6 ms·

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

by 13415 5y ago

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).

ipaddr 5y ago
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.
School-Cotton 5y ago
> As long as the R value is above 1 the spreading is exponential No, this is only true if the R value is constant in time. Not all functions with a positive first derivative are the exponential function.
- gugagore 5y ago
  Are you talking about a situation where the R value approaches 1 from above? e.g. R(t) = 1 + 1/t? Because otherwise the growth is indeed exponential, yeah?
  - School-Cotton 5y ago
    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.
    - 13415 5y ago
      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. [1] https://www.sciencedirect.com/science/article/pii/S0022519321000436 https://www.sciencedirect.com/science/article/pii/S002251932...
      - School-Cotton 5y ago
        Can you explain the difference between a function being "exponential in the beginning" and "having first derivative bounded away from zero at the beginning" ?
        13415 5y ago
        How about this: 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..?

by 13415 5y ago

ipaddr 5y ago

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.

School-Cotton 5y ago

> As long as the R value is above 1 the spreading is exponential No, this is only true if the R value is constant in time. Not all functions with a positive first derivative are the exponential function.

gugagore 5y ago
Are you talking about a situation where the R value approaches 1 from above? e.g. R(t) = 1 + 1/t? Because otherwise the growth is indeed exponential, yeah?
- School-Cotton 5y ago
  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.
  - 13415 5y ago
    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. [1] https://www.sciencedirect.com/science/article/pii/S0022519321000436 https://www.sciencedirect.com/science/article/pii/S002251932...
    - School-Cotton 5y ago
      Can you explain the difference between a function being "exponential in the beginning" and "having first derivative bounded away from zero at the beginning" ?
      - 13415 5y ago
        How about this: 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..?