The maths on masks and other Covid controls
In the middle of a major Covid outbreak, mitigations such as masks stop infections and help save lives. But over a longer period of time, the effects of public health restrictions may be much less pronounced. Keith Lynch explains.
The above may sound troubling. But everything you’re about to read is informed by the key statistic that defines the trajectory of a Covid outbreak, the Reproductive (or R) number.
You’ve likely heard this mentioned over the past two years. It came up frequently at last year’s 1pm press conferences when Delta infiltrated Auckland.
A simple rule of thumb defines Covid’s future: when the R number is above 1, an outbreak is growing. When it’s below, it’s fading.
There are several iterations of R. R0, or the basic R number, outlines how many people, on average, an infected person would pass the virus on to in a population with absolutely no immunity.
This number is important because it tells you just how infectious a disease is and therefore how difficult it is to control. The first iteration of Covid was thought to have an R0 of about 3. Delta’s was thought to be about 6.
R0 also tells us what proportion of a susceptible population needs to catch the virus before a Covid wave subsides, University of Auckland computational biologist Dr David Welch explains.
This brings us back to population or herd immunity. As the Mayo Clinic in the US outlines: ‘‘Herd immunity occurs when a large portion of a community (the herd) becomes immune to a disease, making the spread of disease from person to person unlikely. As a result, the whole community becomes protected – not just those who are immune.’’
Permanent herd immunity is not possible with Covid, because our protection against infection wanes over time.
But Covid waves end once enough people are infected and (for a period at least) the virus has nowhere to go.
I’ll illustrate how this dynamic works using an example from Welch.
‘‘If R is 2 at the start of an outbreak, meaning each case on average transmits to two others, by the time half of the population has been infected and has recovered, the virus will only transmit to one other.
‘‘That is because it ‘tries’ to infect two people but finds that, on average, one has already recovered and cannot be reinfected. In this example, the R number is now effectively 1 and infections will start to fall.’’
In the above example, the R is 2. If it were 6 or 8, a whole lot more people need to be infected before you reach that temporary immunity tipping point. (We’ll get back to this.)
R doesn’t tell us how deadly a virus is. If a virus imparted no symptoms at all it wouldn’t matter how infectious it was. But that’s clearly not the case with Covid.
Putting a number on Omicron subvariant BA.5’s R0 at this stage of the pandemic is close to impossible as it’s spreading in populations with some immunity. A number of those I spoke to for this piece suggested Omicron’s R0 wasn’t that far off Delta’s.
Four Australian academics recently published a piece where they estimated BA.5’s R0 was in the range of 6 to 10. (In recent weeks, a claim that BA.5 had an R0 of 18.6 did the rounds. This isn’t true.)
Is that all I need to know about R?
No. What we can better determine these days is Re. This tells us how many people an infected person passes the virus on to in real-world conditions where spread is constrained through immunity or public health measures that change behaviour (such as masking or gathering limits). So you start with R0 and end up with Re.
This number changes over time. In March 2020, New Zealand knocked the Re below 1 by shutting the borders and locking down. Therefore, Covid was eliminated.
But no country, other than China, has been able to knock the Re below 1 for sustained periods and avoid large outbreaks since the emergence of the Omicron variant.
You may be asking: how did New Zealand manage to keep Delta cases well under wraps over Christmas 2021 if it has a comparable R0 to Omicron?
The answer boils down to immunity. Omicron and its offspring may well be more transmissible than Delta, but its key advantage is its ability to sidestep our immune response.
The reason New Zealand enjoyed a relatively normal Christmas in 2021, even though Delta was in the community, was primarily down to mass vaccination reducing the spread of the virus.
Omicron spread like wildfire a month or so later (despite tighter restrictions) because it could evade that vaccine-induced immunity.
OK, so now what?
Imagine on one side there’s the virus (defined by its R0) and on the other there’s our efforts to fight back.
Ideally, countries want to stop a virus like Covid in its tracks, which means pushing the R number below 1 via public health measures. Just as we did in 2020, using lockdowns and closed borders.
We did the same around last Christmas without lockdowns, with vaccination likely keeping R well below 1.
