth is rapid. For example, if the actual current cases are 4080, a 100% error in the estimate above of 2040, that just moves the time to reach those 43068 cases from 31 days away to 24 days away. But an error in the exponential growth rate is a multiplicative time distortion, leading to an exponentially large error at any given point in the future.
- svara 7y ago
  Could you expand on your observation regarding the true growth rate? I don't think that's accurate. Italy's outbreak is entering its fourth week, they have a very constant daily factor of ~1.33. Most countries are on the same trajectory. The only ones to have slowed down are China, South Korea and possibly Iran, though I really doubt the Iran numbers. You can see that here, all the others are linear in a log plot: https://studylib.net/coronavirus-growth https://studylib.net/coronavirus-growth
  - rrss 7y ago
    The distinction 'kragen is making is between actual cases (total number of people with the virus) versus cases confirmed via testing. The daily growth of ~33% probably reflects increase in testing capacity more than increase in actual cases. Here are some studies supporting the doubling time estimate of 6-8 days: https://wwwnc.cdc.gov/eid/article/26/5/20-0146_article https://wwwnc.cdc.gov/eid/article/26/5/20-0146_article https://www.nejm.org/doi/full/10.1056/NEJMoa2001316 https://www.nejm.org/doi/full/10.1056/NEJMoa2001316 https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)30260-9/fulltext https://www.thelancet.com/journals/lancet/article/PIIS0140-6...
  - kragen 7y ago
    Even Italy hasn't been over 23% in over a week; over the last week they've averaged 19% growth per day, far from the constant 33% you allege: >>> (24747/7375.0)**(1/7.0) 1.188799592827802 That's a 4-day doubling time, which is how they've outdistanced every other country in the world. Presumably if the Italians would put on some masks and kiss each other less† they'd get down to the same kind of rate as China, Korea, and Iran. More broadly, we're currently at 167676 confirmed cases worldwide; the first day we have numbers for is January 16th, when there were 45 cases. It's been 59 days since then (31-16+29+15) giving a 15% daily growth rate >>> (167676/45.0)**(1/59.0) 1.1495551283620273 but some of that 15% is the discovery of several thousand existing but previously undetected cases over the next several weeks. So the overall growth rate is a little lower than that 15%. (If the Italians were to keep spreading the disease at this rate, by mid-May they'd have more cases than the entire rest of the world; unfortunately for the plausibility of this prediction, their case count would have to be over half a billion people at that point, requiring vast influxes of guest patients from the rest of the world to meet such a quota.) I did projections at the beginning of February based on a 3.5-day doubling time (22% daily growth) which was what we seemed to be seeing at the time. They said it would infect the majority of the world's population in February. That didn't happen. † Hey, I'm guilty of this myself; the last time I kissed somebody I'd just met that day was, like, Tuesday. Here in Argentina we can expect rapid contagion.
earthtourist 7y ago
Another very rough way to estimate this: If COVID-19 requires 10x more hospitalizations than influenza, and peak influenza maxes out hospital resources, then we need at least 10x more capacity. Because there are so many variables, no one knows yet what the numbers will work out to be. The only safe thing to do is to expand capacity as much as possible by taking extreme measures.
- chinathrow 7y ago
  This is the right point of view. If you start building hospitals now, you might have a chance when the wave hits. By now, such a post will not get some downvotes as reality trickled in. Have a look at the state of capacity in Italy: it's closed to maxed out with lots of improvised wards.
  - masklinn 7y ago
    > This is the right point of view. If you start building hospitals now, you might have a chance when the wave hits. Probably not unless you have popup / prefab hospitals. > Have a look at the state of capacity in Italy: it's closed to maxed out with lots of improvised wards. Italy is not "close to maxed out", it's way overcapacity. It might seem like it's at capacity if you count the total number of ICU beds in the entire country, but most of the cases for now are in the north, so the actual radio is way higher. Lombardia was at ~200% capacity circa wednesday.
    - chinathrow 7y ago
