It’s complicated. Photo: Getty
It’s complicated. Photo: Getty

Covid-19March 11, 2021

How many people need to be vaccinated before NZ can get back to normal?

It’s complicated. Photo: Getty
It’s complicated. Photo: Getty

Chris Hipkins yesterday presented a Covid-19 vaccination timetable. But to reap the rewards, we need enough people to get a shot. Thomas Lumley does the maths.

The government plans to offer Covid vaccination, free, to everyone in New Zealand – no issues about residency or visa. This is what you’d expect; vaccinating other people makes you safer, so it’s important not to be picky about eligibility even if we have to be picky about priority in the short term.

Vaccination will be offered to everyone, but we can’t expect that everyone will accept. Some people won’t be eligible. Some will intend to get vaccinated but they have complicated lives and it won’t happen. Some will have understandable, if largely misdirected, concerns about the safety of this particular vaccine. And some people are just opposed to vaccines. In the past, New Zealand hasn’t been great at getting people vaccinated, as our outbreaks of measles and whooping cough have shown.

How many people do we actually need to vaccinate? We don’t know for sure; it’s complicated. We can look at what factors matter in that number.

The vaccine has two beneficial effects. Being vaccinated reduces your risk of getting sick and it also reduces the risk that you will pass the virus to someone else. The Covid vaccines are good at preventing illness in vaccinated people; the Pfizer/BioNTech vaccine is about 95% effective. The more people we vaccinate, the fewer people run the risk of ending up in a hospital bed if Covid does get loose in NZ.

Scientists don’t know as much about the vaccine’s ability to stop spread of the virus. It’s easy to count people who end up in hospital, and it’s not that hard to find everyone in a group who has Covid symptoms and test them for the virus. It’s a lot harder to find all the infections in people without symptoms – you need repeated PCR tests on at least a random sample of people, or antibody tests. It would be a lot harder to get 40,000 people to sign up to a clinical trial if they had to come back for frequent PCR test, and even weekly tests will miss some cases. The antibody tests will miss fewer cases, but will have some false positives.

We do have some data. First, the Pfizer/BioNTech vaccine currently being administered is the same vaccine used in Israel, and there’s new research studying its effectiveness there, published in the New England Journal of Medicine. The researchers estimate that vaccination (after two shots, and a waiting period) reduces your risk of “documented infection” with the SARS-2-CoV virus by 92%, and “documented infection without reported symptoms” by 90%. “Documented infection” means someone got a test and it was positive, and “without reported symptoms” means their medical records didn’t list any Covid symptoms. Neither of those is exactly what we want to know about – they both rely on people asking for tests and reporting their symptoms accurately – but they are still wonderful news!

Another study in England (which is going to be published in Lancet) followed up vaccinated healthcare workers. This is a much smaller study, but had a much better measurement of infection; like our MIQ staff, the the study participants were already getting repeated PCR tests. This study estimated 86% protection against any infection with the SARS-2-CoV virus, but with a fairly wide margin of error in both directions.

Taking these two studies together, there’s a reasonable hope that a full course of the Pfizer/BioNTech vaccine will reduce the risk of infection by 90% and, based on that, reduce the risk of infection followed by onwards transmission more than 90%. It might not be that good, but it’s unlikely to be very much worse and could even be better.

What does the 90% mean? Does it mean 90% of people get full protection and 10% get no protection? Does it mean every individual person gets 90% protection? Again, we don’t really know. It’s likely to be somewhere in between. In the Pfizer clinical trial, a small number of people had their immune response studied in detail. They all produced antibodies that neutralised the virus, and they all showed some sort of T-cell response. The vaccine doesn’t just fail for 5-10% of the population. On the other hand, it would be surprising if there wasn’t also some variation between people in how well it works. For what I’m going to do next, it doesn’t really make a difference.

