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Estimating actual COVID 19 cases (novel corona virus infections) in an area based on deaths

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– The goal of this videois to help us all estimatethe actual new COVID-19
cases per day in your area. And it’s based on
analysis by Thomas Pueyo,he wrote an incredible
blog post on Medium. This is the link and I’ll also include itin the description below. This is the data that he uses
to do some of his analysis. Now, some of you might be thinking,I know the number of
COVID cases in my area,they’re reporting it
on the news every day. But that’s the reported number of casesand that’s based on the peoplethat happened to get the test. There are a lot of people who
might not have symptoms yetor their symptoms are not severe
enough to get the test yet. So the actual cases are likely far largerthan the number of confirmed cases. And we can see that in graphical form. Once again, this is a diagram
put together by Thomas Pueyo. It’s a screenshot from his blog postwhich once again could be found here. This is all his analysis, or
based off of his analysis,but this shows you what was
happening in Hubei Province,which is the province where Wuhan is. And there’s several
interesting things here. The vertical axis is the number of casesand what we see on the
horizontal axis is per day. And so for example, we
could pick January 23. The yellow bar tells us the
number of confirmed new casesthat day. So these are people who
would have been testedand then they tested positive,and it looks like that
number is about 300. But then we have this gray bar. This gray bar is the actual
number of new cases that day,which is close to 2,500. So roughly eight times as high. Now you might be saying,how did they know the
actual number of casesif they didn’t test everyone?Well, the way they did that iswhen someone tested
positive, they asked them,when did you first get the symptoms?And if they said, Hey, I first
got the symptoms 10 days ago,they would be included as a true new case. An actual new case 10 days
before that on January 13,so that Chinese officials were ableto actually make these
gray bars in hindsight,based on when people said
they first got the symptoms. And there’s a lot of really
interesting information here. First of all, we can see that Wuhanwas shut down on January 23. So let’s draw a line
between the pre shut downand post shut down. And you can see just as the city officialswere starting to see confirmed cases,the actual cases were far higher,but then they shut down the cityessentially significantly
slowing down the spread rate. And a few days later, the actual caseswhich were they were able
to calculate in hindsight,start to flatten out and then go down. But even though they were going down,the confirmed new cases continued to go upbecause there is a delay. You can even see the
delay right over here. And that is roughly the amount of timebetween when people show symptomsand they are actually tested. Now you might be saying, all
right, this isn’t too bad. It looks like things eventually
became okay for Wuhan. But this is because they did
a very serious shut down. If they did not do this shut downand slow the spread of the virus,you would have seen this
exponential growth continue. It’s also worth remembering
what I just drew this curve on. This isn’t the total number of cases. This is the number of new cases per day. If you want the total number of casesat a given point in time,you would have to sum up
the gray or the yellow barsdepending on whether you want to lookat actual or confirmed cases. So as of January 22, if you total upall of these gray bars over
here, as of January 22,you get approximately 12,000 cases,while if you add up
all of the yellow bars,that is roughly only 444 confirmed cases. So before the city even
went into shutdown,and this is what the Chinese
doing reasonably good testing,you had a far higher number of casesthan the confirmed cases
would make you believe. And as large as the
ratio is on a given daybefore the city shut down,between the number of
actual new cases per dayand the number of confirmed
new cases per day,it’s probably higherin a lot of the geographies where we live,because we’re not testing
as well as the Chinese did. For example. This is data once again
compiled by Thomas Pueyoon his blog post. This is just a screen capture of itand I’m really just giving his analysis. This shows the total test performed,and the tests performed per
million citizens as of March 3,and you can see for example,where I live the United
States is not doing so well. And so the number of reported casesin places like the United Stateswhere we are really just
starting to ramp up testingis far understating the number
of actual cases out there. So how do we go about estimatingthe actual number of cases in our area?Well, once again, I’m going
to use Thomas’s analysis,we’re gonna be looking
at the number of deathsand estimations of mortality rate,time from infection to death,and how fast the virus actually spreads. So in other videos, I’ll talk more aboutsome of Thomas’s analysis. But for mortality rate,
it’ll make the math simple. And this actually does seem
to be a pretty good estimate,we can assume that there’s
a 1% mortality rate,the reports are as low as
point 0. 6% in South Korea,and then as high as roughly
5% in places like Iran. But it looks like the higher numbersare where the hospital
system is being overwhelmed. And then the lower numbers at the 0. 6%,might not be fully accounting
for all of the mortalitythat will happen due to the casesthat are actually out there. So we’ll assume a mortality rate of 1%. The other thing we need to think aboutis the time from infection
to death in those 1% of caseswhere someone does die. And to figure that out,I will look at this data right over here. This top chart, and it
comes from this link,which Thomas cites. And I’ll give the link
in the description below. This is the incubation period. This is an estimate of the timefrom when someone gets infectedto when they start to show symptoms. And this estimate is roughly five days. And then once you see symptoms,how long does it take to
