Understanding R nought | Current events in health and medicine | Heatlh & Medicine | Khan Academy

– [Voiceover] So, I put up
the definition of R nought, and it’s kind of a funny spelling, and the pronunciation of
N-O-U-G-H-T is just N-O-T, not. So, what it means, and
the definition is here, we’re just going to go
through, what it means is the number of new cases that an existing case generates on average. So, the way I think about
it is just in math terms. If you have R nought, you
can just take literally the new number of cases
divided by the existing number, and that should give
you the average, right? And then a couple of points
here over the infectious period, and, of course, some infections
can be infectious for let’s say a few days, and some
are going to last for years. In fact, some can last for decades, where you can still spread it, even 30 years after you first got it. And then, a susceptible population. What that refers to is kind of
a not vaccinated population. So, not vaccinated. Or you can think of it as a group that has never seen this infection before. So, maybe they are folks that had never naturally gotten this infection either, but basically their immune
systems are seeing it for the first time and are
susceptible to making them sick. So for me, the easiest way
to kind of think through this is to kind of just come
up with some examples. And so, imagine you have four infections. I’m just going to arbitrarily
name them A, B, C, D, right? So, four infections. And each of these infections,
let’s say we kind of go into a community, and we say, how many of you guys
have these infections? And we find that each of them, just to make the numbers easy, they all start out with four people having each of these infections. Okay. So, we decide to go into the future. We say, all right, we’re
going to follow you up some point in the future, and it’s going to depend
on which infection. So, maybe this one we’ll have
to come back decades later, because this one is
infectious for decades, so we have to give it an
appropriate amount of time. This one, we can come
back some weeks later. Maybe some days later over here. It can depend on each one, right? So, let’s just, each one is dependent on how long it’s infectious for. So, you come back at some
time point in the future, and for A, you find out that this person gave it to somebody, and this
person gave it to somebody, and these other two, right here, they actually didn’t end up giving it to anybody, this infection. So you’d say, all right, well
what is the R nought, right? So, the R nought is going to
be new cases, which is two, over old cases, which is
four, or existing cases. So, R nought equals 0.5 here. And what about B? Well, this one let’s say you
get two people over here. Let’s say this person
gives it to somebody, and this person also gives it to nobody. So again, you just count up the numbers. You say, well, okay, here we have four divided by four equals one. So again, it’s an average. So, even though some
people gave it to more and some people gave it to less, the average is going to be one. And for C, similar kind of thing. I can say, well let’s say you
have a few people getting it, maybe two over there, maybe one over here, and this person gives it to
let’s say three people, right? So, in total I’ve got four,
five, six, seven, eight. Actually, let me make
these numbers even nicer. So, let’s just say we’ve
got eight people total. So, R nought equals eight divided by four. We started with four. And in this case R nought equals two. And D, I’m just going
to make this one like an almost ridiculous sounding,
but let’s say we have tons of people that get sick. So this one, for whatever
reason, a lot of people when we come back a few
weeks later, we see that just many many many
people have gotten sick, and, of course, on average
we’re going to have to take the total number of
people that we see here and just divide it by the number four. So, I’m just going to
quickly scrawl this out. Let’s see what we get here. I’m going to get up to– I’m trying to get up to 72. Let’s see if I just– I don’t want to overshoot that number. So, we’ve got 30. We’ve got 40, 50, 60, and
then I’ve got to just do 72. So, this one, whoops. This one divided by five, what do you get? You get 72– Sorry, divided by four rather. Seventy-two divided by four
is going to give us 18, right? So, this one has an R nought of 18, and I wanted to visually show that to you, just so you can see kind of
what that would look like. And so, so far this is all making sense, and we can say, okay, well,
we don’t have to worry about these first folks anymore,
because we already followed them for as long as we needed to, right? So, they’re not going
to spread it anymore, because we made sure that we followed them for weeks or days or decades, whatever the infection requires, but now we’re interested
in these blue folks, right? So, we want to know, well how
are they going to spread it? Let’s start with this one right here. Let’s say this person spreads
it to a single person. This person spreads it to one– Let’s say one, one, and two, and this person sends it to nobody. Let’s actually just quickly
make sure I do the math here. So, this is at a future time point, even further in the future, I guess. And now, our R nought is– Again, you have to think about
new versus existing, right? So, existing we had two blue ones. So, we had two down here, and
we have one new person here. So, our R nought value
is going to stay fixed. That’s kind of the idea I want to express. The R nought is not going to change. It’s kind of a measure
that we think is unique to a particular infection. So, four over four remains one. R nought over here I just
said is not going to change. So, we can already kind of
assume what’s going to happen. It’s going to be okay, well on
average it’s going to be two. So, maybe some less, some more, but overall it’s going
to be that number, right? So, we’re going to get
something like this, and that also kind of easily tells you how quickly it’s going to spread. It’s going to double
every time you come back. So, every few days, if
that’s what this is, every set number of days
it’s going to double. So, you’re going to say, okay, instead of we started with eight, and now we have 16. And over here, with this one over here, it’s just going to be an
enormous number, right? It’s going to be 72
times 18, which equals– I actually did the math here. It’s 1296 cases that are
new, and we started with 72. So, that’s R nought of 18. So, I’m not going to draw that
in, but just a lot, right? A lot of people. So, what you can already
kind of see happening here is that when you have an
R nought less than one, which is kind of the case here, you basically see that this
is going to start dying out. So, this infection starts to die out, and it’s almost gone already. We started with four. We only have really one person
left with this infection. Over here, when R nought
equals one, exactly one, it’s going to be stable. So, kind of moving over time, you see that the same number of
people, in this case four, are going to have the infection. And over here, when R
nought is greater than one, and it depends on how much
greater, it’s going to spread. So, the infection is spreading. And this is why this
number is so important, and it’s helpful, and to add
a little bit of context here, Ebola, for example, has got
an R nought of about two. So, that was the example I had in mind when I wrote that down. And infection D, this is
a little bit like measles. So measles, you can see, is much much more inclined to spread than
Ebola, for example. All right. Now, so before I leave you
feeling completely hopeless about this situation, because
this looks pretty scary, the way that these
infections are spreading, let me point out something. So, I don’t want it to seem like you can’t actually
intervene, and, in fact, there’s a few things we
can do to reduce the spread of these infections that have
these high R nought numbers. One of them would be
to block transmissions. So, you can make sure that
if you have a sick patient, they are isolated. If you have a healthy person
that has to be around them, for example, let’s say a nurse
or a doctor or something, you can make sure that they’re
wearing protective clothing. So, you could isolate the patient. You can wear protective clothing. All these kinds of things help
to block transmission, right? And, in addition, you can also think, okay, well, what if a person does actually get exposed to an infection? For example, let’s say measles. This is actually a great example. And Ebola doesn’t fit this
second category, unfortunately, not yet, today being October 12th, but we have vaccines
against measles, right? So, you can actually vaccinate people, and in the case of
measles it would be MMR. So, measles is MMR vaccine, and if you actually use this vaccine, and it has a certain effectiveness, that effectiveness prevents a lot of folks that have had the vaccine
from getting sick. And so, these are a couple
of ways to reduce the spread of these very very infectious agents.


  1. For perpetuating you are educated, it's actually "r naught" not "nought". At least your pronunciation is right. Naught meaning zero, nothing, non-existent.

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