      > Lombardia was at ~200% capacity circa wednesday. Source? Mine is: https://www.giornaledibrescia.it/italia-ed-estero/coronavirus-gallera-siamo-vicini-a-un-punto-di-non-ritorno-1.3467066 https://www.giornaledibrescia.it/italia-ed-estero/coronaviru... Google Translate: "«We have very few free places in intensive care, now we are in the order of 15 or 20 available. Every day we get someone new, tomorrow 3 more arrive and San Raffaele is creating an area with 14 seats which will be ready, however, in a week. Today we recover them by closing the operating rooms, where there are respirators that can also be used to support the breath »."
dchichkov 7y ago
The dynamic in the Bay Area might be different from that in Europe, because of no public transportation.
- pengaru 7y ago
  I agree in general for US vs. EU, here far more travel is done via automobiles. But the Bay Area does have MUNI and BART, it's not a no public transportation situation.
lurquer 7y ago
Back of the envelope math... 30,000 cases a few weeks ago in China... use the articles math... (calculating) ... everyone from here to Alpha Centauri is infected and in ICU today. That may be correct... this could all be a fever-induced hallucination. It's more likely, though, that the articles assumptions are idiotic.
pascalxus 7y ago
Take a look at this dashboard, specifically the bottom right section. The last 3 days, it seems that the number of reported cases is going down quite steeply. https://www.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6 https://www.arcgis.com/apps/opsdashboard/index.html#/bda7594... now, I know, today's number's aren't fully in yet, and there are day to day fluctuations. but, if you trust the numbers for the last 3 days, it looks like the number of cases is not increasing exponentially. I know the actual case number is much higher, but, what matters is the relative percent increase or decrease from day to day, and it does not seem to be increasing in the last 3 days. am i wrong? Starting a few days ago, almost no one is going out, except to do their big shopping. so how can the virus still spread?
- twoodfin 7y ago
  Starting a few days ago, almost no one is going out, except to do their big shopping. so how can the virus still spread? I think this is a very localized view of behavior. There are many large regions, pockets, demographic slices of the country where life is going on roughly as it was a few weeks ago.
  - craftinator 7y ago
    > I think this is a very localized view of behavior. There are many large regions, pockets, demographic slices of the country where life is going on roughly as it was a few weeks ago. Check out the Nashville music and party scene... It's hopping right now. I think #NashvilleUndefeated is their slogan. In Portland OR, I've observed a slight decrease in activity, but only by 5-10% from what I normally see.
- kens 7y ago
  The Johns Hopkins data (used in your link) has had a lot of problems the last couple of days. They've been doing various refactorings such as switching from per-county to per-state data, and it's causing a lot of issues. (It's a bit alarming that the number of cases is so high that even the people just tracking the data are getting overwhelmed.) I've been following their data for a while and I admire their work, but I've stopped believing their numbers without double-checking. (Yes, I've filed bugs.) In addition, the last day on the graph has always made it look like cases are tapering off because it's partial data. https://github.com/CSSEGISandData/COVID-19/issues/650 https://github.com/CSSEGISandData/COVID-19/issues/650
xhkkffbf 7y ago
The key thing is to avoid counting cases. Those are affected by the number of test kits and the test kits are just now becoming available. Of course the "cases" will soar. It's more important to look at ICU bodies and deaths. Those aren't as affected by supply issues.
eanzenberg 7y ago
The disparity of death rates among countries has more to do with infrastructure than the virus. Germany and Switzerland are proving this is just a flu, albeit a pretty bad one (0.1-0.5% death rate). More testing will prove this out by increasing the denominator by 10x.
- usaar333 7y ago
  No one is getting out with a death rate that low. SK is nearing 1%. The numbers are only so low in Germany/Switzerland because its a) growing fast and b) they are testing aggressively. More precisely (and morbidly), the death rate is low because not enough time has passed yet.
  - eanzenberg 7y ago
    You proved my point. Aggressive testing will plump up the denominator. Deaths cannot escape so the numerator is accurate. In Germany and Switzerland if all the serious cases are deaths then the death rate is 0.1-0.5%.
    - rrss 7y ago