What does all this mean for outbreaks? Think about Toby and Siouxsie’s Break the Chain animation. Each case infects an average of two or three other people, and the epidemic explodes, but if we can prevent some of the transmission, the growth slows or or the outbreak fizzles out. A year ago, when the animation was published, “breaking the chain” meant avoiding contacts, but vaccination works in much the same way.

If everyone is vaccinated, 90% of the links will be cut. Most people won’t pass the virus on to anyone; a few will pass it on to one person; a tiny fraction will spread to more. Instead of exploding, the outbreak will collapse. Most of the time a case won’t spread to anyone else; a few will spread to one other person; a tiny fraction will spread to more.

Cutting transmission by 90% would need nearly everyone to be vaccinated. What if only 50% were vaccinated? Well, suppose someone with the virus would have passed it on to two people, but one of them is vaccinated. Instead of two new cases, we get one new case. Or, in a super-spreader event, suppose they would have passed it on to 10 people, but half of them of them are vaccinated. Instead of 10 cases, we get maybe four or five or six cases.

If infected and vaccinated people were spread evenly throughout the country, 50% vaccination would reduce transmission by 50%x90%=45%. For every 100 cases before vaccination we would average only 55 cases after vaccination. Is that enough? Unfortunately not. Under the same approximation about even spread, the R number for the virus, the expected number of new cases for each existing case, is about 2.5. Reducing that by 45% gives about 1.4, which is still over the critical threshold of 1.0. Vaccinating half the population isn’t enough on its own, though it might be enough to stop an outbreak at level 2 instead of using lockdowns.

In fact, 50% reduction gives a picture a lot like the Break the Chain animation. To get R from 2.5 down to below 1.0 we would need more: at least 64% vaccination: 2.5x(1-0.64)/0.9=1. We’d like more than that, to get R down further and provide some margin of safety.

Things are more complicated than that, though. First, the B1.1.7 strain of the virus, the one responsible for the Valentine’s Day cluster, spreads faster than the original strain: R is higher, so we need more people vaccinated. If R was 3.5 before vaccination, we’d need about 75% of the population vaccinated just to get R to 1.

More importantly, the virus and the vaccine will not be evenly spread through the population, so the spread of an outbreak can’t be described by just one number like R. We’ve seen that the virus is more likely to escape to south Auckland, which has more border workers than other parts of the country. What matters to the virus isn’t the fraction of people in the country who are vaccinated, it’s the fraction of people exposed who are vaccinated. Vaccinating people in south Auckland, who are more likely to be exposed, has more benefit than vaccinating people randomly around the country.

A problem, though, is the uneven spread of vaccination that isn’t targeted. People who don’t get vaccinated tend to clump together, because there are reasons for not getting the vaccine. The clumping means that some communities will have higher than average vaccination rates and some will have lower than average. If 75% of the population is vaccinated, but only 50% of the contacts of a particular case are vaccinated, an outbreak will spread locally.

We see this happen with measles even in countries with good national vaccination programs, and the solution is to get high-enough vaccination rates not just on average for the whole country, but everywhere. Having, say, 75% or 80% vaccination everywhere will mean a higher rate for the country on average, perhaps 85% or 90%. That’s ambitious, but achievable. To get there, it’s important for everyone to have easy access to the vaccine itself and also to credible, culturally appropriate information about it.

And, as a final complication, while the vaccine works very well against the original strain and the B 1.1.7 strains, it’s only about 60% effective in preventing disease for a new set of emerging variants. We’ll probably need a second edition of the vaccine to handle these variants and finally crush the curve. We might even need booster shots over time, but there’s nothing impossible about that. Covid won’t go away entirely, but it will be an occasional scare, like measles or whooping cough, rather than the most urgent problem in the world.

The Spinoff’s science content is made possible thanks to the support of The MacDiarmid Institute for Advanced Materials and Nanotechnology, a national institute devoted to scientific research.

Mad Chapman, Editor
The Spinoff has covered the news that matters in 2021, most recently the delta outbreak. Help us continue this coverage, and so much more, by supporting The Spinoff Members.Madeleine Chapman, EditorJoin Members

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