Ebola transmission rate and exponential growth


Link to White House video of President Obama's 2014-10-18 Weekly Address
Embed of White House video of President Obama's 2014-10-18 Weekly Address:

Text of the address:
Remarks of President Barack Obama
Weekly Address
The White House
October 18, 2014

President Obama:


We have to remember the basic facts.

First, what we're seeing now
is not an "outbreak" or an "epidemic" of Ebola in America.
We're a nation of more than 300 million people.
To date, we've seen three cases of Ebola diagnosed here-
the man who contracted the disease in Liberia, came here and sadly died;
the two courageous nurses who were infected while they were treating him.

Our thoughts and our prayers are with them,
and we're doing everything we can to give them the best care possible.
Now, even one infection is too many.
At the same time, we have to keep this in perspective.
As our public health experts point out,
every year thousands of Americans die from the flu.

Back to remarks by the author of this blog:

I have zero training in anything related to health care,
but I know a little math.
President Obama,
along with many commentators who have been making the same points
Obama just made,
absolutely misleads Americans on what the significant issue is.
It is not how many Americans currently have Ebola;
it is what the transmission rate is
(and, of course, the mortality rate for those who contract Ebola).

Let me illustrate with two alternative estimates for the transmission rate.
In each case, we will assume that after a person contracts Ebola,
he has 20 days in which he may pass it on to others.
(This seems reasonably realistic:
Thomas Eric Duncan, for example, evidently contracted Ebola on September 15,
died on October 8 (23 days later),
and evidently passed the disease on to
at least two of the nurses who cared for him in Dallas,
Nina Pham and Amber Vinson.)
We will consider alternative scenarios for different transmission rates
(how many other people each Ebola patient passes his disease on to).

In the first scenario,
assume the transmission rate is 1:
each Ebola patient, after the 20 days are up. has one successor patient.
That means one more patient every 20 days.
Over a year, there would be about 18 total patients (365/20).
Nothing I would worry about much, in a nation of over 300 million.

In the second scenario,
assume the transmission rate is 2:
each Ebola patient, during his 20 days of contagiousness, passes it on to two people.
(As Duncan did to his two Dallas nurses.)
So after one generation of transmission (20 days), there are two patients.
After two generations (40 days), 2x2 = 4.
After three generations (60 days), 2x4 = 8.
After n generations (20xn), 2n Ebola victims.
The useful number to keep in mind here is 210 = 1024, or roughly 1,000.
Thus after ten generations (200 days), there would be at least 1000 patients;
after twenty generations (400 days), over one million victims;
after thirty generations (600 days), over one billion victims.

In the general case, the transmission rate is R
(the above two scenarios were the cases R = 1 and R = 2).
So after n generations, there would be Rn victims.
If R is between 1 and 2,
you get results intermediate between the above two scenarios.
If R is less than 1 (exponential decay), the disease eventually dies out
(the lower R is, the sooner it does so).
If R is greater than 2, things are even worse.

So what I am saying is:
What is critical is now how many people currently have Ebola,
but what is the rate at which people pass it on.
Where did Obama acknowledge that point?
I don't see where he did.

In my opinion,
the nation should not be concerned with treating the unfortunate people who have contracted Ebola,
but in ensuring that those people do not pass their disease on to others.
The emphasis should be on containment, not treatment.
If treatment can be done with zero risk of passing the disease on, fine, do it.
But if the typical American hospital (i.e., not the NIH, not Emory, not Nebraska)
is no better at preventing transmission than Texas Health Presbyterian Dallas was
(and according to the New York Times they were well-regarded in Dallas),
we really need to be very, very careful about how cases are managed
and the disease controlled.