Stay in Lockdown
Is the curve Flattening
Or is it Fattening
Do you have the nerve
To fatten the curve
COVID’s not Flattering
Note: The prime minister confirmed yesterday that New Zealand will not go out of Lockdown level 4 early.
Some sources think New Zealand’s number of cases have peaked
(passed the midpoint?).
“New Zealand has 82 new Covid-19 cases – and Director-General of Health Ashley Bloomfield has raised the possibility cases may have peaked.”
“It may well be it [Covid-19] has peaked now.”
“The number of cases does seem to be levelling off,” Bloomfield said.” See:
Questions to consider:
- Is the curve flattening?
- If the number of cases has peaked/ passed or is near the midpoint (personally I don’t think it has), could this mean that NZ could be out of Lockdown in less than 4 weeks?
- If NZ is nowhere near the midpoint yet, how long will it be until the midpoint is reached?
- Can regional releases from Lockdown work?
Q1. Is the curve flattening?
We will consider the following two graphs:
The bar chart shows the daily number of cases. Clearly this is not yet showing a downward trend. This may happen at any time.
Note: To view the images larger, Right-Click on an image and open it in a new tab.
The second chart shows the cumulative number of cases.
The blue line shows the straight line mentioned in previous posts.
The red line is marginally non-linear. We can see today’s number of cases and yesterday’s have risen above the straight line and today’s are similar to the red curve.
The equation of the red curve is:
If we had used 1.0 instead of 1.005 as the exponent/power/index, the curve would be linear (a straight line).
It is very likely that we will need to adjust the 1.005 higher within the next few days.
However if the exponent remains close to 1, it may be simpler to use a straight line (instead of the red curve) with a slightly bigger gradient than the blue line to more closely match the end points (rather than the least squares approach used for the original blue line) or else (round) the maximum gradient. e.g. for Day 25 and Day 38 we could use:
y=72.1x – 1700.5
The idea is to sandwich the number of cases between the two straight lines to get a range to estimate cases in the future.
There are less than 200 cases more using the red curve than using the original blue straight line 105 days (15 weeks) from Day 25 (23 March).
Using the two straight lines gives a result about 30 greater than the curve estimate.
We can use the blue line (the original straight line) as an indicator of how well the case curve is flattening.
Recall the equation of the blue straight line is:
y=70.65x – 1681.27 (2dp)
The number of deaths we could conclude would need to be not above this line to have a good indication that the curve is flattening and that the midpoint has been reached.
Today is Lockdown Day 11. While I never expected the number of deaths to be linear (a straight line), we need to look at the number of cases in future days to determine if the curve is flattening.
The rise of the number of cases above the straight line indicates that the curve is currently not flattening as well as it has been.
Regardless, with only 11 days in Lockdown, it is too early to draw any conclusions.
The curve was always expected to be exponential (power of e) or at least quadratic before flattening significantly.
New Zealand has been very lucky so far with only one death and 1039 cases to date.
We conclude it is unlikely that the midpoint has been reached yet.
We will wait until today’s Australian figures before we comment further on this and Question 3 in another post.
Q2. If the number of cases has passed or is near the midpoint (I don’t think it is), could this mean that NZ could be out of Lockdown in less than 4 weeks?
Once we consider the midpoint may have been reached, we would need to look at least for another week for confirmation. The outbreak would still not be over for more than double the time to the midpoint.
One quarter up to one-third of infected people may be asymptomatic (not showing symptoms) and hence may not have been tested, and may still possibly infect to others. The first confirmation that the novel coronavirus could be transmitted by asymptomatic people came in February. See:
Maybe up to one-half of infected people may be asymptomatic- 48% from Japanese cruise ship data:
“A total 255 (48%) of the confirmed cases were asymptomatic when the respiratory specimen was collected. Of these, 8 were crew and 247 were passengers.” See:
National Institute of Infectious Diseases. Field Briefing: Diamond Princess COVID-19 Cases. NIID (Government of Japan). 19 February 2020. https://www.niid.go.jp/niid/en/2019-ncove/9407-covid-dp-fe-01.html.
“Dr David Buchholz: Right now in New York, we’re only testing the sickest possible people. So we have no idea. However, there was a study in Iceland, which tested [a large segment of its] population, and 50% of the people who tested positive had no symptoms.” See:
We would therefore need to be in Lockdown for at least another 14 days to ensure that the outbreak is over since asymptomatic people can only be identified by contact tracing infected cases and testing their contacts.
While randomised testing may pick up some asymptomatic infections, contact-tracing would still be required to locate anyone they may have infected.
We conclude that the whole country should not be out of Lockdown within the initial four weeks of Lockdown. It would be unwise for the whole country to come out of Lockdown early.
Some people consider that regional releases from Lockdown may be possible. However
“West Auckland liquor stores have stopped selling spirits and pre-mix drinks during the lockdown because too many people were travelling from far away to buy them.
The move was expected to ease the huge queues that have been snaking around several blocks outside Trusts West Auckland stores as thirsty Kiwis geared up for the second weekend cooped up in their homes.” See:
I may cover this more in another post.
It may be possible to allow some business categories (not currently considered essential) to reopen before the end of the Lockdown period. A limited number of online businesses have already been allowed to trade again.
See my next post for further considerations in particular for Question 3.
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