By Grant Jacobs 29/01/2020


There are a few misunderstandings about the coronavirus outbreak from Wuhan getting around. Below is a short explanation of one of them: what is R0, and what does it mean. Current estimates for R0 centre around the mid 2s—call it 2.5 or thereabouts—not the higher values some are scare-mongering online.

In following posts I may explain other things—if there’s something you’d like covered, let me know.

What is R0?

R0 (R-naught) is the basic reproduction rate, how many other people one infected person typically infects. I’ve emphasised typically as it is an average of many different scenarios. R0 estimates also assume everyone is susceptible to the disease.

You’ll often see these quoted as a single number. In practice a range of scenarios are played out in modelling, with a range of values for R0 estimated. The single figure offered is the ‘most typical’ value you’d expect, but the range of values matters, too.

Current estimates

There are several estimates of R0 of 2019-nCov that have been published. More are coming out as I write… the science for this outbreak is moving very fast. (See References and Sources, below, for links.)

Most estimated values for R0 range from 1.4 to 3.8, with all the estimates having typical values in the mid 2s. Call it 2.5, or perhaps slightly less. I’m struck by that these have generally the same result, despite different methods.

(One paper leans to the high side, with estimates of 3.5 to 5.5. The World Health Organisation estimate leans the other way: 1.4 to 2.5.)

As one comparison, the R value of SARS was between 2 and 5.

Wild claims

There is a claim that R0=14 making ragged attempts at scare-mongering online.* There’s another of R0=3.8 doing the rounds. This one looks to be a case of clinging on to one research group’s initial estimate even after it was revised to around 2.5. Both are higher than what scientists are finding.

Best advice? – ignore them. Use the sound stuff, not speculation.

R0 is not the last word

This number does not in itself predict how ‘nasty’ an outbreak will be. In particular, it doesn’t indicate how many people will ultimately be infected. For example, other diseases with higher R0 values have been contained and the number of seriously affected kept modest. SARS is an example. (It’s worth mentioning here that one of the major differences in this outbreak is the near immediate release of information.)

R0 values of less than 1 indicate that unless things change the outbreak will peter out – the disease isn’t infecting enough people to keep going.

Values higher than 1 mean that unless we change things the outbreak is likely to persist. The aim then is to put in place things that reduce R0 to lower than 1.

Even then it’s not a fixed thing

It depends on how likely other people are infected. That can be influenced by all sorts of things including better basic hygiene, proper sneezing technique, and so on.

It’s a good reminder to practice that basic hygiene. The NZ MoH and the CDC some prevention advice (merged here):

  • Avoid close contact with people who are sick
  • Wash hands frequently, especially after contact with ill people or their environment. Use soap and water for at least 20 seconds. If soap and water are not available, use an alcohol-based hand sanitiser
  • Avoid close contact with sick farm animals or wild animals
  • If you are sick, practice cough etiquette:
    • maintain distance
    • cover coughs and sneezes with disposable tissues (or clothing), then throw the tissue in the rubbish.
    • wash hands.
  • Stay home when you are sick.
  • Avoid touching your eyes, nose, and mouth with unwashed hands.
  • Clean and disinfect frequently touched objects and surfaces.

There’s no need to panic over these. They’re really just the usual sensible things to do anyway. We just need to be reminded every now and then.

These should help make R0 lower than the estimates for the early stages of the Wuhan outbreak.

Current estimates reflect Wuhan

The current R0 estimates also reflect the situation in Wuhan. They’ll reflect the lack of awareness of the illness in the early stages of the outbreak, and, for example, factors like the densely-packed lifestyle of these larger Chinese cities.

It also reflects how quickly people are isolated after infection. In the early stages of the outbreak this will probably not have happened until someone was quite ill. Now we’re aware of the illness, it’ll happen sooner.

Based on this, it’s reasonable to expect other countries to do (much) better than the earlier stages in Wuhan. We would be dealing with far fewer cases, sooner.** (The current R0 in Wuhan is now probably being dramatically reduced with the entire city effectively being under lockdown.)

There can also be variation in different people’s ability to spread the disease. R0 averages over these. For some illnesses everyone’s ability to spread it is more-or-less similar. Other illnesses are dominated by a few so-called ‘super-spreaders’, with most people not contributing much to the spread.

