Thomas Lumley runs the numbers on herd immunity and vaccination:

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.

The government said the borders open at the end of the vaccine roll-out. The new strains then mean we need 75% vaccination rates.

The government is looking to make vaccination a condition of employment for frontline workers. But that hardly seems strong enough. A public health order could also make it a condition of working at the front-line, overriding any other clauses in employment agreements.

Recall the pieces (here and here) at Newsroom in 2019 by Eloise Gibson showing that piles of hospital staff didn’t have measles vaccinations in the middle of a measles epidemic. At least 20 DHB staff caught measles. Who knows how many were vaccinated; only two DHBs bothered to track whether their staff were vaccinated.

A small-sample survey commissioned by MoH last year suggested pretty high rates of vaccine hesitancy in some communities, but that it could be overcome if safety were sufficiently assured. About half of those hesitant said it came down to safety assurance.

It’s going to be tough to hit 75% without some decent effort. The safety record overseas, with millions of doses safely delivered, should help.