      People do not die instantaneously when they are infected. There is potentially a multi-week lag between people showing up in the confirmed cases number and people showing up in the deaths number. Two weeks ago, Germany had ~100 cases. Today, Germany has 11 deaths. Germany has a total of 57 cases with outcomes (46 of 57 recovered). South Korea has ~900 cases with outcomes (~75 dead). China has ~70k cases with outcomes (~3k dead). Let's wait a few weeks before reaching conclusions about the mortality rate in Germany and using that as evidence to prove covid-19 is just a mild flu. Deaths / cases with outcomes is an overestimate (19% for Germany). Deaths / total cases is an underestimate (0.2% for Germany). Somewhere in between is the true mortality rate.
    - baq 7y ago
      CFR isn't a number, it's a function. it has a discontinuity at the point where hospitalized case count becomes greater than available hospital bed count.
mcguire 7y ago
"The Bay area currently has 204 confirmed cases (as of 3/15). Multiplying that by either 10x or 50x (Harvard's estimated ratio of confirmed:unconfirmed cases) to get the actual number of confirmed cases today: 2,040 - 10,200 actual current cases in the Bay area." Er, ah, uh, .... Multiply 204 cases by an estimated ratio of confirmed to unconfirmed cases of 10 to 50 gives 2040 - 10,200 estimated current cases in the Bay Area. "Just because if I multiply by a 50x ratio, it returns a number larger than the 7.8MM total residents in the Bay area." As you just discovered, a raw exponential increase cannot continue for very long, if only because infected individuals begin to have difficulty finding uninfected individuals to infect. "80% of those will be "mild" which means "possibly as bad as having pneumonia but not needing a hostpital stay." 14% will require a hospital bed." You may want to knock down the severity numbers a bit, since it seems likely that severe cases will be reported and confirmed in larger numbers than less severe cases. "Potentially, even assuming aggressive social distancing, the Bay area needs 11x more beds than it has available in the next 30 days." You probably should do this calculation in terms of bed-days: how long a given case occupies a bed on average before release/death. Finally, as far as I know, the severity for old and infirm cases is much, much higher than the severity for those of you who are young and healthy. You may want to modify your model for local demographics.
tunesmith 7y ago
I have a question about test positivity rate. UW Virology has been at about 8%, and that's them soliciting tests from all over the nation over the last week during a time when testing was very constrained. Even then, UW only reached capacity yesterday, they had capacity to spare until then. Divide worldometers "cases per day" stat by the the CDC website testing data as of a few days ago (the most recent day they declare their numbers complete), and you get around 8%. Finally, the Friday press conference mentioned the LabQuest LabCorp tests coming online and adding significant capacity, and that their test positivity rate as of then was about 2%, and this is all during a time when testing is limited, and presumably, only the most urgent or probable cases are being sent off for testing. I don't have a lot of exponential-math insight, but those rates seem low if the virus has spread like crazy already. How does that reconcile with the math in this article?
anewguy9000 7y ago
maybe im getting old, but this reads like very well-written marketing for drodio.com. the long-winded introduction, use of caps and sense of urgency it piggybacks on top of and the obvious straw man. i mean if you don't know how to do the math, then following the steps as presented in the article (ie. "add this, then times it by that.." etc) you're not actually reaching your own conclusions; that's just hand waving credence to the conclusion that the reader cannot fairly evaluate. EDIT: writing my originally short comment i noticed many other subtle cues as well. for example: the author's prediction of the article going viral (establishing trust because they've been "right" before) the open invitation to criticize the article (suggesting that what you're reading is essentially the result of consensus) the claim that it's being written despite any criticism it might receive because the subject is so important (moral authority) all of these points are presupposed by the author, and not actually derived from the work. the more i think about it the more subtle and manipulative it appears. i hope im wrong, poke holes in it! but given the subject we're discussing it's really rather unsettling. we are indeed in a crisis, drodio be damned.

