The situation is becoming more dismal with exponential growth well under way
Almost five days have slipped by since I wrote that we needed a COVID19 reset. Since then, the infection trajectory has taken off, as I both feared and expected. The extent of the crisis must surely now be starting to become more apparent to the people of New Zealand.
My argument five days ago was that we needed to tighten restrictions across the northern North Island for a period of four weeks to give the vaccine a chance to catch up. Also, we needed to set hard borders at defendable points alongside the existing soft borders in Auckland, Northland and the Waikato.
Somewhere close to Waiouru is a defendable point in the North Island, with associated border points on broadly similar latitudes across the North Island. I reckon there are five or six border points to totally seal the two parts of the North Island. Cook Strait can provide the hard border between the North and South Islands.
There were over 260 online comments on that article and a consistent message from many was that Aucklanders would not stand for another period of Level 4. That may well be the case. But unless infection prevention measures are increased one way or another, then the outcome is inevitable.
What models can tell us
I have my own simple spreadsheet-based models of what lies ahead. They won’t be greatly different from the models of any of the professional modellers. All of the models essentially do the same thing, which is to analyse the evidence from overseas and explore how that might play out in New Zealand under different assumptions of the infection growth rate.
The fundamental of any disease modelling is to work out the reproduction rate of the disease, which can be expressed in terms of an ‘R value’, or alternatively as the compound rate of growth, or even expressed more simply as the doubling time.
Regardless of the specific metric, the fundamental assumption is that growth is exponential until some new factor is introduced that limits spread of the disease.
My preferred approach starts by looking at the rolling seven-day average of new cases to see how that is changing. Seven days is sufficient to provide dampening of the noise, but to still give messages that are timely. I also use five-day averages to pick up trends more quickly. I also look at three-day averages but typically there is too much noise in these to get any clear messages.
The data tell me that the seven-day average ending 14 October is 49 new cases per day, which is 71% greater than the average of 29 cases per day for the preceding seven-day period ending 7 October. Comparing the 7-day period ending 7 October to the period ending 30 September, cases increased 57% from 18 to 29. That number of 18 cases per day for the seven-day period ending 30 September had essentially not changed in any meaningful way for the three weeks before that.
Go back a little further, and the seven-day average dropped from 66 cases on 1 September to 17 cases on 10 September. That was amazing success for which the specific infected communities can take great pride. They certainly did their bit!
So, what we have is that until 10 September we were winning the battle in spectacular fashion once we caught up with the initial circulating infection, then we held the line for another three weeks through to around 30 September although without making further progress, but since then things have fallen apart greatly.
I note that Dr Caroline McElnay said in her 14 October briefing that the doubling time is now around two weeks. But the latest 71% increase between successive seven-day periods suggests it is less than that. Indeed a 71% increase in a week is approximately a compounding increase of 8% per day and this gives a doubling time of only 9 days.
If I do the same analyses but using five-day rather than seven-days periods, then the estimate of daily growth rate becomes 9% and the doubling time declines to 8 days. Regardless of the exact number, it is evident that the rocket ship has taken off.
I don’t want to scare people unnecessarily, and I happen to think that this latest doubling every eight to nine days may not be maintained, even without further community restrictions, as there could still be an element of noise in that. So, I will now be conservative and assume that the doubling period from here on is indeed two weeks.
That would mean that there are five doubling periods through to Christmas. The last two weeks leading into Christmas could expect to have about 1500 case per day. However, if I reduce the doubling period to 10 days, then the daily case numbers by Christmas increase to about 6000 per day. That demonstrates the power of exponentiation and the sensitivity to specific assumptions. The margins between very different outcomes can be very fine.
As the immunity level consequent to the vaccine increases, these numbers may be dampened somewhat. But the numbers are already moving too fast for the vaccine to do all the hard work. As for further lifting of restrictions in the next few weeks, that surely has to be off the table.
Looking at the R number
The most recent estimate provided in the daily official briefings in response to questions has been that the R number is between 1.2 and 1.3. However, that number needs updating using the figures for the last few days. My calculations are that it is currently at least 1.5 and could be as high as 1.7. It is definitely more than 1.3! That means that on average each infected person has been infecting more than 1.3 other people.
The reason for the lack of precision with estimating the R value from the growth in case numbers is that it is necessary to first make an assumption as to the ‘serial interval’, which is the average number of days between when ‘person A’ becomes infected and when the people that they pass it on to become infected. I am currently using estimates for serial interval of between 4 and 7 days, and they all lead to an estimated R value of 1.5 or above.
One of the flawed assumptions currently in the mainstream media is that a 90% vaccination rate is some magic number that will save us, or at least go close thereto. It will not. It seems to have arisen from modelling results by Sean Hendy.
As soon as Shaun Hendy presented his findings that day at the 1pm official briefing, I said to myself that his outcomes can only come from one very specific assumption. So, I downloaded the paper and sure enough it was clear that it came from the specific assumptions as to the R rate, and with this number constant across different groups of the population.
The figure of 90% is great for an initial target. But we cannot stop there. Our Asian population has now achieved over 98% first vaccination rate. The rest of us need to raise our sights.
Something that I have seen minimal mention of in the mainstream media is the impact of immunological naivety.
New Zealand, Australia and Singapore all had great success in keeping the virus out during 2020 and well into the first half of 2021. That means that most of us have had zero exposure to COVID coming into the last few months and hence have very poor natural immunity. The immunological term is ‘naivety’.
It is this immunological naivety that helps explain the very high infection rates that have recently occurred in New South Wales, Victoria, and Singapore. We have that same vulnerability in New Zealand.
In contrast, India had sero-positivity of around 68% by late June 2021. That meant that most people had been exposed to the virus with asymptomatic infections and it was this that eventually helped bring their pandemic under control.
A high sero-positivity rate in specific regions of Sydney may also explain why New South Wales rates have declined so much in recent weeks. But that may well change in coming months as the virus escapes to other unvaccinated demographic groups in New South Wales that still have immunological naivety.
The big picture
A key characteristic of the current situation in New Zealand is that most if not all epidemiologists are expressing considerable concern about the current trajectory. That will be because however they tweak their models, they cannot get the models to flatten the curve within current settings.
In contrast, the Government ministers in recent days have been tending to say that the current settings can avoid a health system crisis if we all just try a little harder to be good citizens and obey the current rules. Perhaps the Government has some catching up as to what is now upon us. On the current path, our health system is indeed going to struggle, and everyone needs to think about this.
Right now, in the crisis we find ourselves in, we cannot rely only on the vaccine.
There are of course no easy solutions. Also, there are lags between decisions and effects. Accordingly, daily case numbers within the coming week of well over 100 are probably already well baked in. The experience of Victoria, New South Wales and Singapore demonstrates starkly how quickly numbers can grow.
As time goes by, the range of options and outcomes narrows. It is not going to be nice, but within those constrained parameters, there is still merit in the idea that a ‘stitch in time saves nine’. We do need hard borders and we do need to obey the rules, whatever those rules might be. We need a circuit breaker. At the very least we need to be clear as to the implications of the present path.