not true - infection rate grows sigmoidal and not exponential. that's why at the moment you can observe a stabilization despite few changes in regulation as of now compared to the summer. infection spread saturates periodically after suceptible clusters are depleted.
what would make sense is a steady and controlled Durchseuchung with specific protection of vulnerable people (like old and sick) - b/c the best immunity is gained by infection.
but Durchseuchung never sounded good - that's why that term got so popular. it sounds ugly and brutal. but it's what was happening all the time with many diseases in the past thousands of years.
Even if it was, it still means risking death or permanent organ damage + good chance of passing the infection to others. Not the best value proposition & definitely not webscale.
I think it could be technically accurate, if you include that vaccination before getting infected gives better immunity than most other options. (It is almost like a booster shot, but worse in almost every possibly way)
Also probably true without the vaccine first, but the initial survival rate without vaccination is a lot lower.
Here you can find linked three studies by the CDC that support the idea that natural immunity is harder to get and less effective (besides, as others have said, there's the non trivial chance of side effects or not even surviving the virus)
I don't care about what the "experts" think or say, I care about studies.
Update: https://www.nature.com/articles/d41586-021-02795-x#ref-CR5 reports many studies that claim that we should be vaccinating people after a natural infection to get "super immunity", but that is different from what the OP was claiming (natural immunity > vaccine immunity)
> This article is a preprint and has not been peer-reviewed [what does this mean?]. It reports new medical research that has yet to be evaluated and so should not be used to guide clinical practice.
That doesn't help if you die of the infection first, and COVID is extremely lethal among the demographics that most need the direct benefits of immunity.
That's a bit misleading. As long as the R value is above 1 the spreading is exponential. That follows directly from how the R-value is defined. What you mean is that the curve will take a sigmoidal shape for a while once the number of immune people has reached a certain threshold. In that case, the R-value is slowly approaching 1 again, and finally will go below 1 (which finally results in a curve that is not sigmoidal, of course). Other measures like lockdowns do the same to the curve, as is easy to observe by overlaying the measures over the curve, just not with an initial increase of cases that leads to hundreds of thousands of deaths. Estimated Infection Fatality Rates during the first Covid wave - where there was full hospital care available - ranged from 0.5% to 2%. So for Germany's 80M people that would be in the ballpark of 400,000 to 1.6M deaths - under medical care. Even if you take the original estimates of around 0.3% the results wouldn't have been flattering.
In a nutshell, the German government and every other country on earth is doing what you propose, except that they are vaccinating at the same time and try to keep the curves flat (but your use of "slow" also suggests this, so it's not clear what else you're suggesting).
That’s one possibility, but there’s no reason it has to converge to 1 (i.e. linear). R(t) = 100/t is also not exponential.
Of course, the epidemic curve described by that function would indeed bounded below by an exponential function on part of its range, but the same is true of any function with positive derivative, and calling for example f(x) = x^2 exponential for that reason makes the term meaningless.
This is presumably what the OP meant by “as long as R>1, the curve is exponential”. But this is literally equivalent to saying “as long as f’(x) > 0, f is exponential” which is just not a useful concept.
You're nitpicking out of context, I didn't give a definition of an exponential function, I was talking about the spreading of the Covid 19 disease. For example, the R0 value of SARS-CoV-2 was estimated 5.8 in the US and "...between 3.6 and 6.1 in the eight European countries"[1] Obviously, it depends on many factors like population density and contacts of persons/day, but generally the disease will start spreading exponentially with R_t values approaching this number or staying constant.
The initial spreading will be exponential in the beginning - as every actual curve illustrates - if the disease is left unchecked as OP suggested, until R_t values go down again due to immunity. That's all I meant to say.
Can you explain the difference between a function being "exponential in the beginning" and "having first derivative bounded away from zero at the beginning" ?
exponential in the beginning == this part of the function can be approximated by a function ae^xb where a>0 and b>1
vs.
first derivative bounded away from zero in the beginning == any function that increases, including linear functions with constant first derivative and polynomials with linear first derivative
Or do you think all increasing functions are the same..?
Consider for example the functions f(x) = x + 1 and g(x) = e^{ln(2) * x}. Then f(0) = g(0), f(1) = g(1), and f(x) > g(x) whenever 0 < x < 1.
It is easy to show that for any function whose derivative is continuous and positive at 0, there is an exponential function (properly translated such that they agree at 0) that has similar properties.
You should be specific about what properties you're talking about. What you're saying is that any function increasing function grows faster than some exponential function on a finite interval.
Still, you can observe f(x) on x ∈ [0, 1] and see that it is growing linearly.
And you can observe g(x) on ∈ [0, 1] and see that it is growing exponentially.
I do not see the value in discussing the rate of exponential growth of f. Where as for g, there is a parameter with value ln(2).
If data looks like f, don't try to fit an exponential function to it (whether it's a least-squares fit, or any other objective f > g.
Exponential implies a doubling of R value. Starting with an R value of 1.1 the length of time required for doubling of the infected population is longer than other factors which will lower the R value to under 1.
what would make sense is a steady and controlled Durchseuchung with specific protection of vulnerable people (like old and sick) - b/c the best immunity is gained by infection.
but Durchseuchung never sounded good - that's why that term got so popular. it sounds ugly and brutal. but it's what was happening all the time with many diseases in the past thousands of years.