Op-Ed: What the coronavirus R-number is and how to interpret it

Posted May 23, 2020 by Tim Sandle
In the latest of the series of articles about the novel coronavirus, we consider the R-number: what it is and why it is important not to over-interpret it. In this context, long-term trends are important.
Some countries have made facemasks required as a precautionary measure against COVID-19
Some countries have made facemasks required as a precautionary measure against COVID-19
This is the eighth article in the series. Last time we looked at the risks surrounding return to work, and reviewed mitigating factors for those set to work in offices as well as some thoughts for home workers.
In the video below we return to some core thoughts about the coronavirus itself – the SARS-CoV-2 virus - and consider aspects of viral infectivity. Specifically, this video is about the R-number. We’ll also touch on how the virus infects.
To begin with, how infective is the virus? To understand viral infectivity, virologists use the basic reproductive number, which is the average number of other people an infected person could infect – the higher the number, the more people who could be infected. This is denoted R0 (R-zero or R-nought) or, generally by the general media, as ‘the R number’. However, it is not an exponential, only a potential in terms of infections.
R is a dimensionless number, it is not an infection rate and it does not relate to time or any other parameter (so R cannot tell us how fast an infection will spread through a given community). Scientists calculated the R number through mathematical models, where the accuracy is dependent upon the quality of the data imputed.
As a quick aside, many people have been watching or re-watching the movie Contagion. In this film, the methods depicted for calculating the R-number for the fictious disease were inaccurate (as The Vice outlines in an on-line article). This is because R is conflated as an exponential – which I’ll look at in a minute.
With COVID-19 this ‘R’ number is between 2.0 and 3.0. To put this into context, this is far higher than flu (which averages at 1.3) (these figures are according to the Royal Society for Biology). The larger number, the more likely an epidemic or pandemic and the greater the spread through a community. However, any quoted R value can only be considered in context and a time point in history.
Furthermore, HIV and chicken pox may have the same R number, but to contract HIV bodily fluids need to be shared; with chicken pox, the virus can contracted by breathing in particles in the air – the same R-number but, under general circumstances, chicken pox could be easier to contract.
Also, looping back to the reference to influenza, as a note of caution, the R values for past outbreaks may not be valid for current outbreaks of the same disease, so you should treat comparisons made by the media with caution.
This also relates to what I said earlier about R not being an exponential. You cannot look at an R-nought value of 2 and conclude this means there will be two people infected today, four tomorrow, eight the next day, and so on. This is because the R-number is just one part of a bigger picture – a picture affected by time, space, society, public policy (each of which is dynamic and subject to constant change). We also need to consider the means of transmission.
In terms of how deadly the virus is, estimates about the mortality rate vary, which is partly a reflection on the highly variable nature of data collection between countries, plus variations relating to testing regimes (countries like the UK have been very slow to introduce testing) and also with the accuracy of test kits.
There are also vast differences in relation to the social policies in put in place across each region. The R number can be modified through measures like social distancing together with other public policy interventions. This means R is not a biological constant, health policies can alter it.
Therefore, R data needs to be looked at over a long time period. This is the consequence of a lag in reporting the cases coupled with the natural delay in the onset of symptoms. We also need to consider what is probably a large number of asymptomatic carriers. R is also very general, it cannot tell us the difference in terms of infection rates between a hospital, care home, workplace, wider community and so on.
We also need to be more nuanced, such as considering differences between the number of people who are currently infectious as well as the recorded number of new infections. Consider this point - as past infection rises, the effective R falls as there are less people who could get infected, but the drop in R doesn’t mean a fall in those who are infected.
Hence, we also need to consider the proportion of the population that remains susceptible to infection. Virologists all this the endemic equilibrium.
This means it is quite challenging to get good estimates for the R number – and figures issued by governments should not be taken at face-value as single events, instead look at the trend.
The following video expands on some of the points raised in this article:
Some scientists recommend, in addition to R, factoring in the number of new cases per 100,000, across a given period of time.
If you want to read up on the R number, the book ‘Mathematical and Statistical Estimation Approaches in Epidemiology’, edited by Gerado Chowell and others is a useful starting point.