servodude wrote:so now consider a series of days where an increasing population are being infected every day
- and then that stops, after the day of most infections no more people are infected
for every successive day there is a peak at the mode of the time to death distribution
- but it is over-layed and obscured/dwarfed by that of the day following
until the absolute peak falls at the mode of the distribution function after the day of maximum infection (because no-one is infected later)
The bold is not necessarily true. I can't explain it a 7-year old because they don't understand
counterexamples, but the following shows that the claim is not true.
Consider the case where
1% die 1 day after infection
2% die 2 days after infection
3% die 3 days after infection
4% die 4 days after infection
And the rest recover,
The mode for deaths is 4 days after infection.
Now let the number of infections be
99, 100, 101, 102, 103, 000, 000, 0000, 000, 0, 0
deaths will be
xx, xxx, xxx, xxx, 10, 10.1, 9.16, 7.17, 4.12, 0, 0
(The xxx are because those calculation requires infection data from days that are not given, long zeros are for alignment)
The peak deaths occur on the day after peak infections, not four days after peak infections.
The delay between peak infections and peak deaths depends on both the shape of the peak in infections and the shape of the peak in the mortality curve. For a lot of reasonable cases the delay will be the mode, but "reasonable cases" makes assumptions about the shapes of the peaks.
servodude wrote:but it still holds that the day of maximum death follows the day of maximum infection by the mode of the distribution function for infection to time of death
As above it does not hold.