• Supermarkets to close on Good Friday, will open on Easter Sunday
• Fifty eight new coronavirus cases today - total now 647
• Nearly 10,000 reports of suspected lockdown breaches made
• Revealed: Covid-19 clusters double in NZ - here are the regions hit
• Three police officers in self-isolation after being spat on by person with symptoms of Covid-19
Fourteen thousand fatalities. Two-thirds of the population infected.
Up to 32,000 needing hospital care. Four thousand Kiwis potentially needing ventilators.
The numbers constantly flowing out of New Zealand's best modelling teams are big and scary, to say the least.
They reflect the enormity of the threat which could face the country if its unprecedented shut-down proves to have been made too late.
But there's still much that the researchers producing these figures don't know about Covid-19, or how our own behaviour might squash those numbers down.
The figures are found in six separate modelling reports - some dated back to February - which the Government dumped at once this morning.
Each of the reports tells a different story, based on what data the researchers had at the time and what particular scenarios they explored.
Weeks before the Government moved to lock down the country, Otago University researchers used Australian data to estimate that rampant spread of Covid-19 could infect 65 per cent of the New Zealand population, although only a third would experience symptoms.
On March 16, the same team offered some further figures: Nearly 150,000 Kiwis might get sick enough to need hospital, and about 36,600 might need treatment in an intensive care unit.
About 27,600 could die – the vast majority of them being older than 60, with Māori, Pacific Islanders and those living in deprived areas being particularly at risk.
The week that Prime Minister Jacinda Ardern made the call to shutter New Zealand for four weeks, two more reports hit the desks of ministry officials.
One repeated the numbers set out in the March 16 draft report.
The other, which carried a higher level of certainty, indicated that if the country's dramatic step to stamp out Covid-19 failed, and Covid-19 was allowed to spread uncontrolled, New Zealand might lose up to 14,400 people.
That was roughly the equivalent of Havelock North's population.
Depending on how easily Covid-19 spread from one person to another – and for how long authorities forced people to reduce contact with one another – between 44 per cent and 66 per cent of Kiwis might become sick and between 22,000 and 32,000 might need to go to hospital.
Somewhere between 5540 and 8000 might need a bed in an intensive care unit and between 2770 and 4000 might need a ventilator to help them survive.
The modelling even included a "worst day", in which some 11,200 people would need to be hospitalised and 2800 would require critical care.
New Zealand's meagre ICU capacity – a stocktake found there were merely 200 beds in public hospitals, although officials say that can be trebled – would begin overflowing by just the 92nd day of an epidemic curve that kept climbing.
The University of Otago team hasn't been the only group of researchers crunching the numbers.
Scientists from Te Punaha Matatini ran models that showed that without a lockdown and other strict measures around 80,000 Kiwis could die, and up to 89 per cent of the population could become infected within 400 days.
Any relaxing of those measures could result in hospitals being overwhelmed with a surge six times that of hospital capacity within a few months.
That capacity would be exceeded at the point that 40,000 people contracted the virus.
Under the best-case scenario, assuming that New Zealand's promising approach of elimination failed to stamp out the contagion, and that the country had to stay locked down, the death toll could be as little as 20, and hospital capacity might remain within limits for more than a year.
The maths behind the models
All of these estimates have been worked out using what's called an SIR model, which allows researchers to simulate what happens when someone in a given community catches a disease.
The "S" stands for the people who are susceptible to the disease – or everyone who hasn't had it yet – and the "I" is people who currently infectious.
The "R" represents the people who are recovered, meaning they've had the disease but are no longer infectious and now have some immunity.
After someone catches the disease, they move from "S" to "I" and can now pass the disease to those who are susceptible, but not those who have recovered.
Once they recover they move from "I" to "R". Ultimately, the model tells us how an infection spreads across a population.
One of the key parameters it works off is something called the basic reproduction number, or "R0", which is the average number of people who will catch the disease from an infected person.
Some of the University of Otago modelling has given some particularly rosy figures.
Heavily suppressing Covid-19 over nine months, for instance, could result in just seven deaths – but these were working off the implausible assumption that the virus had an R0 value of 1.5.
Rather, Covid-19's R0 value is thought to be somewhere between two and three – and thus the potential case rates are higher.
Professor Shaun Hendy, the University of Auckland physicist who heads Te Punaha Matatini, described SIR modelling as a "kind of old-school, standard method".
"In this case, SIR models give us long-term scenarios, but with each one, we have to make assumptions about what the Government is going to do."
University of Otago researchers had been using slightly more complicated SIR models than his team, with more up to date data, which explained some differences between the two groups' models.
A new model
This week, Hendy's team is working on a new type of model.
It's called an individual-based or stochastic model, which could overcome some of the obvious weaknesses with SIR models.
One was the assumption that anyone in a population could effectively infect anyone else on any given day.
"We can think of an SIR model like pouring milk into a cup of coffee and stirring the milk," Hendy said.
"Eventually, the milk gets everywhere. But when we look at individual-based models, we can start to look at an individual-based structure.
"You don't meet everyone every day in the country, but some small fraction of the people.
"These models allow us to put in social structures and other bits of information, then you can better guess what the R0 values are.
"Mathematically, both the SIR and stochastic models end up being roughly equivalent – but with stochastic ones, you can play around with the data and do more than you can with SIR models."
One example was modelling how R0 values would change before and after Kiwis were ordered to stay at home.
So what ingredients went in the mix?
Hendy's colleagues have already been drawing on Statistical Area 2, or SA2, data, which is collected by the Government.
