## What does the ‘R Rate’ really mean?

**Wednesday 21st Oct 2020, 12.07pm**

We’re all pretty used to hearing lots of pandemic-related terminology by now. I mean, last year, who knew what ‘social distancing’ meant? Not me! But it can be difficult to get to grips with what exactly all these new terms mean. For instance, what does the ‘R Rate’ really mean? We asked Emmanuelle Dankwa, a statistical epidemiologist from the Department of Statistics, to help us bust some myths!

**Emily Elias: **By this point, we are all armchair experts in Coronavirus, because we’ve been staying in our armchairs for a very long time. But as we decode our daily news alerts, we’ve decided to do a bit of myth-busting over the R rate. On this episode of the Oxford Sparks Big Questions Podcast, we are looking at infectious disease modelling. And we’re asking, what does the R rate really mean?

Hello. I’m Emily Elias and this is the show where we seek out the brightest minds at the University of Oxford and we ask them the big questions. And for this one, we’ve tracked down a researcher who knows the letter R inside and out.

**Emmanuelle Dankwa:** My name is Emmanuelle Dankwa and I’m a DPhil student in Statistics at the University of Oxford, specialising in infectious disease modelling.

**Emily: **Obviously, there has been a lot of talk about the R rate. Everybody seems to have a vague idea of what the R rate is, but what is the R rate? What does that actually mean?

**Emmanuelle: **Okay. So that quantity is actually a number and it is the basic reproduction number. It refers to the average number of new cases that an infected individual will give rise to in a population in which there is no immunity.

So I’ll give an example. If the R number associated with a disease in a particular community is, say, three, that means that if there was no immunity whatsoever in the population, we would expect each infected case to give rise to three new cases.

**Emily: **When I see news articles and things online, everybody seems to be referring to the R rate, but you said R number. The R rate and the R number, are those the same thing or are they different?

**Emmanuelle: **No, they aren’t the same thing. They are different. So R0, which is the other name for the basic reproduction number, it’s a number and that’s just what it is. When it is being referred to as a rate, it might be misconceived as though it is a quantity related to time. But it isn’t, it is simply a number. And so it doesn’t give us an idea of how long it will take for an infected person to pass a disease on to X number of people. It just tells us how many people will be infected.

**Emily: **So, how is the R number calculated? Let’s go on a journey, shall we? Well, friends, there are three big factors, and the first of which is friends and family and co-workers. Scientists call it the contact rate and that is how often we interact with each other and how close we get. Think of all of this rule of six business.

The second is about spreading. The likelihood or probability that our socialising and mixing in our communities with people in the community will actually give rise to the infection. And the third factor, how long is an infectious person contagious? If you’re contagious for two weeks, the R number is going to be a lot higher than if you’re infectious for two hours. So there are a lot of variables that scientists are trying to deal with, then?

**Emmanuelle: **Yes. Three main variables, although we could consider others.

**Emily: **We’re obviously in the middle of this pandemic, but shall we talk about some misconceptions about the R number?

**Emmanuelle: **Definitely.

**Emily: **I’ve got some myths for you and I’m hoping that you can separate fact from fiction. I feel like I should have some game show music or something right here.

Myth No. 1. If the R number goes above two, then we are totally screwed. True or false?

**Emmanuelle: **So if the R number exceeds one, what we will be experiencing is an increase in the number of cases. When the R number is less than one, we will see the number of cases decreasing. And if the R number is equal to one, there will be a stable incidence of the disease.

And so ideally to eradicate the disease or to decrease the number of cases, we would want R0 to remain below one. If R0 is 1.1, it’s not really good. But, of course, it is better than if the R0 was, say, 1.3.

**Emily: **And so if we hit two, are we screwed?

**Emmanuelle: **That’s not a good thing. We definitely aren’t totally screwed, but that isn’t what we would like to have.

**Emily: **And I guess at that point we would need to see much more severe measures to keep things like our human contact and our likelihood of infection, all those other variables, in check.

