
Please poke holes in my Covid-19 math (SF Bay Area) - drodio
https://drodio.com/calculating-covid-19s-possible-impact-in-your-region/
======
kragen
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.

~~~
Jamesbeam
I heavily disagree on the doubling time being closer to 7 days.

If you have a look at Germany who is having a very good overview of the spread
of the pandemic since testing is free, available, and done rapidly (5h
turnaround time ) capacity for 12.000 tests a day ) you get a close to 3 day
case doubling time currently if you look at the official German numbers from
the Robert Koch Institute. And we'll start seeing in a week or two how good
the drastic containment measures they are starting now are impacting the
growth or viral spread.

11.03.2020 1,288.00

12.03.2020 1,567.00

13.03.2020 2,369.00

14.03.2020 3,062.00

15.03.2020 3,795.00

16.03.2020 4,838.00

In a country like the US where the Author makes his calculations the
government frankly has zero clue how many people are infected already because
testing is not free, not available and not rapid ( current turnaround 3 -5
days ) for most citizens. There is a chance that the case doubling time is
worse, or bigger, but if Germany who had a lot better reaction to the viral
threat is having problems reaching a case doubling time of 6+ days and if you
think about that China is at 80.000 cases now but put the most drastic
containment measures in at only 600 confirmed cases there is a huge
probability we are all in for a very wild ride.

That said every day counts because there are promising randomized control
studies going on in China which hopefully give doctors access to a drug they
can actually help people with. Right now all they can do is support your
breathing and pump you full with a cocktail of meds they have no idea if it
will work for the specific patient or not. Everyone who lands into ICU with
Covid-19 is basically a guinea pig for the rest of us healthy people at this
point.

In the end all that matters right now is that we don't know enough about the
illness to treat it effectively, and we are in desperate need of time because
no government was prepared for a pathogen like this that usually is a once in
a century event.

P.S: This is a current snapshot. If the containment measures like in China are
working the case doubling rate rises quite fast. China is at over 21+ days
now. But I think it's important to take this day by day and re-evaluate the
numbers. The "doomsdays predictions" will most likely be wrong and just a
theoretical numbers game.

~~~
kragen
You're probably right that Germany has the most trustworthy numbers. The
numbers you give work out to 30% growth per day, a 2.6-day doubling time;
[https://en.wikipedia.org/wiki/2019%E2%80%9320_coronavirus_pa...](https://en.wikipedia.org/wiki/2019%E2%80%9320_coronavirus_pandemic)
says Germany is at 6245 today, very close to the 6304 you'd predict from your
numbers, although the Robert Koch Institut hasn't updated their page yet.

So, what accounts for the difference? The paucity of international travel (but
then why is the spread so much slower in every other country — Germany is
hardly famous for close physical contact with strangers)? Or is it just that
Germany's comprehensive testing is allowing them to detect almost all the
cases, while everybody else is underestimating by a factor of 10 to 50 or more
— a constantly exponentially growing factor?

