Confused by R₀? Fear not! The bumbling biochemist is here to try to explain. Also fear not if you didn’t get the intended rhyming-ness of the intro – R₀ is pronounced “R naught” and I remember being in a math class where the teacher kept saying “R naught” and I had zero idea that he was talking about that little zero! In epidemiology (the field that studies disease prevalence/spread), R₀ refers to how many people, on average, an infected person infects.Aka the “reproduction number,” it can tell you about how “efficiently” a virus (such SARS-Cov-2, the novel coronavirus that causes the disease COVID-19) is spreading. Here’s why R₀ is all the rage in this coronavirus age…

Quick note: there are 2 ways in which R₀ is used, which can be kinda confusing. When characterizing a virus “in general”, scientists often use R₀ to mean “basic reproduction number,” which is how infectious the disease is in the worst case scenario (a totally susceptible community). But R₀ is more typically used to refer to the “effective reproduction number,” how the virus is actually spreading – which depends on us! and is the usage I’m going to be referring to from now on unless specified. It’s sometimes referred to as Re or just plain R. Also, here’s a great explainer from U of M:

The fundamental concept is this: if R₀ is greater than 1, the rate of new cases is increasing (in the overall picture sense you’ll have more newly-infected people tomorrow than you did today). If R₀ is less than 1, the rate of new cases is decreasing (you’ll have fewer newly-infected people tomorrow than you did today). And if R₀ is exactly 1, the rate of new cases is steady (you’ll have the same number of newly-infected people tomorrow as you did today). Only if R₀ is less than 0 is the virus on its way out – it needs an R₀ of 1 (each person infecting 1 other person) to sustain itself.

As I mentioned briefly before, R₀ is aka the “reproduction number” and it’s a term that’s also used when talking about more “conventional” reproduction – yup, epidemiologists adopted this term from demographic lingo for birth rate. That little zero (the “naught”) stands for the zeroth generation – like patient zero. But, instead of talking about the actual patient zero – the first person ever to get Covid-19, we can assign this “patient zero” to be any population at any time. So we can calculate R₀ for a city or a state or a country or the globe today or yesterday or last week, etc. And we’ll get different numbers. Because, although R₀ depends in part on how infectious a virus is (if you’re exposed to someone are you super likely to get it, like the measles, or is it harder to catch, like ebola?) which is represented by the “basic reproductive number” it also depends in large part on peoples’ behavior.  

Effective R₀ isn’t some fixed number. This is one aspect of the coronavirus that we as individuals actually have some control over. Even if you get infected, you can’t infect someone else if you don’t come into unprotected contact with anyone else. This holds true whether you have symptoms and know you’re infected or you don’t have symptoms and think you’re fine. And, if someone else has the virus, they can’t give it to their friends if they don’t see their friends. So, by doing all this painful social distancing, we’re lowering the R₀.

If viral jargon ain’t your jam, let me try an analogy –  imagine a pyramid scheme to sell something – tupperware’s kinda cliche, so let’s sell Erlenmeyer flasks (the glass tupperware of the science world) instead… So you have this scheme where a person gets 2 friends to sell flasks and tells each of their friends to recruit 2 friends to sell flasks. And each of those friends is tasked with recruiting 2 friends to sell flasks. You quickly end up with a lot of new flask sellers! But turns out flask-selling isn’t very fun… so each flask seller quits after working for some period of time. So the number of active flask sellers at any time depends on how many sellers each recruits, how long it takes them to recruit friends, and how long each person sells for. 

If each flask seller recruits at least one friend to sell flasks, you will always have flask sellers, even if people keep quitting. If each person recruits multiple flask sellers, you’ll keep getting more and more sellers. But, if people stop recruiting other sellers, one all the current sellers quit, you won’t have any flask sellers. And this is the equivalent of what we’re trying to do with the coronavirus. As much as I love Erlenmeyer flasks in real life, in this scenario I want to stop the flask selling!

The viral equivalent of how many friends each flask seller recruits is the R₀. The seller recruiting 2 friends is an R₀ of 2. And that’s bad news – you’re gonna get way too many flask sellers! 1 seller recruiting 1 seller corresponds to an R₀ of 1 – each infected person infects 1 other infected person. When R₀=1, the virus is sustaining itself at its present level. And, if the flask sellers don’t on average recruit one friend per current seller, that’s like an R₀<1 – you’re putting the coronavirus out of business!  

We want R₀<1, where each person is on average, infecting fewer than one person (this sounds silly, so it might be easier to think of it as something like 10 people infecting 7 people (R₀ = 0.7)). Even with an R₀<1, the total number of ever-infected people is only ever going to go up. But the number of currently-infected people will start going down. How fast depends on how fast the disease is spreading versus how quickly people are recovering. You can still end up overwhelming your hospitals & exceeding their capacity if people aren’t getting better more quickly than people are getting worse.

Speaking of speed, another term you may hear talked about is the “doubling time” – how long it takes for something to double. This is usually used to refer to a doubling in the number of new infections or the number of deaths. This depends in part on R₀ and in part on the “serial interval” – the average time between one person getting infected and that person infecting another person. For this coronavirus, it seems to be ~4 days. 

It’s hard to know a “true” R₀ because the data on who is actually infected is incomplete, etc. Similarly, trying to compare infection numbers isn’t helpful unless you take into account how many people are getting tested. It all gets really statistically, but if you want to go there, go here:

more Covid-19 resources:

more on topics mentioned (& others) #365DaysOfScience All (with topics listed) 👉 

Leave a Reply

Your email address will not be published.