- [Narrator] Hey, there. In this video, we're gonna simulate some different versions
of an infectious disease to try to get a handle on the basics. We'll explore three phases. The epidemic phase,
when the disease is new. The endemic phase, when the disease has
been around for a while. And the eradication phase, when we finally get rid
of the disease for good. This city has two kinds of
locations: homes and non-homes. Three blobs live in
each home and each day, each blob will go to up
to three different places near where it lives and then return home
at the end of the day. The disease will have
three different states. Blobs start out blue in
the susceptible state. If a blob catches the
disease, it becomes infectious and can then infect other blobs
that are in the same room. Blobs stay infectious for two days and then they enter this
recovered state, turning gray. And in this model, recovered
blobs are permanently immune. This is called an SIR model. This is, obviously, a lot
simpler than real life, so we're not going to try to make any specific predictions about COVID-19, but the goal here is to get a feel for the overall patterns
of disease spread, so this should do the trick. All right, let's run our
first full simulation. We'll start with 10 infected blobs and an infection chance of 1% each time blobs interact in the same room. Let's pause here. This graph stacks numbers from the three different
states on top of each other. For example, at the end of the third day, out of the 1,000 blobs, 798 of them are susceptible, 172 are infectious, and the other 30 have already recovered. This R-naught number that
I mysteriously put up here is called the basic reproduction number. It's the number of new infections caused by each infectious
blob before it recovers, on average assuming there's no immunity. For example, if R-naught equals three and we start with two infectious blobs, each would infect three
more blobs on average and stop being infectious itself. So the new number of infectious blobs would multiply by three
getting to six total. And this multiplication repeats leading to exponential growth. At least, that's what we would expect. The real world is chaos though, so it doesn't work out so cleanly. That's one reason I like
running simulations. They force us to look at the messiness. Here, R-naught was calculated by averaging over many possible
versions of the simulation all with the same settings. The result is 2.5 so if
everything were clean and tidy, we'd see the number of
infections multiply by 2.5 over the two-day infectious period. But at least for this run, the
growth is quite a bit faster. This is part of why we don't precisely know R-naught for COVID-19. In the real world, we don't get to run the
simulation a bunch of times to average things out. Anyway, let's see what
happens as we keep going. As more and more blobs become infected, the growth slows down. R-naught pretends that all
the blobs are susceptible, but that quickly becomes untrue so we should really add this factor S here for the fraction of blobs
that actually are susceptible. R-naught times S is given its own symbol, usually R but sometimes RT. It's like R-naught but for some later time when immunity is slowing things down. Instead of the basic reproduction number, R is just called the
regular reproduction number. And as long as I'm
throwing some terms at you, S goes down over time so
instead of exponential growth, this becomes logistic growth which flattens out after a while. We won't dwell on logistic growth here, but I'll link to some videos
in case you're interested in going more deeply into the math. When R is above one, the
epidemic is still growing. When it's equal to one, the number of active cases stops growing. And when it's less than
one, the cases decline. And when this fraction of
susceptibles is small enough for R to go to one, it's
called herd immunity, which we'll talk more about later. But one thing we should note now, herd immunity means the number
of cases will start dropping, but it's not an absolute cap. The total number of
cases can go much higher if a lot of cases are
happening at the same time. In this case, at the peak of active cases, 41% were infectious at the same time. And when all was said and done, 85% were infected at one point or another. So that's the basic shape of an epidemic, but let's run through
a few more simulations with different infection
rates to get a better sense of what different
situations might look like. I picked infection
rates that would lead to R-naught values of 1.5, 1.1, and 0.9. (classical music) Looking at R-naught equals 2.5 again, the results are pretty close
to what we saw last time. When R-naught equals 1.5, as we'd expect, we'd see a smaller peak
and fewer cases overall, but it's still a pretty large
portion of the population. When R-naught is 1.1, there's still an exponential
light growth at the beginning, but it's just a 10%
increase every two days so we don't see a big spike this time. And when R-naught equals 0.9, it's less than one so we
expect the disease to decline even before any immunity builds up. And it's good to see that
that is indeed what happens. Right now, you might be thinking as I was, okay, I get that R-naught
determines whether it'll grow, but how do things like the
length of the infectious period or the size of the population affect how the growth plays out? To help answer this, I made some more variations
on that first sim. The first one has the
same settings as before with a two-day infectious
period and 1,000 blobs. The second has an
infectious period of one day instead of two. The third one has an
infectious period of 10 days. And the last one has 10,000
instead of 1,000 blobs. And in each case, I adjusted
the infection chance to keep R-naught close to 2.5. Before we hit go, try
making some predictions about the peak number of infections, the total number of infections, and anything else you think
