It is a worrying sight that the number of Coronavirus cases goes up every day.
Here is the graph of the total number of cases from February 26 to March 11th
which rises pretty alarmingly by 50% in these 15 days
Another channel 3Blue1Brown already said that we should expect a logistic curve for the number of cases
but there are two questions we want to know about this curve. First of all, what is the plateau?
Is it the entire world population?
Or 27 percent of the world population like in the Spanish flu in 1918?
Another question is, when will the number of infected cases be reasonably close to this plateau?
In other words, when will this epidemic practically end? Is it July?
Will the coronavirus persist for a year, or even an entire decade?
On the hopefully unlikely assumption that things go as is now, the plateau is somewhere around 1.87 billion
and the approximate time frame for the entire epidemic is four to five years
But you want to know where these numbers come from, and more importantly, whether you should trust these numbers
The epidemiological model I'm using is called the SIR model
which is one of the simplest, although, with reasonable accuracy
It compartmentalises the entire population into three parts which are labeled as S, I, and R respectively
S here stands for the susceptible population and the initial value is taken to be the entire world population
because this is a novel virus where nobody has immunity
I stands for infected population
These are the people currently ill, and we don't know whether they will recover or die from the disease
which is taken to be around 53,000 as of March 11th
And R is supposed to stand for "recovered" population, but here I put "recovered" in quotations
because we have to take deaths from the virus into account, for reasons explained shortly
This is taken to be around 73,000 as of March 11th
Just to be clear, the vast majority of these 73,000 is recovered
For an infection, people first go from being susceptible to being infected, then to the "recovered" stage
The main reason we put death in this R stage is that whether you recovered or died from the virus
you can't infect others and can't be infected, and this model only cares about the spread of the disease
We also have the sum of these populations to be n, the entire world population
and we take this to be roughly constant
The model relates the dynamics of S, I, and R by some simple equations: here they are
It looks complicated, but it really isn't
These two terms are really the same, just with opposite signs
and these two terms are also different only in signs
When we go back to our basic three-part model, all these equations mean is that
the rate of the first transition is proportional to both S and I
nd the rate of the second transition is only proportional to I
The reason we think that the rate of first transition is proportional to S
is that the more people who are susceptible to the disease, the more people will get infected
and the reason why this is proportional to I, is that the more people infected, the more people will get infected
And the rest of this expression is just the constant of proportionality
Now for the second transition, the more people get infected
the more people recover or die from the disease each day
So these equations now make more sense, and we want to find out the constants beta and gamma for coronavirus
To do this, we just need to find some data on daily new cases whether it is newly infected, recovered, or died from coronavirus
and the data of S, I, and R on the previous day
and you can do this by visiting the Worldometer website
The value of beta and gamma seems to be changing every day, but we can still take the average
and the result I obtained is that beta is roughly 0.0724 and gamma is roughly 0.063
Based on these values, assuming that they don't change over the course of the epidemic
we will get the figure I presented in the beginning of this video
i.e. the total number of cases combining both currently or previously Infected
will reach a plateau of around 1.87 billion
Now this figure is very horrifying to say the least because that amounts to a quarter of the entire world population
These so called constants beta and gamma are super important in the entire model
We took this set of constants and we end up with a plateau of 1.87 billion
within a time scale of around four to five years
This set of data we obtained is the average of the betas and gammas we get over 15 days
However, if we look at the most recent data averaging over much shorter time
we get this set of more horrible constants
The reason why it is more horrible is that the plateau is at 6.6 billion and
the time scale is at around ten months from now
The difference here is the value of beta increases by a lot and the value of gamma is much lower
This means that the ratio between beta and gamma increases by a lot
and this ratio pretty much determines the behavior of this epidemic
This constant is so important that we usually call it the basic reproduction number
It roughly corresponds to the expected number of new cases from one single infection
If this ratio is bigger than 1 we are still initially in the exponential growth stage, like right now
and if this ratio is smaller than 1, we will be in exponential decay
In fact, if we set beta to be 0.05 and gamma to be 0.06, so that the ratio is less than 1
the plateau will be at around 319,000, and this epidemic will practically finish after around 20 days
That means around early April
But the problem is how to change these constants so that we get this optimistic scenario
We can approach this in two ways, namely, decreasing beta, and increasing gamma
Recall this model that we saw previously
Beta appears in the first transition and can be thought of as the likelihood
that a susceptible individual becomes infected
And gamma appears in the second transition and can be thought of as the likelihood
that an infected individual recovers or dies
So to decrease beta is the same as decreasing the likelihood of infection
and increasing gamma is the same as increasing the rate of recovery
For decreasing beta, it can be done by stricter government border control, which not many are doing well
and whether or not you are infected
staying at home as much as possible decreases the chance of infections happening in the first place
Of course, observing personal hygiene is also important in decreasing infection
Developing vaccines can also decrease the value of beta significantly
but this definitely takes quite a bit of time to do
For increasing gamma however, there is not much that we can do about
other than developing better medicine to treat patients
These are of course quite common sense
but this video hopefully shows how powerful these measures can be in the long run
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