This represented blocks of between 1000 and 4000 people in city and district council areas, and often fewer than 1000 people in rural and urban areas.
"Basically, it allows you to see how the population of a suburb like Grey Lynn goes up and down every hour," Hendy said.
"In the morning, it decreases as people go to work.
"At the same time, the population of the Auckland CBD increases. So the idea is to estimate how many more contacts people might have because they've gone from Grey Lynn to the Auckland CBD, where the population density is much higher."
But his team wanted to delve deeper.
They're looking at using aggregate-level cellphone data to better map how people move from place to place.
Anonymised bank transaction data could give them a clearer picture of how widely people under lockdown are travelling to their local supermarket, where they're more likely to encounter other people.
"That would give us a little bit of a sense of one of the remaining ways that this disease might be transmitting."
Hendy hoped the simulations might also tell us what testing strategies are working best.
"While we've got a basic individual model up and running now, we want to combine that with the case data that's coming out each day, along with clinical data that we are getting from overseas.
"By next week, we are hoping we'll be able to say how well the containment is working."
But one of the inherent problems with case data was it was old by the time it came out.
"It really just represents what has happened about a week ago. Sometimes some of what shows up reflects stuff that happened 10 days ago, when a case first became infected."
After this lag in the system had been cycled out, and numbers were more reflective of a New Zealand under lockdown, then we'd have a better idea of what the bold measure has achieved.
Caveats and question marks
No model is perfect - and Hendy said people needed to be aware of some other issues with them.
For instance, much of the data pouring out from around the world was coming from healthcare systems under stress, with the potential for bias.
Hendy and his team were themselves working under unusual pressure.
"Usually we'd develop these things over a timescale of years. Even the review process would take three or four months, but we simply don't have that luxury right now."
Further, many of the models had frameworks built for mapping the spread of influenza.
That had some similarities with Covid-19 - but also some obvious differences, especially when it came to how much less contagious and lethal the flu was.
Before an enormously influential paper out of Imperial College London was published this month, many nations, including New Zealand, were trying to tackle Covid-19 through a flu-based approach of "flattening the curve".
"So, some of the factors that we think about when it comes to mitigation, we're still extrapolating from what happens with influenza," Hendy said.
And then modellers mapping scenarios months or years in advance didn't know how peoples' behaviour might change, or whatever big steps the Government might take.
"We're doing our best to come up with plausible scenarios that we can test in models, but really, we don't know exactly how many Kiwis are staying home, and how many are going to the beach.
"If people simply ignore the lockdown, our data might turn out to look like those worst-case scenarios we've put out there."
Was there the possibility we were only seeing the tip of the iceberg?
One paper by Oxford University researchers put forward a dramatic hypothesis that half of Britain had already been quietly infected – and was instantly challenged by epidemiologists around the world.
"I don't think we're looking at anything that extreme," Hendy said.
"But we're almost certainly not seeing the full picture, and the daily case numbers we are getting are only coming from the testing criteria at the moment."
Widening that testing criteria – or running random testing in the community – could help fill in some of the gaps missing in modelling.
"But the problem with broadening the criteria, of course, is that everybody will rush in and want to get tested."
"So people should ultimately be aware that we are making heroic guesses about how some of the current measures we have in place will work. They might work better than we expect, or they might not be as effective as we expect.
"Eventually, we'll see that in the outcomes, but right now, as researchers, we are trying to make our best guesses."
At the same time, one of the public health professors behind the Otago modelling, Nick Wilson, said the models were still more robust than those his colleagues used for making calculations around issues like tobacco taxes.
"The economy is actually a much more complicated thing than a virus."
He compared his team's models to ones Nasa might design to help it safely land space probes on Mars, amid a blizzard of potential variables.
"You create a model, then you run it many times until you can get it accurate," Wilson said.
"So the virus is a little bit like that space probe to some extent. Some of the aspects, like the spread of infection you are going get if the epidemic curve grows out of control, can be accurately worked out.
"The weak side of the model is how humans are responding. Things like social distancing, lockdowns, changes in hygiene behaviour… it's difficult to know how long this can be sustained for because we have very little experience with this."
Why we model
For the Ministry of Health's director-general, Dr Ashley Bloomfield, the numbers all pointed to one critical fact.
"The modelling shows that without the actions currently being taken, the uncontrolled spread of Covid-19 would exact a high price in New Zealand in terms of its impact on our health services, including our intensive care units, and deaths," he said.
"What is consistent across all the models is that we had a stark choice – let the virus spread unchecked and see large numbers of New Zealanders get sick, our health system overrun and many people dying, or taking firm measures to save lives."
Bloomfield said all the scenarios showed an unacceptable level of deaths in New Zealand without strong action – and such scenarios were already tragically playing out overseas.
"Even with the sorts of strong measures we have in place to stamp out the virus the modelling is still predicting there could be a heavy toll on our health system and loss of life," he said.
"That shows how seriously we need to take the virus, stick to the rules of the lockdown and maintain measures that reduce the risk of the virus entering the country."
There had been some other international modelling studies which, while based on similar information, were specific to their country and stage of the epidemic.
For New Zealand, there was the real hope that our isolation, low population density and limited mass public transport might help stem the impact.
"There is broad support from the modelling that containing the spread of the disease is crucial to reduce and delay the impacts of the epidemic on human health and to allow health systems to prepare," Bloomfield said.
"The impact and effectiveness of the measures announced by the Government – our lockdown, closed border, internal travel restrictions, work closures, excellent hygiene practices, greater physical distancing and testing, contact tracing and isolation – all play a critical role in reducing the impact on the health and wellbeing of New Zealanders."