might or might not vary. (classical music) Not too surprisingly, the
timelines are different. The one-day infection peaked
and burned out quickly, the 10-day infection took longer, and in the city with 10,000 blobs, it also took longer for
the disease to spread from 10 initial blobs
to a significant portion of that larger population. But the peak and total
infection percentages turned out to be almost
the same in each case. The only thing slowing the spread in these simulations is herd immunity so the fraction infected
stays pretty steady in different situations
with the same R-naught. I chose 2.5 as the example R-naught because that's in the range of early estimates of
R-naught for COVID-19. There's some uncertainty there and it'll be different
in different places, but according to our current
understanding of the disease, if we did nothing at all, it would be reasonable to
expect something like this. So that's what's worrying about it. All right, that's the epidemic phase. On to the endemic phase. In our model so far, the disease ends up
dying off all by itself. Unfortunately, this doesn't
happen in real life though. There are two reasons for this. First, immunity is often
not perfect or permanent. And second, long-term
immunity isn't inherited so there's always a constant stream of new susceptible people. To put this into our model, we'll give the blobs an average
lifespan of three weeks. At the beginning of a simulation, the ages will be all spread out and then when an older blob dies, it'll be replaced by a
new susceptible blob. So with that in place,
let's run some more sims. This time, we'll track
R-naught and R in real time. R-naught is still gonna be calculated from an average of many sims, but R is gonna be based on
counting the new infections on this one run of the simulation so it'll bounce around a bit
based on random happenings especially when the numbers are small, but it will let us see
the growth in real time. Anyway, here we go. (electronic music) Now we can see a little bit more clearly why infectious diseases
don't go away on their own. At first, there is this initial epidemic with R greater than one just like before. And then, again, we get to a
point where R is less than one leading to a decline. But this time, the infection
count doesn't decline all the way to zero. Once it gets low, the
number of susceptible blobs starts increasing again and in
turn, R climbs back above one and then the number of
infections starts to rise again. There's an equilibrium here with R always getting
pulled back toward one. And as we saw before, on average, we expect R to be one at
the herd immunity level. We can calculate the herd immunity level for any value of R-naught. As we said before,
R-naught times S equals R and herd immunity is where R equals one so the fraction of susceptibles for herd immunity is one over R-naught. And herd immunity is usually given in terms of the fraction of
people no longer susceptible so it ends up being one
minus one over R-naught. When R-naught equals 2.5, we get 60%. If you've heard estimates of 50-70% for herd immunity for COVID-19, this is where that range comes from. Before we move on to
the eradication phase, I wanna say again that the
goal here is to get a sense for the broad patterns at play. The size and the timings of these cycles and the average number of people
infected will depend a lot on the properties of the real disease and how we react to it. And there are some other
factors like seasonality or mutations that can
complicate this picture. But even with these real
world complications in place, an endemic disease always fluctuates around this herd immunity equilibrium. All right, on to eradication. 10 days into the simulations, the blob city will discover a vaccine. After that point, when a blob
dies and a new blob appears, that blob will have a chance of getting vaccinated, turning green. They're just like the gray recovered blobs but they're green instead so
we can keep track of them. We'll again use this disease
with R-naught equals 2.5. Here, herd immunity is
when 40% are susceptible or when 60% are not susceptible so I would expect a 60% vaccination rate to get rid of the disease,
but we should check that and let's also look at 50%, 35%, and 20%. Again, before we hit go, try
to make some predictions. Will 60% actually result in eradication and what will happen with the lower rates? (electronic music) All right, so 60% did indeed do the job, but none of the others did. Before running these, I'll admit that I thought
that 50% might do it since some blobs would be immune from actually having the disease, but it turns out that
as long as there is room between this vaccination floor and the herd immunity threshold, the disease still has room to
wobble around in equilibrium. True eradication turns
out to be really hard. We'd have to do this for all populations that can carry the disease. This is hard enough for humans, but for many diseases,
it includes animals too. So that's just infeasible. But eradication isn't the only goal. More vaccinations still mean
smaller spikes in infections and fewer sick blobs overall. It's encouraging to think
about being able to manage, if not eradicate a disease, but right now we're still very
much in the epidemic phase. If you find yourself doing okay right now and want to find some way to help but just aren't sure what to do, one thing you can do is hit
that button below the video to donate any amount to GiveDirectly. GiveDirectly puts your donations directly in the hands
of other humans in need. It's a top rated charity for making donation
dollars do the most good. It's tax deductible and
the button is right there. Whether you're in a place to give or not, I do appreciate you watching to the end. Thanks. (soft classical music)
I wish he would have added one that limited the amount of places that half of the blobs go.