58 points by drodio 7y ago

"Multiply the number above by 1,024 (assumes a doubling of cases every 3 days) if you assume no social distancing measure are put in place: 2.1MM on the low end, mulitplying by a 10x ratio. " Poke -- lots of measures are already being put into place (Stanford is effectively shut down, the big tech companies are making everyone work from home) etc. Edit oh you have this right after: "Or, multiply it by less if you want to take into account various amounts of social distancing we're all doing. I'll cut that number above down by a huge amount – 90% – on the assumption that we all learn to stay home and self-isolate immediately, just to be super aggressive on my assumptions about how humanity will rise to the occasion" Still, kinda weird to start with assumption of no measures when there clearly are some already.

freepor 7y ago
Yep - the Bay Area actually has a great chance at curbing this because a larger fraction of workers than anywhere else can effectively work from home.
cperciva 7y ago
The 90% might be conservative. If the rate of spread can be reduced by 50%, it will reduce the number of cases after 30 days by 96%.
- dmurray 7y ago
  And if it can be reduced by 60%, we will see exponential decay instead of exponential growth. (assuming R=2.4 is the average number of people each victim infects, which is a number I've seen used a lot). It seems plausible that social distancing can reduce human contact for the average person by 50%, and for people with some flu symptoms by 80%. All this is to agree, the growth rate is by far the biggest factor in getting an estimate of peak impact.
- danenania 7y ago
  Does anyone have insight into how moderate/voluntary vs. strict social distancing impacts the rate of spread? Anecdotally, the streets in the SF Richmond District feel a lot emptier than usual when I go out for walks/runs (pretty much the only reason I'm going out anymore). Seems like it could be up to a 50% reduction. That should already be helping, but I wonder if spreading might follow a power law pattern where "super-spreaders" account for a vastly disproportionate share of transmissions. If that's the case, it might require a strict lockdown to meaningfully reduce the exponent?
lkbm 7y ago
> "Or, multiply it by less if you want to take into account various amounts of social distancing we're all doing. I'll cut that number above down by a huge amount – 90% – on the assumption that we all learn to stay home and self-isolate immediately, just to be super aggressive on my assumptions about how humanity will rise to the occasion" Dropping 90% is not a great way to calculate this. Look at the math for 61 days out (from March 8): https://youtu.be/Kas0tIxDvrg?t=465 https://youtu.be/Kas0tIxDvrg?t=465 I don't think our social distancing and hand washing will be near enough to prevent millions of deaths, but it's important to recognize that a small change in the growth rate does make a huge difference. Estimating how much we can affect the growth rate is hard, but I think models should be based on a iffy guess on that value rather than an iffy guess on the resulting count. (Expert models certainly are.)
sneak 7y ago
All the bars and restaurants are still open, and people are still allowed to visit friends and family. Most nCoV transmission is in small groups with close contact, not stadiums. Closing offices and schools is a good first step, but as long as bars and restaurants are still open and food delivery services are carrying it all over town, it’s a drop in a bucket.
- edmundsauto 7y ago
  California just announced all bars are to close, and restaurants limited to half normal capacity.

creato 7y ago

> Multiply the number above by 1,024 (assumes a doubling of cases every 3 days) if you assume no social distancing measure are put in place: 2.1MM on the low end, mulitplying by a 10x ratio. (Just because if I multiply by a 50x ratio, it returns a number larger than the 7.8MM total residents in the Bay area.) This is why the spread of a virus like this is a logistic curve, not an exponential. An exponential is a good model at first, but extrapolating too far doesn't work like this.

ignoramous 7y ago
> This is why the spread of a virus like this is a logistic curve, not an exponential. More on this by 3Blue1Brown: https://www.youtube-nocookie.com/embed/Kas0tIxDvrg https://www.youtube-nocookie.com/embed/Kas0tIxDvrg
- hef19898 7y ago
  Somewhere after, or around, thee 5 minute mark: "true exponentials are basically non-existent in real life"
gbrown 7y ago
The reality is even more complicated - sure, a logistic curve is a reasonable fit if we assume that the data is accurate and the population homogeneous and well mixed, but in practice things get more complicated quickly. There's a huge network of potential contacts, with a large degree of heterogeneity and important subcomponents at multiple geographic scales. In addition, the network is dynamic, not static, so that both highly granular and population scale phenomena can change the contact distribution. Two important questions are: 1. What can we actually measure with confidence to relate to a model of interest 2. At what level of sophistication is it feasible to actually model things Neither question is particularly straightforward in the face of ongoing epidemics.
- fsh 7y ago
  The data from China almost perfectly follows a logistic curve. Unfortunately, extrapolating such a smooth function is pretty much impossible before it starts saturating anyway.

trimbo 7y ago

> to get the actual number of confirmed cases today I think for this part you meant "actual number of cases"? Since the confirmed number was 1/10th of that.

olivierduval 7y ago

Something is missing: the average duration of covid patient in hospital. Hopefully, it is less than 30 days so some patient will go to hospital, stay a few days (then die or go home) and then leave their room in hospital... I don't think that it was accounted for in the calculation for number of beds in hospital

coldcode 7y ago
If you wind up in the ICU, it may be 2-4 weeks before you can be released, regular hospital beds don't count. You also have to assume how many assisted breathing systems (respirators/ventilators etc) are available. You can't simply assume the number of beds are available either since people may already have some other serious issue and be in one. In China they constructed massive hospitals out of large spaces on the fly, something I can't see happening in our for profit system, so the capacity is not likely to be very flexible at expanding quickly enough.
- karlkatzke 7y ago
  The US does have the ability to set up large quarantine hospitals on the fly, but they are in tents. These are the same type of military tents that were/are used for migrant internment on the border. I'm struggling to find a name for the group that I participated in an exercise with, but in my volunteer Search and Rescue days I was a 'victim' for a practice exercise of deploying a tent hospital for a combined human and animal pandemic. The ability to set up these hospitals is there, what isn't there is the skilled nursing staff for ICU patients, or ventilators for patients who needed them. I'm really not sure how China handled that portion of caring for those that fell ill.
  - AstralStorm 7y ago
    The problem being required large number of ventilators which even US will have problems delivering in such case. Only China has the hardware on hand.

