Mathematical modelling can tell us much about outbreaks like Auckland's ongoing battle with Delta – but there's plenty of questions that it can't answer. University of Canterbury mathematician Associate Professor Alex James puts some context behind some of the figures and forecasts we read in the media.
First off: what are the indications that level 4 has worked so far?
Alert level 4 definitely worked, even with the highly transmissible Delta variant.
The big drop in daily case numbers after two weeks of lockdown showed the R value [the number of people that one infected person will pass on a virus to, on average] was below one.
So what can models help us with?
There are two or three modelling groups in Aotearoa tracking the current outbreak.
These models have different details, some have a very detailed structure and recognise demographic differences across Auckland like the number of essential workers in each suburb.
Others take a more general approach where they recognise these differences but don't include specific details.
One thing these approaches have in common is that they are stochastic, based on random processes and probabilities.
If an infectious person pops to the dairy it's not guaranteed they will infect someone but there is a chance or a probability they might.
These models consider all the events that could happen and predict the average number of cases we expect to see each day and the probability that there will be no more cases.
What are the limitations?
When case numbers are large, an average is fine, even though there will always be some variation.
When case numbers are low, the variation becomes more and more important.
The size of this variation is driven by the "K value".
This is the number that tells us how different everybody is and, in particular, how likely we are to be a superspreader or cause no more infections.
The original Covid variant was super-spready, so the majority of people didn't infect anyone else, not even their family, but a few people infected a lot of others.
We know with Delta, almost everyone in your household will get it, but outside the household we still see a lot of variation.
This variation changes in different environments: people on the West Coast interact in different environments to people in central Auckland, this changes K.
To estimate K and quantify this variation you need a lot of data on who infected whom which is difficult to get.
Can models still predict when an outbreak will end?
It's the K value, the variation, that can governs the tail of an infection and when we reach elimination.
Difficulties in estimating K translate to difficulties in predicting when we reach elimination.
When case numbers are low, each case is different and the people that really understand the details are the contact tracing teams.
Having worked as a mathematical modeller for more than 20 years I'd currently put more faith in Dr Ayesha Verrall or Dr Caroline McElnay saying the outbreak is almost contained than I would in any model prediction of elimination.
Are there signs that we're reaching elimination?
Seeing cases numbers jump from around 10 each day to more than 30 looks like a step in the wrong direction, but if all these cases were expected – maybe family members of an infected person or close work contacts - it may not be such a bad sign.
All these people expected to get the disease and were in very strict isolation long before they were infectious.
We know they were very unlikely to have infected anyone else.
The more worrying cases are those that nobody sees coming, the mystery cases, the person who arrives in hospital for something unrelated and turns out to have Covid too.
If the contact tracers can't track down the source of their infection that means there are other infected people out there that we don't know about.
Also, the cases that have been in the community while infectious.
Even under level 4 restrictions most of us still have opportunities to infect someone, especially if we are an essential worker.
It's this detailed information that drives the tail. Including it in models is almost impossible, but without it models can't give any predictions on how long it will take to be over.
Even with this data, models will only give a probability that the outbreak is over they can't predict exactly how long it will take.
Who can give us the best advice on when this outbreak may be over?
Models are great at predicting average case numbers under different situations.
They've proved invaluable to New Zealand's Covid response, but currently the people with the best information are the contact tracing and public health teams.
Through their meticulous interviews they are the best people to know whether a mystery case is likely to have set off another chain of transmission or if the virus has stopped there.
At this stage, they are likely to have better advice than modellers.
What could happen if Auckland moves to level 3 next week?
New Zealand's alert level 4 is one of the strictest lockdowns in the world.
Keeping it going for an extended period is hard for everyone, financially, mentally and socially.
But without it we might see more mystery cases and they will have had more opportunities to infect others.
The extra transmission events we would see at level 3 could be enough to push the R value back above 1 and case numbers would rise.
Are there any general predictions we can make about how long this outbreak will actually last?
For a while, alert level 4 was doing an amazing job at bringing case numbers down.
In the past few days that decrease has slowed considerably.
At this stage in both our previous large outbreaks we had fewer daily cases than we have now and we were also dealing with less transmissible variants.
However, these speculations aren't as useful as the in-depth knowledge our contact tracers have about the nature of the cases.
To move to level 3 and be certain of elimination, decision makers need to know about the details of the cases rather than just numbers and probabilities.
We can all help by doing our best to minimise our own transmission opportunities just in case we are the next mystery case.