Hacker News Reader

Hacker News

Comment by WildParser | Hacker News Reader

Parent Full thread

WildParser

Exactly. Things with R0 < 1 will fizzle. Herd immunity is 0. Little mathematical exercise. For Massachusetts:

a) Take the number of deaths per day, divide it by the total number of deaths. f'/f.

b) Take a look at this in a log-chart. Use 7 day averages for f' and f to get a cleaner picture.

You will see that f'/f falls down exponentially since pretty much the beginning.

c) determine the exponent by estimating the derivative ln(f'/f)'.

d) Now use that to calculate the function f.

e) Calculate an enddate when it will fizzle.

View on HN

If people are infectious for some finite number of days, f'/f will always tend to zero, even if f' stays constant.

It falls down exponentially! Just look at it. If you do a bit of math you will see that f will just converge.

I think it really depends on your underlying dynamics, but I just want to point out that f'/f going to zero does really not imply that f will converge.

If for example you are in a still strongly growing (but no longer exponential) regime where you can approximate the currently infected number of persons as proportional to t^2 , and there is some constant IFR, then f'(t) is also proportional to t^2. f(t) will then be growing as t^3, so f/f' will go as t^-1, which will look quite similar to an exponential decay at the timescale of the process.

And I still politely ask you to just look at the data. There is nothing in the data that points to "somehow" and "maybe". It is just a straight linear line in the logscale.

You may see some wobble caused by outbreaks here and there, but the mechanics of COVID-19 are always the same.

Going to zero exponentially does mean it will converge mathematically. And t^-1 won't look like the things that can be observed. There is no such thing as a constant upward trend away from the exponential. If you look carefully and do some regressions you can see some ups and downs. Changes in the behaviour of the people are able to modify the trend, but there is no constant movement away from an exponential.

You can always add an upper exponential bound that will converge below single digits per day before there is any chance that the lines cross.

I'm not doubting that it looks like what you say for the area you looked at. I just wanted to make a more general point that it is not sufficient to look at f'/f and conclude that things will be fine if that is tending towards zero.

I'm not claiming that is what you were saying, I just wanted to call out this point in case other people read this that may come to this conclusion.

FWIW, the solution to f'/f = exp(-t) is f(t)=c*exp(-exp(t)), which actually looks like an epidemiological curve, but like any sigmoid it will be hard to determine the actual saturation point until after it has already passed the inflection point.

Yes, it's important to go down exponentially - which exactly is the thing it is doing - not just in one place...

Good luck that most countries on the planet have already passed the inflection point, so finding the saturation point isn't that difficult anymore.

Interesting to see that just asking people to look into this will generate downvotes. It's just basic mathematics. And it really isn't that hard to verify...

I think the downvotes were not for asking people to look at it, but because the comment can come off as overly dismissive of the severity of the situation.

Maybe, I'm not really a polite person. I think using a working formula for f would greatly help to evaluate the consequences of actions and helps to detect outbreaks early.

In my area they made masks mandatory and cut down the protection of hospitals - now we have an infected nurse. I think politicians currently are using seriously wrong models for their actions.

I had a discussion with one of the "official" epidemiologists. It went like the discussion with you - just at the point where we are now he decided to go into all-caps swearing, said that he will never look into this, called his models perfect and then blocked me.

Reply on news.ycombinator.com