The game changed entirely with the emergence of Omicron and its ability to evade the protection against infection (but thankfully not serious illness) brought on by previously our best player – vaccination.
This has led to an unpleasant Covid paradox. We are currently relying on infections to stop infections. As Professor Michael Fuhrer of the School of Physics at Monash University in Australia puts it: ‘‘An infection wave isn’t like an ocean wave (once you dodge it, it is past) – the infection wave ends because of infections.’’
This is the reality of 2022 – we had hoped vaccine-induced immunity would take the place of millions of infections to keep Re close to 1.
As I mentioned, Omicron’s high R0 means a lot of people need to be infected before an outbreak settles down, and the Re falls below 1.
This dynamic has prompted a number of experts to point out that, over longer periods of time, public health measures now have a limited impact on Covid spread.
But, at the same time, others (internationally and in New Zealand) continue to call for a high suppression strategy. The argument goes: if we wear masks, isolate when we’re sick and breathe cleaner air, the horrors of this pandemic can be somewhat squashed.
Yet, as Adam Kucharski, professor of infectious disease epidemiology at the London School of Hygiene & Tropical Medicine says, it’d be good for the public to know what these appeals actually mean.
Kucharski’s opinion is that many proposals for suppression (where Omicron’s R number is pushed below 1 and Covid dies out) are actually just mitigation (where the R number decreases but remains above 1).
I know this appears awfully academic. It’s not. If the R number can’t be pushed down below 1, Covid will continue to spread until a proportion of the population is infected.
So there’s nothing we can do?
This has led to an unpleasant Covid paradox. We are currently relying on infections to stop infections.
I didn’t say that. While we seemingly can’t push the R number below 1 in the midst of an Omicron onslaught without infections, we can blunt it somewhat.
And again ... the higher the R0 or the more infectious a virus, the more people who need to catch it before you reach a level where enough are immune, and the virus has nowhere to go.
Ideally you want to infect as few people as possible to reach that point, particularly in a wave like this winter’s, where hospitals are under severe stress.
‘‘One way is to gradually infect people, doing the best job of flattening that curve as you can, up until you reach that threshold,’’ Dr Stephen Kissler, an infectious disease expert from Harvard University, tells me.
‘‘And the complete opposite strategy is to let it rip where you have a big surge, and eventually you’ll reach that (temporary) herd immunity threshold, but you’ll actually surpass it.’’
If a wave peaks at a lower point, fewer people are infected as it retreats.
In both scenarios, the population achieves the immunity threshold, but the former means far fewer people are infected, which, of course, results in fewer hospitalisations and deaths.
Flattening the curve essentially means restraining the Re as close to 1 as possible.
This can be done by bringing about immunity through vaccination or other public health measures. Masks certainly have a role to play in any Covid duel.
How effective are masks then? Covid modeller Professor Michael Plank, of the University of Canterbury, pointed to a study from May looking at data from six continents that found (realistic and good) mask wearing could lead to a 19% drop in R.
Key takeaway: when we’re in the midst of a major wave, public health measures including masking can reduce sickness and save lives.
And in the long-term?
Over a longer period of time, the maths tell us the effects of public health controls are likely much less pronounced.
If countries cannot push the R number below 1 for a long period of time – that is, they can only mitigate, not suppress, Covid – then infections are essentially being delayed, not avoided.
Those New Zealanders who have evaded Covid so far aren’t home and hosed. They are – depending on their behaviour, of course – more likely to catch it in the next wave.
Now, you might be screaming at me, ‘‘Keith! The R number only reached about 1.3 during the recent BA.5 wave. Surely we can knock off a measly 0.4.’’
But the only reason the R number hasn’t been higher in recent weeks was because of all our immunity.
Imagine New Zealand managed to eliminate Covid again and keep it out for several years.
The problem would then be that in 2026 we’d essentially be starting afresh with Covid. When Covid came back, the R number would once again be about 5 or so – not 1.3 – because our collective protection against infection would have vanished.
Of course, in real life all our immunity will wane unevenly over time. Yet we are now essentially reliant on immunity – at this point mostly brought on by infections – to get Omicron’s R number down.