**Emmanuelle: **Exactly.

**Emily: **Okay. So Myth No. 2, then. If the R0 or R number is higher, it means that the disease is more severe.

**Emmanuelle: **No. And that is a straight false there. So R0 is not a measure of disease severity. It doesn’t tell us how severe the disease is. And so it will be incorrect to say, for instance, that when R0 is four, the disease is more severe than when R0 is two. The R number just gives us an indication of the number of new cases that will arise from a single case. And it says nothing about the severity or even the clinical characteristics of the disease associated with infection.

**Emily: **So false?

**Emmanuelle: **False.

**Emily: **The higher the R number does not mean the worse the disease?

**Emmanuelle: **Exactly.

**Emily: **Okay. So Myth No. 3, I’ve got for you. When we get that beautiful, beautiful vaccine in its beautiful glass bottle and we’re ready to pump it into the population, if we get a vaccine we could decrease the R number to 0 and be completely done with this pandemic. Is that true?

**Emmanuelle: **That is also a straight false. Now, as I explained earlier, the R0, the R number, is the number of new cases that an infected case will produce in a completely susceptible population. So the definition of R0 is related to a population that has 100% risk. Now, what vaccination does is it decreases the number of people at risk.

So, yes, we will be observing less cases if we have a potent vaccine, but that doesn’t reduce the R0, because the R0 assumes a completely susceptible population. What vaccination does instead is to reduce an associated number, which is the effective reproductive number. Let’s call it R.

So R is similar to R0, but R takes into account the presence of immunity within a population, as well as current behaviour. And so R can change and that is what is decreased when we have a vaccine. But R0 cannot change because of its definition.

**Emily: **You scientists, you love to name everything R. You couldn’t come up with a different name for it? Okay. So if then we have some immunity within the population thanks to the vaccine, how many people need to get vaccinated in order for it to have a widespread effect on the R rate?

**Emmanuelle: **Now, imagine for a second that the world now has an approved vaccine and we know that it will be ideal for everyone to receive this vaccine and be protected by it. However, this may not be practical in all contexts. There may be economic constraints, there may be logistical constraints, and some individuals may also have health conditions which put them at an increased risk of developing serious complications from getting vaccinated.

So what do we do? How can everyone be protected? Now, even though not everyone can receive the vaccine, it is possible to confer indirect protection upon some people in the population that have not been vaccinated if we have a good proportion of people that are vaccinated.

**Emily: **Do you have any examples of some work you’ve done in the past with other infectious diseases where this has been the case?

**Emmanuelle: **Yes, I do. And so we worked on Hepatitis A and we were looking at the spread of Hepatitis A within a community. Now, the policymakers wanted to institute routine vaccination schedules, but they did not have vaccines for everyone. And so they wanted to know which proportion of the population can be vaccinated in order to ensure that the incidence of Hepatitis A was either stable or decreasing.

We calculated the herd immunity threshold, which is the term given to the proportion of the population that needs to be vaccinated in order to make this work. And we arrived at 68%. So that means that, given our model assumptions, if we have 68% of the population being vaccinated against Hepatitis A, we would expect that there will be a decrease in the incidence of the disease or a stable incidence.

**Emily: **Okay. I think this might be my final myth. When this is all over, everything will just go back to normal. Is that true or false?

**Emmanuelle: **So if by normal you mean back to how it was before COVID, then I don’t believe everything will go back to normal. Especially in the area of innovation for solving infectious disease modelling problem. There has been lots of innovations, there has been lots of data generated.

And in addition to that we are seeing increased collaborations between different fields. So you have public health practitioners collaborating with clinicians and statisticians, and even economists. So some things may go back to normal, however, I don’t think that pandemic preparedness is one of those.

I think that COVID has taught us a lot of lessons. And we will be in a better place in the future to mitigate an outbreak, or better respond to an outbreak, as a result of the innovations and the increased collaborations and the large amounts of data that are now available to facilitate further research into the spread of infectious diseases.

**Emily: **This podcast was brought to you by Oxford Sparks from the University of Oxford, with music by John Lyons and a special thanks to Emmanuelle Dankwa.

And if you’ve got a big question, get in touch. You can find us on Twitter, on Instagram @OxfordSparks. We’re also, yes, still on Facebook. Plus we’ve got a website, oxfordsparks.ox.ac.uk.

I’m Emily Elias. Bye for now.