Early estimates of R0 really are estimates. They’re modelled on what data there is at the time. (It’s one reason I’m impressed with how similar the results are.)

Details, details, details

There are quite a few assumptions in how these values are estimated. I haven’t covered these here: I want to keep this short and helpful to those who want the key points.

These details matter, and they vary from one research groups efforts to another. Exploring these is more about what researchers are facing in modelling values like this in the early stages of an outbreak. It’s interesting, but probably beyond what most people want to know right now.

One factor I should mention: the date range the researchers are drawing their data from. It’s harder to make estimates from earlier data.

Other questions to cover?

Some other questions I could cover are listed below. Let me know if any would be of use, or if something else is bugging you.***

The source of the virus It’s not from snakes. Great for headlines, but it’s unlikely. There is also some suggestions the outbreak may not have started from the fish market.

Case fatality rates They’re easy to confuse with mortality rates. Like the R0 value, misunderstanding of this is causing concern.

Progress at the speed of open, collaborative science The pace is incredible.

I’ve since written about some of what scientists are working on, including suggestions for reading ‘fast science’ and some other places to read, and about the unconfirmed claim pangolins may be a source of the virus. There’s also an article listing all that has been written about the outbreak at Sciblogs.

Other articles in Code for life

For new parents or parents-to-be facing vaccine opinions

Catty lives, scientific and viral (Book review) (This novel includes an epidemic theme. And cats. And some very nasty academics.)

Political parties and GMOs: we all need to move on

Rubella, not a benign disease if experienced during early pregnancy

Sea stars and mosaics

Footnotes

* This likely comes from a documentary maker peddling an anecdotal claim by ‘a health worker’. While doing background reading and for this and other pieces I came under ‘special attention’ of one Twitter account claiming to be a NZ  political party, that is in fact not a political party—not even an unregistered party—that harangued me for hours for politely pointing out that R0s typically centred around 2.5 or so. They insisted that an anecdotal claim ‘proved’ it was 14… It was one of the strangest experiences I’ve had on Twitter. They’d block me, unblock me a few hours later, throw some more stuff at me, then block me again.

** By some estimates Wuhan may have large numbers of mild or asymptomatic cases, a fraction of which may become severe. (Remember, Wuhan is under lock-down; these people are not going anywhere.) There is some discussion on this, but this is not necessarily impending doom. One discussion about this I would like to read is paywalled, which I have to admit makes me grumpy. (To be fair, the paper it draws on is open access, but it’s useful to read what people conclude from others’ work.)

*** I’m not the answer to all solutions myself, but I can draw on the expertise of others.

References & Sources

These tweets and papers or preprints contain some of the estimates:

Dr. Maia Majumder and Prof Ken Mandl 2.0 – 3.1. (Published paper) Revised from 2.0 – 3.3.

Jonathon Read and others 2.5, 95% CI 2.4, 2.6.  (Link is to preprint, note the estimate was revised from 3.8, 95% confidence interval, 3.6-4.0. This is likely the source of some confusion of some people reporting R0 values up to 4.0 or having a typical R0 of 3.8.)

World Health Organisation 1.4 – 2.5.

Julian Rious and Christian Althaus 2.2, 90% high density interval: 1.4-3.8. (Preprint)

MRC Centre for Global Infectious Disease Analysis 2.6, uncertainty range: 1.5-3.5. (Natsuko Imai and others; report here.)

Shi Zhao and colleagues 3.30 (95%CI: 2.73-3.96) to 5.47 (95%CI: 4.16-7.10) (Link is to preprint.)

Tao Liu and others 2.90 (95%CI: 2.32-3.63) and 2.92 (95%CI: 2.28-3.67) (Two different estimates using different methods, link is to preprint.)

Featured image

“Coronaviruses are a group of viruses that have a halo, or crown-like (corona) appearance when viewed under an electron microscope.”

The 2019-nCov outbreak in Wuhan is caused by a coronavirus. (The image is likely of SARS, a different coronavirus.)

Photo Credit: Content Providers(s): CDC/Dr. Fred Murphy – This media comes from the Centers for Disease Control and Prevention’s Public Health Image Library (PHIL), with identification number #4814.