Spare_account 7y ago

>The Bay area currently has 204 confirmed cases (as of 3/15). Multiplying that by either 10x or 50x (Harvard's estimated ratio of confirmed:unconfirmed cases) to get the actual number of confirmed cases today: 2,040 - 10,200 actual current cases in the Bay area. >... >80% of those will be "mild" which means "possibly as bad as having pneumonia but not needing a hostpital stay." 14% will require a hospital bed. I have an issue with extrapolating the number of serious cases this way. I assume the 80% figure for non-serious cases is based on the number of formally tested patients. Therefore the 80% figure doesn't include all the community-spread undiagnosed cases that must also be non-serious (or they would have been in hospital). The percentage of serious cases amongst the true number of cases is presumably much smaller than 20%?

rrss 7y ago
The 80% figure comes from a study of 72k cases in Hubei. It may have the problem you suggest, but China was/is testing much more aggressively than the United States. http://weekly.chinacdc.cn/en/article/id/e53946e2-c6c4-41e9-9a9b-fea8db1a8f51 http://weekly.chinacdc.cn/en/article/id/e53946e2-c6c4-41e9-9...
asdfasgasdgasdg 7y ago
There is also the issue of assuming that social distancing only reduces the number of cases by 90%. Social distancing affects the exponent. Depending on how aggressive it is it could reduce the height of the peak by a lot more than 90%. I also have no idea the basis for the 10-50x assumption r.e. confirmed/unconfirmed cases.
- nwallin 7y ago
  No, social distancing affects the base, not the exponent.
YZF 7y ago
It's the nature of all these figures that you can calculate them relatively easily for known cases but are somewhat more illusive for all infections. That said I think you can put an upper bound on the number of undiagnosed cases out there by looking at deaths and hospitalizations (in places where that data is reasonably accurate). There's at least a few ways of getting ballpark figures: - https://cmmid.github.io/topics/covid19/severity/diamond_cruise_cfr_estimates.html https://cmmid.github.io/topics/covid19/severity/diamond_crui... (EDIT: this gives some estimates by age correcting the data from the diamond princess cruise which I think is one of the best data sets we have since most passengers got quarantined/tested/monitored). - looking at data from countries with reasonably strong testing regimes and responses. E.g. Israel or Canada are two I'm following. In Canada 12% of the cases so far required hospitalization (EDIT: https://torontosun.com/news/provincial/ontario-sees-spike-of-39-new-cases-of-coronavirus https://torontosun.com/news/provincial/ontario-sees-spike-of... ) - Surveillance test data for countries that do that. 20% does sound on the high side from what I've seen read. My mental ballpark is 5%-10%. I'm sure there are local variations (smokers, air pollution, age distribution, general health...) EDIT: The US has 62 reported deaths. Just estimating based on 0.5% ifr that gives 12,400 cases. Then you have to back-adjust this. Let's say by 2 weeks? That's maybe on the order of 100k+. Obviously this will have a very large error bar but it gives us some intuition. Feel free to poke holes at my math ;)

mokus 7y ago

Why start today? There were 5 cases confirmed in the US as of Jan 25, 50 days ago, at least some of which appeared to be community transmission. Applying this math for the US as a whole with the 10x initial factor gives 5 * 10 * 2^(50/3) ~= 5.2 million cases TODAY. If we don’t believe that number (or do we? Hell, I have no idea at this point), why do we believe the same math with today as initial conditions?

jessriedel 7y ago
I don't think the OP math is sensible. (At the absolute most basic, if you're trying to be "conservative" about modeling the effects of social distancing on exponential growth, you should cut the growth rate rather than cutting the absolute number by some percentage.) However, that said: it makes more sense to model growth as exponential once you've documented community transmission as the primary driver. When the US had 5 cases, they were all imported from China and basically contained.
- mokus 7y ago
  I had recently seen a claim that among the first 5 US cases, some had been apparent community spread, but searching back now I can’t find any substantiation for that claim. So yeah, looks like my assumptions here were wrong. Sorry. Using the same math from feb 26 instead, which is the date I saw a CDC article published about first suspected community transmission, the figures are instead 15 * 10 * 2^(18/3) = 9600, which is more plausible. In any case, the calculations are extremely sensitive to the growth rate which, as you say, is also a thing we can control by modulating behavior. The extent to which we will actually do so is debatable, of course. As far as I’m aware I’m still expected to show up on site for work tomorrow.
  - Izkata 7y ago
    Using the "Total Cases" graph (logarithmic view) here [0], it looks like Mar 1 is when the US's reported cases became exponential, and is probably a better baseline. [0] https://www.worldometers.info/coronavirus/country/us/ https://www.worldometers.info/coronavirus/country/us/

dnautics 7y ago

The exponential growth-to-the-whole-population makes a major assumption: everyone is susceptible. Given the virulence of COVID-19, and the surprising lack of total population penetration in Hubei (now that we know just how late the quarantining efforts were given the apparent latency between carrier status and symptoms) one wonders if there isn't, say, a genetic factor which makes one more susceptible than others, for starters, and if COVID-19 simply has/will burn itself out in many places.

