...and after posting I was thinking about it again... and I did as you suggested and checked the numbers...
Major covid issues might not come through for 3-7 days after the infection and therefore you cannot compare todays hospitalisations to the number of people testing positive for infection today... Also, at the time of the start to your numbers (December 1), Omicron wasn't the most prevalent strain of the virus. This is starting to change and as pointed out the doubling rate (1.5 - 3 days for Omicron) is much quicker than Delta.
So lets expand on the numbers you have provided (and much appreciated too).
New Cases
19 Dec - 2,566 against 6 Dec - 208 cases (lowest point). That is a 233% increase in the daily increase in new cases.
Hospitalisations
19 Dec - 227 against 6 Dec - 152 cases which is a 49% increase in numbers. A nearly 50% increase in this number isn't alarming I guess...
At this point it is probably important to look at active cases. All the data here is accessible from
Recoveries and Active cases for COVID-19 in Australia | covid19data.com.au
(Yeah I cant see a problem with NSW numbers - looking like its going to be manageable)
(Vic increasing but not as exponential as NSW yet their hospitalisations are growing much faster - anyone has thoughts on this?)
NSW active cases (header provided for clarity)
Active cases 1 19/12/2021 14,050 2 18/12/2021 11,760 3 17/12/2021 9,659 4 16/12/2021 7,647 5 15/12/2021 6,233 6 14/12/2021 5,179 7 13/12/2021 4,677 8 12/12/2021 4,366 9 11/12/2021 4,058 10 10/12/2021 3,683 11 9/12/2021 3,372 12 8/12/2021 3,196 13 7/12/2021 3,060 14 6/12/2021 3,036 15 5/12/2021 3,043 16 4/12/2021 2,960 17 3/12/2021 2,851 18 2/12/2021 2,692 19 1/12/2021 2,633 20 30/11/2021 2,595 21 29/11/2021 2,669 22 28/11/2021 2,703 23 27/11/2021 2,699 24 26/11/2021 2,308 25 25/11/2021 2,619 26 24/11/2021 2,596 27 23/11/2021 2,580 28 22/11/2021 2,641 29 21/11/2021 2,677 30 20/11/2021 2,734 31 19/11/2021 2,789 32 18/11/2021 2,867 33 17/11/2021 2,864 34 16/11/2021 2,866 35 15/11/2021 2,910
So assuming it might take 4-7 days before someone might need to attend hospital, I will compare the data from 5 days prior.
19 Dec - 227 Hospitalisations / 14 Dec - 5179 current cases = 4.38%
6 Dec - 152 Hospitalisations / 1 Dec - 2633 current cases = 5.77%
The slight difference might be Omicron being less damaging to the host with a change from Delta to Omicron now.
If you extrapolate this out, 19 Dec - 14,050 Current Cases * 4.38% = 615 hospitalisations on 24th December. I think we will reach our tipping point around 23rd December (515 hospitalisations).
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...and after posting I was thinking about it again... and I did...
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