On day 1, no one you know is sick. It feels like a normal day. It may stay like this for a long time, until

one day, a few people you know are sick. And suddenly a few days later, it will seem

like everyone is sick, and it will feel like it happened instantly. Everything looks fine, until it isn’t fine. This is the paradox of pandemics, and it’s

why with an outbreak like COVID-19 you hear health officials calling for huge, drastic,

and rapid responses in the early days when infection numbers are still relatively small. Some people worry these actions are over-reactions. Sports teams playing to empty stadiums, or

not playing at all. Canceling huge gatherings and festivals. Temporarily closing schools and offices. Telling people to avoid personal contact. Media sensationalism. All too much, for something that isn’t even

a big deal yet. But this way of thinking fails to appreciate

how disease outbreaks work: It was really never fine to begin with, but we don’t notice

until it’s too late. [MUSIC] Hey smart people, Joe here. “How bad will the coronavirus outbreak get?” That’s what we all want to know, and the

answer is in one of these curves. This is what a rapid global pandemic looks

like. Little to nothing to slow the number of new

infections means a lot of people sick in a short amount of time. A slower global pandemic looks like this. The rate of new cases is lowered, and they’re

spread out over a longer period of time. And which one of these paths we end up on

is important because of this line. It represents the capacity of our healthcare

system: the number of beds, doctors, respirators, and everything else. What experts fear is a sudden explosion like

this overwhelming this capacity. And what’s really interesting here is that

even if these two curves represent the same total number of people that eventually get

infected, in the rapid outbreak scenario more people will die because there won’t be enough

hospital beds or ventilators to keep them alive. This is a strange idea. That even if the same number of people eventually

get sick in the end, even without a vaccine or a cure, taking drastic action before we

see things get bad, that will save lives all on its own. What we’re doing isn’t over-reacting. It’s exactly what the science of epidemics

tells us will work. And that’s counterintuitive–it’s something

that literally goes against our intuition–because our intuition doesn’t really “get” exponential

growth. Instead of thinking about viruses, let’s

say you have a pond, and on the pond is a single lily pad. This type of lily pad reproduces once a day,

so on day two, you have two lily pads. On day three, you have four, et cetera. If it takes the lily pads 60 days to cover

the pond completely, how long will it take for the pond to be covered halfway? The answer is 59 days. The area covered doubles from half to the

whole pond on the last day. I bet some of you knew that, though, because

you’re pretty smart. But on what day do the lily pads cover a mere

1 percent of the pond? Surprisingly, that doesn’t happen until

day 54. The pond is basically empty, until it’s

very suddenly not empty. We go from covering less than a percent to

covering the whole pond in just the final 7 days. This is exponential growth and it’s how

pandemics work. We multiply today by some constant to get

the value for the next day. The time doesn’t have to be days, but that’s

helpful to use for something like lily pads (our constant was 2) or COVID-19. Starting in mid-February we’ve seen between

1.1 and 1.4 times more cases each day. A number over 1 tells us every day we’re

seeing more new cases than the day before. You can see the number of total cases starts

to add up really fast. Exponential growth can be scary. But obviously this can’t go on forever and

fill the known universe with viruses, for a few reasons. The virus will either infect everybody, like

our lilies filling up the pond, or what actually happens is the virus stops finding people

to infect: either by running into people who are already sick, or we isolate people who

are sick, or thanks to something like a vaccine spreading resistance in the population. But over time the growth rate will naturally

slow down, and we end up with a curve for the total number of cases that looks like

this. This is called “logistic growth” and we

call this curve a sigmoid, which is a weird name, but luckily it starts with “S” which

also happens to be the shape of the curve. While I was working on this, Grant from 3Blue1Brown

released a *really* good video digging into more of the math behind why and how this changes,

and he’s definitely my go-to when it comes to math, so I’ll put a link down below so

you can watch that later. Now, remember that the height of any point

on our S curve tells us how many total cases the outbreak has caused as of that day. But if we take the slope at that point, that

shows how many new cases that day. Which makes sense, not many new cases early

on, then a whole lot each day, and then not many new cases again as the virus dies out

or goes quiet. If you’ve taken calculus and worked out

derivatives before, then you may see where I’m going here. Plotting the different slopes along our S-shaped

curve, we get this. This is what health officials are worried

could overwhelm our healthcare system. But luckily, we can make it look like this

instead, if we change how our S curve looks. How we do that is by lowering the constant

we multiply by from day to day in our exponential growth. The really important thing here is, for a

virus that humans have never encountered before, like this one that’s causing COVID-19, no

one is immune to it. The only way to lower the growth rate, isn’t

medicine or anything like that, it’s to slow down those infections and keep them from

happening in the first place. A real outbreak plays out like this: You have

a bucket of infectious people, I. And you have a bucket of people who haven’t

gotten sick yet, S. The I bucket is tied to the S bucket so that the more full I is, the

faster S empties into it. But people are also getting better all the

time. So the I bucket has a hole in it that empties

into a bucket R for recovered people at some constant rate. So if we can lower how fast S empties into

I through some drastic action, I will empty out into R, and we’ll stop emptying S. If

our bucket of infectious people is empty, we starve the virus out. So even if we somehow did nothing else to

stop a disease outbreak or pandemic, and the same total number of people get infected in

the end, it is so, so important to slow down how many new cases we see every day, to flatten

the curve and keep a pandemic from overwhelming healthcare. In 1918, in the early days of the worst influenza

pandemic in history, the city of Philadelphia ignored warnings and held a parade attended

by 200,000 people. Three days later, every bed in Philadelphia’s

hospitals was full, and 4,500 people died within a week. At the same time, St. Louis, two days after

detecting the first cases, closed schools, playgrounds, even churches. Work shifts were changed. Public gatherings of more than 20 people were

banned. And this was the result: A tale of two cities. That’s why officials are calling for such

drastic action so early on, canceling events and school and everything else, before most

of us actually know anyone who’s sick. Because with something like this, everything

looks fine until it isn’t fine, and if we wait until it’s our turn to get sick, it’s

too late. Stay curious. And wash your hands. We’ll be talking more about that really

soon. And as always, a huge thank you to everyone

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