hef19898 7y ago
Plus, everyone who got at the beginning, and went through it, will be immune for a certain time. So these interactions have to be taken into account as well. Plus everyone being immune from the beginning. So no, no exponential function. But as the math guy said, "indistinguishable from an exponential in the beginning". Edit: The math guy being 3Blue1Brown in his video linked elsewhere in this thread.
codingslave 7y ago
I personally believe that there is a genetic susceptibility to the virus, but unfortunately, any kind of academic study regarding this is mostly suppressed/shamed. But if you go back an read studies of SARS, many will straight out say that specific genetic pools within China were more susceptible than others.

whatsmyusername 7y ago

"Some people cannot, or will not, practice social distancing for a variety of reasons and will continue to spread the virus to many people. So everyone else must start today." I.E. Trumpettes who believe this is all just a conspiracy against the president.

kragen 7y ago

The biggest hole is that the doubling time is usually closer to 7 days (10% growth in cases per day) than to 3 days (41% growth in cases per day). We do see 41% daily growth in reported cases in times where the testing is catching up to a much larger population of undetected cases, but overall 7 days is a more reasonable doubling time. On that assumption, 2040 × 2⁴·⁴ = 43068 actual cases in the Bay Area in a month. When you're modeling exponential growth, most of your possible errors are just an additive time shift, a small one if the growth is rapid. For example, if the actual current cases are 4080, a 100% error in the estimate above of 2040, that just moves the time to reach those 43068 cases from 31 days away to 24 days away. But an error in the exponential growth rate is a multiplicative time distortion, leading to an exponentially large error at any given point in the future.

svara 7y ago
Could you expand on your observation regarding the true growth rate? I don't think that's accurate. Italy's outbreak is entering its fourth week, they have a very constant daily factor of ~1.33. Most countries are on the same trajectory. The only ones to have slowed down are China, South Korea and possibly Iran, though I really doubt the Iran numbers. You can see that here, all the others are linear in a log plot: https://studylib.net/coronavirus-growth https://studylib.net/coronavirus-growth
- rrss 7y ago
  The distinction 'kragen is making is between actual cases (total number of people with the virus) versus cases confirmed via testing. The daily growth of ~33% probably reflects increase in testing capacity more than increase in actual cases. Here are some studies supporting the doubling time estimate of 6-8 days: https://wwwnc.cdc.gov/eid/article/26/5/20-0146_article https://wwwnc.cdc.gov/eid/article/26/5/20-0146_article https://www.nejm.org/doi/full/10.1056/NEJMoa2001316 https://www.nejm.org/doi/full/10.1056/NEJMoa2001316 https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)30260-9/fulltext https://www.thelancet.com/journals/lancet/article/PIIS0140-6...
- kragen 7y ago
  Even Italy hasn't been over 23% in over a week; over the last week they've averaged 19% growth per day, far from the constant 33% you allege: >>> (24747/7375.0)**(1/7.0) 1.188799592827802 That's a 4-day doubling time, which is how they've outdistanced every other country in the world. Presumably if the Italians would put on some masks and kiss each other less† they'd get down to the same kind of rate as China, Korea, and Iran. More broadly, we're currently at 167676 confirmed cases worldwide; the first day we have numbers for is January 16th, when there were 45 cases. It's been 59 days since then (31-16+29+15) giving a 15% daily growth rate >>> (167676/45.0)**(1/59.0) 1.1495551283620273 but some of that 15% is the discovery of several thousand existing but previously undetected cases over the next several weeks. So the overall growth rate is a little lower than that 15%. (If the Italians were to keep spreading the disease at this rate, by mid-May they'd have more cases than the entire rest of the world; unfortunately for the plausibility of this prediction, their case count would have to be over half a billion people at that point, requiring vast influxes of guest patients from the rest of the world to meet such a quota.) I did projections at the beginning of February based on a 3.5-day doubling time (22% daily growth) which was what we seemed to be seeing at the time. They said it would infect the majority of the world's population in February. That didn't happen. † Hey, I'm guilty of this myself; the last time I kissed somebody I'd just met that day was, like, Tuesday. Here in Argentina we can expect rapid contagion.

