
Flattening the Curve Math - luu
https://nostalgebraist.tumblr.com/post/612592471097147392/flattening-the-curve-is-a-deadly-delusion#notes
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gus_massa
Merkel said that she expect that the 40%-70% of the total population of
Germany will be infected. [https://www.indiatoday.in/world/story/coronavirus-
angela-mer...](https://www.indiatoday.in/world/story/coronavirus-angela-
merkel-germany-1654541-2020-03-11) She only has a PhD in Quantum Chemistry,
and is not an Epidemiologist, but I guess she has good advisers. Anyway, as
the current article says, using the SIR model the expected part of the
population is higher. The exact number is not clear, but for simplicity and
some optimism we can assume a 50%.

All the shared graphics use a Gaussian-like blob with a 0 at 0. I didn't fit
them, but they look very gaussian-like to me. Some may be a spline or a Bezier
curve or whatever the graphic program has. I agree that using a Gaussian is a
weak point of the original article, I'd like to see a SRI simulation, it's
just a simple differential equation.

The exact graph is an asymmetric blob with two sigmoid-like parts. Here is a
nice graph
[https://simple.wikipedia.org/wiki/SIR_model](https://simple.wikipedia.org/wiki/SIR_model)
It is not a Gaussian, but it can be somewhat approximated by a Gaussian, at
least in a hand drawn graphic.

The main point of the original article is that the number of beds in hospital
with the equipment to treat the bad cases is much lower than the estimated
patients that need them at the peak of the infections. He estimate 170,000
ventilators and 3,000,000 patients that need a ventilator at the peak (in
USA). It's almost a 17x, not a 2x or 3x like in the graphics in the news.

To flatten the curve, if we decrease the height it will increase the width to
conserve the area. (The shape will change, but not too much. In an exact
simulation you will see the difference, but not in a graphic with a blob.) So
the width must be increased x17. So if we estimate that at the current
infection rate the pandemic will last 1 year, the flattened version will last
17 years.

The exact number depends on the shape, so using a gaussian instead of the real
model will change it. The exact end point is arbitrary, because with both
graphic it will fade slowly. Let's say between 15 and 20 years.

The exact numbers of peak patients and beds in hospitals are controversial. I
think he is using that the 20% of the patients need hospitalization, but I
hope the real number is much smaller because many mild cases are not tested.
Let's be optimistic and say 5%? That reduce the flattened epidemy to somewhat
like 4 years.

Most people assume that it's enough to get toilette paper and hand sanitizer
for a month, and after a month or two the flattened epidemy will be over. It
will be longer. I hope that we can get a vaccine in a year to kill most of the
tail of the curve, and even the peak if it is flattened enough. The author of
the original article is less optimistic and ask for more containment measures.