Numbers from Plank help illustrate the dilemma.
Let’s say the current iteration of Omicron has an R0 number of 5. Across a population this means 80% will need to be infected to get the Re back to 1, Plank says. (And if immunity only lasts about a year, 80% will need to get infected each year.)
Now imagine New Zealand masks up very well and manages to bump the R number down to 4 (a 20% drop). An R number of 4 still means 75% of the population need to be infected every year to push the Re back down to 1.
Plank uses the following (admittedly imperfect) analogy.
‘‘It’s a bit like being strapped to a pole with a bungee rope. Walking forward gets you further away from the pole but not as much as you’d like because some of your energy gets taken up in stretching the rope.’’
If Omicron’s R0 is actually 8, then 87.5% need to be immune to bring Re to 1. Then a 20% reduction from mask wearing takes the R to 6.4, meaning 84.4% of people need to be infected. Therefore, a 20% reduction via masking has even less impact.
‘‘This,’’ as Plank outlines, ‘‘is where the maths of endemic infectious disease is quite cruel in the face of attempts to reduce the average prevalence of a highly infectious pathogen: some of the benefit of the intervention gets sucked up in compensating for the reduced level of immunity.’’
British Covid modeller James Ward put it like this: ‘‘Actions taken to reduce transmission (ie lower R0) may have surprisingly weak effects on total infection rates. This is because they reduce infections, but also mean that more people are then susceptible, which pushes infection levels back up. The net effect is still a reduction in total infections, but a much smaller one than you’d expect.’’
Iwant to make a few things clear: masks and mitigations still have an impact. Using a mask, particularly a good one, will reduce the chances of you catching Covid over a particular period of time.
As public health expert Professor Michael Baker pointed out in a recent interview with Stuff: ‘‘If people isolated perfectly and wore masks perfectly, the pandemic would stop. If everyone did them well, the pandemic would stop or would trickle along at a very low rate.’’
At the same time we need to acknowledge people don’t behave perfectly.
Baker also makes this very valid point: While masks are imperfect, ‘‘we have to use all the tools because we have limited options’’.
When taking a bird’s eye view of Covid battle strategy, we can’t lose sight of the realities for New Zealanders who could get seriously sick or die. But at the same time, at a population level New Zealand should be aware of what the maths tell us about the future.
It would, of course, be much better to knock the R number below 1 via masking, working from home, better sick leave, ventilation and vaccination. And some will make the argument we can do that.
Baker also makes the argument that mitigations bring other benefits – for example, suppressing the flu, which is significantly less transmissible than Omicron yet still kills a lot of people.
It may be that the cost-benefit equation of masking or ventilation still makes sense – particularly in specific high-risk places like rest homes.
It may be that the reduction from 80% of people getting infected to 75% getting infected – as in Plank’s model above – is worth the cost.
It may also be the case that delaying some Covid infections, even if for a relatively short period, is beneficial particularly if new vaccines or treatments are imminent, Welch says.
And we know masks and other mitigations can certainly flatten larger peaks, protecting the health system.
But it’s increasingly hard to make the case that such measures will have a transformational impact on Covid – that they’ll push the R number below 1 in the long-term – given what Covid now is and what we’ve seen around the world.
So while masking may not be very onerous in a population, public health professionals and politicians will need to ask is it worth spending huge sums on, say, ventilation if it turns out it will reduce spread only by, say, 20%. Maybe it should be spent somewhere else?
Fuhrer put it this way in a recent social media post: ‘‘Suggesting there’s some simple magic bullet with negligible impact to normal life, and all we need to do is care enough to do it, is highly misleading.’’
The reality is pushing Re below 1 is a bit of a red herring, Plank says. Right now, yes, it’s below 1 but again only because of immunity. ‘‘The key issue is that the longer Re stays below 1, the harder it gets to keep it there because there is less and less immunity in the population. The bungee starts pulling you more and more strongly back towards the pole.’’
So where does that leave us? With a necessity for immunity. And right now that’s being brought on by infection. It’d be much better if it was brought on by improved and regular vaccination.