earthtourist 7y ago

Another very rough way to estimate this: If COVID-19 requires 10x more hospitalizations than influenza, and peak influenza maxes out hospital resources, then we need at least 10x more capacity. Because there are so many variables, no one knows yet what the numbers will work out to be. The only safe thing to do is to expand capacity as much as possible by taking extreme measures.

chinathrow 7y ago
This is the right point of view. If you start building hospitals now, you might have a chance when the wave hits. By now, such a post will not get some downvotes as reality trickled in. Have a look at the state of capacity in Italy: it's closed to maxed out with lots of improvised wards.
- masklinn 7y ago
  > This is the right point of view. If you start building hospitals now, you might have a chance when the wave hits. Probably not unless you have popup / prefab hospitals. > Have a look at the state of capacity in Italy: it's closed to maxed out with lots of improvised wards. Italy is not "close to maxed out", it's way overcapacity. It might seem like it's at capacity if you count the total number of ICU beds in the entire country, but most of the cases for now are in the north, so the actual radio is way higher. Lombardia was at ~200% capacity circa wednesday.
  - chinathrow 7y ago
    > Lombardia was at ~200% capacity circa wednesday. Source? Mine is: https://www.giornaledibrescia.it/italia-ed-estero/coronavirus-gallera-siamo-vicini-a-un-punto-di-non-ritorno-1.3467066 https://www.giornaledibrescia.it/italia-ed-estero/coronaviru... Google Translate: "«We have very few free places in intensive care, now we are in the order of 15 or 20 available. Every day we get someone new, tomorrow 3 more arrive and San Raffaele is creating an area with 14 seats which will be ready, however, in a week. Today we recover them by closing the operating rooms, where there are respirators that can also be used to support the breath »."

dchichkov 7y ago

The dynamic in the Bay Area might be different from that in Europe, because of no public transportation.

pengaru 7y ago
I agree in general for US vs. EU, here far more travel is done via automobiles. But the Bay Area does have MUNI and BART, it's not a no public transportation situation.

lurquer 7y ago

Back of the envelope math... 30,000 cases a few weeks ago in China... use the articles math... (calculating) ... everyone from here to Alpha Centauri is infected and in ICU today. That may be correct... this could all be a fever-induced hallucination. It's more likely, though, that the articles assumptions are idiotic.

pascalxus 7y ago

Take a look at this dashboard, specifically the bottom right section. The last 3 days, it seems that the number of reported cases is going down quite steeply. https://www.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6 https://www.arcgis.com/apps/opsdashboard/index.html#/bda7594... now, I know, today's number's aren't fully in yet, and there are day to day fluctuations. but, if you trust the numbers for the last 3 days, it looks like the number of cases is not increasing exponentially. I know the actual case number is much higher, but, what matters is the relative percent increase or decrease from day to day, and it does not seem to be increasing in the last 3 days. am i wrong? Starting a few days ago, almost no one is going out, except to do their big shopping. so how can the virus still spread?

twoodfin 7y ago
Starting a few days ago, almost no one is going out, except to do their big shopping. so how can the virus still spread? I think this is a very localized view of behavior. There are many large regions, pockets, demographic slices of the country where life is going on roughly as it was a few weeks ago.
- craftinator 7y ago
  > I think this is a very localized view of behavior. There are many large regions, pockets, demographic slices of the country where life is going on roughly as it was a few weeks ago. Check out the Nashville music and party scene... It's hopping right now. I think #NashvilleUndefeated is their slogan. In Portland OR, I've observed a slight decrease in activity, but only by 5-10% from what I normally see.
kens 7y ago
The Johns Hopkins data (used in your link) has had a lot of problems the last couple of days. They've been doing various refactorings such as switching from per-county to per-state data, and it's causing a lot of issues. (It's a bit alarming that the number of cases is so high that even the people just tracking the data are getting overwhelmed.) I've been following their data for a while and I admire their work, but I've stopped believing their numbers without double-checking. (Yes, I've filed bugs.) In addition, the last day on the graph has always made it look like cases are tapering off because it's partial data. https://github.com/CSSEGISandData/COVID-19/issues/650 https://github.com/CSSEGISandData/COVID-19/issues/650

xhkkffbf 7y ago

The key thing is to avoid counting cases. Those are affected by the number of test kits and the test kits are just now becoming available. Of course the "cases" will soar. It's more important to look at ICU bodies and deaths. Those aren't as affected by supply issues.

