*With all the questions in the news we asked experts Matt Keeling and Sam Moore, epidemiological modellers at Warwick University and members of the JUNIPER modelling consortium, about herd immunity and COVID-19 vaccines. Here is what we learned.*

If you are nervous about vaccination for yourself or a vulnerable loved one, you might think that herd immunity will help you out. The idea here is that not everyone in a population needs to be vaccinated to force the *R* number down to below 1 and the epidemic into decline.

Click here to see the entire COVID-19 vaccines FAQ.

As we saw in a previous *Plus* article, only a proportion of 1-1/*R*_{0} of the population need to be immune to achieve herd immunity, where *R*_{0} is the *basic reproduction number* of the disease. For COVID-19, a reasonable estimate for *R*_{0} is between 2.8 and 3, so 1-1/*R*_{0} translates to around 64% to 67%.

This means that for a vaccine that's 100% effective, so everybody who gets it is then immune, only at most 67% of people need to be vaccinated to achieve herd immunity. For a vaccine that is only 95% effective, which is the case for the Pfizer vaccine, the percentage rises to 70% but that's still pretty good. Thus, even if you yourself don't get vaccinated, as long as enough other people do, you're quite safe. (See below for the relevant herd immunity calculation.)

Herd immunity only works of the vaccine stops transmission.

Except that you might not be. The problem is that we don't know as yet whether the vaccines developed for COVID-19 actually stop transmission of the virus, or whether they only stop people developing the symptoms. If infection itself is blocked, the vaccine is unlikely to be at the same 95% level of effectiveness championed by the trial.

Of course, if we can vaccinate all the most vulnerable people, stopping symptoms may be good enough — it will stop people getting awfully sick or dying, and stop hospitals being overwhelmed. But until we know if, or to what extent, the vaccines stop transmission as well, the herd immunity calculation above is out of the window. To make sure you're safe from the disease you need to take the jab yourself. (That's quite aside from the moral problem that goes with letting others do something you don't want to do yourself and then reap the benefits through herd immunity.)

It may take a long time to vaccinate enough people to achieve herd immunity, during which time vulnerable unvaccinated individuals will remain at risk.

The other issue is that, even if a vaccine stops transmission, the path to herd immunity is slow. It may take a long time (several months) to vaccinate enough people to achieve herd immunity, during which time vulnerable unvaccinated individuals will remain at risk. There is also the concern that if the vaccine is not evenly spread throughout the population, it can leave pockets of susceptibility which can generate mini-outbreaks.

Finally, more sophisticated models of how herd immunity works need to take into account the age structure and the risk structure of the population. The impact of a vaccine in blocking transmission is greater if the individual protected would have made many contacts and therefore could have spread the infection to multiple people. In contrast, the impact of a vaccine in stopping disease is greatest if it is given to those who are most vulnerable (see here to find out more).

In summary, then, we should not rely on herd immunity to get us onto safe territory: it's very easy to protect those who get vaccinated, but very hard to protect those that don't.

*This article is part of our FAQ about COVID-19 vaccines, put together with expert advice from epidemiological modellers Matt Keeling and Sam Moore. Click here to see the other questions.*

### The basic herd immunity calculation

As we saw in a previous *Plus* article, only a proportion of 1-1/*R*_{0} of the population need to be immune to achieve herd immunity, where *R*_{0} is the *basic reproduction number* of the disease.

If a vaccine has an effectiveness of *x*%, then this means that only *x*% of people who receive it are immune. To achieve herd immunity we therefore require that *x*% of the proportion of people who are vaccinated translate to a proportion of at least 1-1/*R*_{0} of the population. In other words,

where is the proportion being vaccinated. This gives

Substituting gives

For a vaccine that is 95% effective we therefore need to vaccinate at least a proportion of

people, which equates to 67%.

For a vaccine that is 70% effective we need to vaccinate at least a proportion of

people, which equates to 91%.

* Return to our COVID-19 vaccines FAQ*

### About this article

Matt Keeling

Matt Keeling is a professor at the University of Warwick, and holds a joint position in Mathematics and Life Sciences. He is the current director of the Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER). He has been part of the SPI-M modelling group since 2009.

Sam Moore is a postdoctoral research associate who has been working on vaccination modelling for Covid-19 after joining SBIDER within the University of Warwick at the start of the pandemic earlier this year.

Sam Moore

Both are members of JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium. It comprises academics from seven UK universities who are using a range of mathematical and statistical techniques to address pressing question about the control of COVID. The universities are Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster. You can see more content produced with JUNIPER here.

Marianne Freiberger and Rachel Thomas are Editors of *Plus*.

## Comments

## What happens if the vaccine

What happens if the vaccine is 62% effective such as the Oxford-Astrazeneca Vaccine? Then assuming R0=2.8 then we have a proportion of 225/217 which is more than 1. How is this possible? How does this translate? Does this mean that we need to vaccinate more people than the entire population?

## Good point! For every value

Good point! For every value of R_0 there's a minimal efficacy a vaccine has to have for it to be possible to achieve herd immunity (assuming the vaccine actually stops transmission). For R_0=2.8 this means efficacy needs to be at least 1/(1-1/R_0))=0.64 which equates to 64%.