death in those 1% of cases,or whatever the percentage is?Well, there’s varying estimates,but it looks like to
make the numbers easy,we can estimate roughly 15 days. So one way to think about itis five days from infection
to showing the symptoms,and then another 15 days from
showing the symptoms to deathfor a total of 20 days
from infection to death,in what we’re assuming the 1% of cases. So I’ll write 20 days. And now the other thing
we’re gonna estimateis the days to doubling,days to double. This is how long does it
take for the infectionto double in the population. And this is gonna be heavily dependenton what the population is doing,how dense they are, how
much they’re interacting. But we’ll look at some of these estimates. And they’re in very different contexts. And the lower the doubling rate,that means a virus is spreading very fast. While if you have a populationthat’s doing all the right things,they’re taking all the precaution,the doubling rate will be lower. So we could look at a
conservative estimateand take a higher doubling rate
than all of these estimates,it’ll make our math a little bit easier. Let’s just assume a
doubling rate of five daysand I’m using slightly different
numbers than Thomas used,but it will be indicativeand you can do the same analysiswith whatever estimates
that you choose to do. So let’s assume five days to double,which might be conservative,especially for places
like the United Stateswhere we have not taken
anywhere near the actionof a place like China or
South Korea, or Japan. So now let’s use these numbersto figure out what might actually
be happening in our areasbased on the data that
we are presented with. So let’s say that we
unfortunately here on some day,that there is one death in
our region or in our city. Now, based on our estimates,we’re saying that the average
time from infection to deathis about 20 days. That means that that personwould have likely contracted
the virus roughly 20 days ago,20 days ago. And so I’m gonna make a timeline. This is 20 days ago, this
would be 10 days ago,10 days ago, this would be 15 days ago,and then this would be five days ago. Now it’s possible that
they were the only personwho contracted the virus on that day,and then they happen to
unfortunately get very sickand then pass away 20 days later. But if we assume that the
mortality rate is roughly correct,it’s quite possible that 100
people were infected that day. The person that we know
about is that one in 100who actually gets sick
enough to pass away. And so if we assume that on 20 days agothat not one person, but 100 people. So the actual number of people
who are infected that dayis 100 infected that day. Once again, because it’s
a 1% mortality rate. If we assumed a 0. 5% mortality rate,then we would say, all right,there might have been 200
people infected that day,0. 5% of whom get all the
way to death 20 days later. If you assume a 5% mortality rate,which would be a very
unfortunate situation,but that is a mortality
rate that we are seeingin different parts of the world,then you would have say,well, maybe there were 20
people infected that day. When you only have one or two
or three deaths in a regionthat will make the
estimates more difficult. But as unfortunately,we are likely to see a
larger number of deathsin various regionsthat will make this
these backward estimatesmore and more reasonable. Now if the infection rate
in the population doublesevery five days, what
is now going to happen?After five days, you’re
going to have 200 casesin your region, 200 cases. Now, these wouldn’t just be new cases,this would be the cumulative
total number of casesdue to those hundred. Now, this is actually quite conservative,because this is assuming that those 100that were infected 20 days agoare the only infected
cases in your region. There might be other infected casesthat were infected before that date. But I’m just assuming that the hundredthat were infected that
day are the only casesto be conservative, and so
they double after five days,and then they’ll double
again after five more days. And so you will get to 400 casesafter five more days. And then you will, after five more days,you will have doubled
and I can’t even fit iton the screen anymore. You’re going to have 800 casesand then that means today just by evidenceof that one death,you probably have on the order ofand I can’t even draw the whole bar,approximately 1,600 cases. And so this is just to
be a little bit soberingabout how serious this is,and how much the data that we actually getis actually lagging the
circumstances on the ground,particularly in places
like the United States,where we are barely even
getting started testing. For example, in my county,which is Santa Clara County in California. We just had our second deathunfortunately reported yesterdayand there was another death
five days before that. Now, there’s only under 100
reported cases in my county,but based on this analysis,the actual number of
infected persons in my countyis likely to be at least a
factor of 10 more than that,and it could be as high as
1,000, 2,000, 3,000 people. We won’t know for sureuntil we can do the type
of hindsight analysisthat the Chinese had,but this is to just remind us how seriousthe situation actually is. So the big takeaway hereis to take all of this very seriously,especially because the
mortality rate itself can changedepending on how well equippedthe hospital system can
handle the situation. If we all socially isolate and
take the proper precaution,the spread rate will lowerand we won’t overwhelm
the hospital system. And we’ll hopefully be able
to keep the mortality rateas low as possible. But if we don’t take the precaution,and if we’re just complacentbecause we see this lagging datathat’s being reported to us
because of the lack of testingin places like the United States,then it’s very possiblethat we eventually overwhelm
the hospital systemin the next few weeks,which would cause the
mortality rate to go higher.

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