eanzenberg 7y ago

The disparity of death rates among countries has more to do with infrastructure than the virus. Germany and Switzerland are proving this is just a flu, albeit a pretty bad one (0.1-0.5% death rate). More testing will prove this out by increasing the denominator by 10x.

usaar333 7y ago
No one is getting out with a death rate that low. SK is nearing 1%. The numbers are only so low in Germany/Switzerland because its a) growing fast and b) they are testing aggressively. More precisely (and morbidly), the death rate is low because not enough time has passed yet.
- eanzenberg 7y ago
  You proved my point. Aggressive testing will plump up the denominator. Deaths cannot escape so the numerator is accurate. In Germany and Switzerland if all the serious cases are deaths then the death rate is 0.1-0.5%.
  - rrss 7y ago
    People do not die instantaneously when they are infected. There is potentially a multi-week lag between people showing up in the confirmed cases number and people showing up in the deaths number. Two weeks ago, Germany had ~100 cases. Today, Germany has 11 deaths. Germany has a total of 57 cases with outcomes (46 of 57 recovered). South Korea has ~900 cases with outcomes (~75 dead). China has ~70k cases with outcomes (~3k dead). Let's wait a few weeks before reaching conclusions about the mortality rate in Germany and using that as evidence to prove covid-19 is just a mild flu. Deaths / cases with outcomes is an overestimate (19% for Germany). Deaths / total cases is an underestimate (0.2% for Germany). Somewhere in between is the true mortality rate.
  - baq 7y ago
    CFR isn't a number, it's a function. it has a discontinuity at the point where hospitalized case count becomes greater than available hospital bed count.

mcguire 7y ago

"The Bay area currently has 204 confirmed cases (as of 3/15). Multiplying that by either 10x or 50x (Harvard's estimated ratio of confirmed:unconfirmed cases) to get the actual number of confirmed cases today: 2,040 - 10,200 actual current cases in the Bay area." Er, ah, uh, .... Multiply 204 cases by an estimated ratio of confirmed to unconfirmed cases of 10 to 50 gives 2040 - 10,200 estimated current cases in the Bay Area. "Just because if I multiply by a 50x ratio, it returns a number larger than the 7.8MM total residents in the Bay area." As you just discovered, a raw exponential increase cannot continue for very long, if only because infected individuals begin to have difficulty finding uninfected individuals to infect. "80% of those will be "mild" which means "possibly as bad as having pneumonia but not needing a hostpital stay." 14% will require a hospital bed." You may want to knock down the severity numbers a bit, since it seems likely that severe cases will be reported and confirmed in larger numbers than less severe cases. "Potentially, even assuming aggressive social distancing, the Bay area needs 11x more beds than it has available in the next 30 days." You probably should do this calculation in terms of bed-days: how long a given case occupies a bed on average before release/death. Finally, as far as I know, the severity for old and infirm cases is much, much higher than the severity for those of you who are young and healthy. You may want to modify your model for local demographics.

tunesmith 7y ago

I have a question about test positivity rate. UW Virology has been at about 8%, and that's them soliciting tests from all over the nation over the last week during a time when testing was very constrained. Even then, UW only reached capacity yesterday, they had capacity to spare until then. Divide worldometers "cases per day" stat by the the CDC website testing data as of a few days ago (the most recent day they declare their numbers complete), and you get around 8%. Finally, the Friday press conference mentioned the LabQuest LabCorp tests coming online and adding significant capacity, and that their test positivity rate as of then was about 2%, and this is all during a time when testing is limited, and presumably, only the most urgent or probable cases are being sent off for testing. I don't have a lot of exponential-math insight, but those rates seem low if the virus has spread like crazy already. How does that reconcile with the math in this article?

anewguy9000 7y ago

maybe im getting old, but this reads like very well-written marketing for drodio.com. the long-winded introduction, use of caps and sense of urgency it piggybacks on top of and the obvious straw man. i mean if you don't know how to do the math, then following the steps as presented in the article (ie. "add this, then times it by that.." etc) you're not actually reaching your own conclusions; that's just hand waving credence to the conclusion that the reader cannot fairly evaluate. EDIT: writing my originally short comment i noticed many other subtle cues as well. for example: the author's prediction of the article going viral (establishing trust because they've been "right" before) the open invitation to criticize the article (suggesting that what you're reading is essentially the result of consensus) the claim that it's being written despite any criticism it might receive because the subject is so important (moral authority) all of these points are presupposed by the author, and not actually derived from the work. the more i think about it the more subtle and manipulative it appears. i hope im wrong, poke holes in it! but given the subject we're discussing it's really rather unsettling. we are indeed in a crisis, drodio be damned.