It seems unlikely that the pandemic was growing by 30% per day since December;
it would have already infected 450 million people. Can we really impute that
difference entirely to containment measures?

~~~
Jamesbeam
There is a simple explanation why the spread in Germany seems so much higher.
If we look at how the virus spread in Germany we get a very good explanation.

It all started with a small cluster around Munich that showed up around the
end of January ( 27th ) as the first confirmed case in Germany came back from
business travel to China that was contained rather quickly as everyone
involved did a great job isolating and breaking the infection chain and
everyone involved recovered without severe symptoms just like any other flu
for most mid-aged and healthy people. Then for a good month there were no
confirmed cases, so no more drastic containment measures were taken.

After that the Government carelessly allowed Carnival in Germany to happen
thinking they contained the virus and severely underestimating the threat it
could pose. Carnival is one of the biggest celebrations in Germany each year
with millions of people from all over the country coming to see, especially
the Cologne Carnival on the 24th of February. While in general you are not
wrong when you say "Germany is hardly famous for close physical contact with
strangers” the carnival season and Oktoberfest are the two occasions where
Germans do voluntarily have a ton of contact with strangers and party heavily.
The Rhineland is famous for their carnival all over Europe and in some parts
of the world. If you look at pictures of it you’ll see what kind of nightmare
this is if you have a potentially deadly pathogen spreading silently during
the celebration from an epidemiologist point of view.

Three days later a couple from the region were the second and third confirmed
cases that heavily participated in the celebrations while already being sick.
Remember Covid-19 can be contagious up to 14 days before a patient shows
symptoms. On top of that there was no chance to break the infection chain
because the man is still in critical care and couldn't talk to officials and
the woman had no idea where they could have been infected because they had
contact with hundreds, possibly thousands of people over the course of the
celebration days until the husband fell critically ill. So the lack of care
from the Government together with gathering of hundreds of thousands of people
from all over the country in close proximity, kissing, drinking and standing
head to head in a crowd paired with that there were no tests done on people
with covid-19 symptoms for a whole month between the munich and heinsberg
cases is most likely the reason for the explosion in case numbers.

Also remember we are basically looking into the past up to 14 days as people
who need hospitalization now have been infectious for up to that timeframe and
just now start getting very sick. This is an incredible different pathogen to
deal with and easy to underestimate because of this. To fight a pandemic you
need to know the number of infected people, if you know someone is infected
that gives you a fighting chance to break the infection chain if you isolate
all people they have been in contact with. Unfortunately because of the huge
celebrations this was impossible to do and we are where we are now.

"while everybody else is underestimating by a factor of 10 to 50 or more" this
could very well be the case. With the numbers of infected people we see
travelling outside Iran there are estimatons that a large part of the
population is already infected. 7.5 Million people registered on an Iranian
website that allowed for symptom screening. You usually don't register for
such a site if you don't have any symptons that could be related to Covid-19.
Just to show the difference between the real reported numbers and what could
be likely.

If you ask about the containment measures, yes they work incredibly well, but
at the cost of gigantic economic damage and right now I don’t want to be in
the shoes of any leader in any country that basically has to decide between
saving lifes now and that there also needs to be a good future for the
survivors of this crisis afterwards. It’s horrible to think that up to 25% of
a certain population and age could die. But it’s equally frightening to think
that depending how long this takes millions of people and their families could
lose their homes, jobs and potentially starve because we have an almost
complete economic shutdown across all sectors.

------
Spare_account
> _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%?

~~~
asdfasgasdgasdg
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
No, social distancing affects the base, not the exponent.

------
mokus
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
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
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
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/)

------
creato
> 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
> 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
Somewhere after, or around, thee 5 minute mark:

"true exponentials are basically non-existent in real life"

------
andreyk
"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.

~~~
cperciva
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
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.

------
dnautics
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
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.

------
lurquer
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.

------
olivierduval
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
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
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
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.

------
earthtourist
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
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
> 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
> Lombardia was at ~200% capacity circa wednesday.

Source?

Mine is:

[https://www.giornaledibrescia.it/italia-ed-
estero/coronaviru...](https://www.giornaledibrescia.it/italia-ed-
estero/coronavirus-gallera-siamo-vicini-a-un-punto-di-non-ritorno-1.3467066)

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 »."

------
mcguire
" _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.

------
xhkkffbf
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.

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

~~~
pengaru
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.

------
anewguy9000
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.

------
tunesmith
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?

------
pascalxus
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#/bda7594...](https://www.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6)

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?

~~~
kens
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)

~~~
pascalxus
but what about this one:
[https://www.worldometers.info/coronavirus/coronavirus-
cases/...](https://www.worldometers.info/coronavirus/coronavirus-cases/#daily-
cases)

daily new cases (at the very bottom) shows there's very little increase from
the 13th to the 14th.

------
trimbo
> 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.

------
eanzenberg
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.

~~~
antirez
This does not make any sense. North Italy health care is at least as good as
the one in Germany and surely better than the one in Switzerland. Probably
these countries are sampling a lot the general population finding many people
with mild or no symptoms. In Italy because of the size of the problem the ones
getting sampled are now almost solely severe cases.

~~~
mcguire
Take a look at
[https://www.worldometers.info/coronavirus/#countries](https://www.worldometers.info/coronavirus/#countries),
specifically the total deaths and total recovered.

If I take Td / (Td + Tr), I get:

China: 0.05

Italy: 0.44

Iran: 0.14

South Korea: 0.08

Germany: 0.19 (Germany's numbers for both are so low I don't believe this is
useful.)

What's up with that?

~~~
antirez
1\. The population of infected people in Italy for some reason include an
incredible amount of old people. If you see the aggregates VS South Corea,
they have a lot of young people infected. So you get more fatalities per
people infected. (Italy population, together with the one in Japan, is the
oldest of the world, but this yet does not explain the difference, it's like
if the cluster here originated from people at a certain age and also due to
sociality patterns of old people here, or more likely, see "2" below).

2\. Italy, because of the size of the epidemic event we are facing, is
sampling only people that go to the hospital in serious conditions. Other
countries are sampling the more general population, finding a lot of positive
cases with mild symptoms or asymptomatic at all. So there is a selection bias.

3\. It also depends on the way you count people. In Italy we are counting as a
COVID19 victim even people severely ill that once dead are positive for the
virus.

TLDR: you can't compare such numbers.

