Do Science: A back of the envelope about Claire's killer cough

6 min read June 2, 2013 at 2:21pm on Health, Infection and Rant

I'm a big fan of reason. That's why I don't have a lot of time for the anti-vaxxers and the wind farm opponents etc.  It's not always the anti-science crowd who make foolish statements though.  See my discussion on the "40% of backpain to be cured with antibiotics" and "don't shave before a flood or you'll die" idiocy previously.

There's obviously been a lot of discussion about the NSW "No Jab, No Play" legislation and the advocacy journalism of the Daily Telegraph.  So this article came through my twitter feed this morning.

Selfish anti-vaccination conspiracy theorists putting Australia at risk

Even if you didn't read the rest of it, you may have seen the leader: "My body's a deadly weapon. So is yours." Later in the article is this gem:

"If I'd walked in to visit Dad with a simple case of influenza, let alone a more serious communicable disease, I could have killed the entire ward in one cough"

Ok folks...

Yes, I have this on a T-shirt
xkcd: CC-BY-NC-2.5: Original Link


  • I'm going to ignore the fact that patients in wards are usually in rooms and that only the patients in Claire's Dad's room would be at significant risk
  • I'm going to ignore the staff (who are probably at slightly higher risk than the patients).
  • We will assume that Claire passing through the ward counts all the patients on that ward as a "close contact", whereas walking past a single cough would be associated with a much lower level of risk.


  • Influenza is typically thought to be droplet spread, although there is some evidence to support aerosol transmission. Droplet is generally considered to only be transmissible at short range; via directly being coughed on, or by the droplets settling on your hands when you cough and then being contact transmitted to someone else. (That's why you should cough into your elbow not your hands).
  • The attack rate of an infection is the proportion of persons exposed to that condition that become infected.
  • I haven't used my reference manager (Mendeley, by the way) or sourced any data except from things freely available from a Google search.

So, to the science (although it's actually really maths)

  • Influenza attack rate: 2.4%  (reference: here via here)
  • Likely vaccination rate of hospital patients: 75% (figure for Adults >65, a reasonable surrogate, from here)
  • Vaccine efficacy: 60% (lowish average estimate, from here )
    • these last two stats mean the percentage of people with effective immunity is 60% x 75%  = 45%
  • Influenza case-fatality rate: 1% (approx rate for >65 year olds to be consistent with the vaccination rate; whole population rate is much less - of the order 0f 0.1%; data here )

So, the probability of a ward full of  "close contacts" vaccinated at current rates resulting in a death is: Risk of exposure (strike rate) x Risk of no immunity (= 1- effective vaccine rate) x risk of death

= 0.024 x 0.55 x 0.01 = 0.0132% , or 1/7500 give or take a bit.

(open disclosure: that's a bit higher than I thought it would be when I started this)

Although, remember that I have over-estimated very significantly the risks of transmission based on a hospital ward environment, and taken low-end estimates of vaccine efficacy and a very pessimistic mortality rate. (In case you think I'm arguing against vaccination generally, I'll leave it as a thought experiment for you to imagine what would happen with measles, which is aerosol transmitted, and can infect people in a room 20min after a measles carrier leaves, with an attack rate of 70% ish).

The chance of lethally infecting two patients on the same ward is around one seventh that of winning first division lotto and the risks decay exponentially (note that means actually exponentially, not "really fast" as the term is commonly abused).

Why is this important and not just science pedantry?

First, because one of the reasons people want to do away with AVN is because of their long-standing practice of misquoting science to their own ends.  There are lots of people with crackpot beliefs about lots of things.  Aggressive secularists would include religion in this group. But having those beliefs is not a reason to ban organisations. Even their adherents promoting them isn't really even good enough. It is because they are promoting them in a misleading way that AVN is in the sights (as well as their rather shoddy financial affairs and others).

If it is wrong to say "MMR causes autism" (it doesn't), then it is equally not ok to say that a cough could kill thirty (it couldn't). To suggest that one is bad and the other is good because of their position relative to our own biases or current public health policy is censorship, not science.

The second reason is that a standard tool of the vaccine objectors is to cry conspiracy theory.  Big Pharma, health professions and the media are in some Illuminati-backed global plot to falsely scaremonger about the risks of what really are benign diseases, sell vaccines and inject the public with poison.  Of course, you can never disprove this wingnuttery to a believer - because you're part of it, man!  

What I can show you is a pretty decent example of an article in the mainstream media that is falsely scaremongering about the risk of influenza (hint: I've hidden a link to it somewhere in this article) to people in hospitals.  

Don't feed the trolls.

Close to my own heart is the primal terror that infectious disease seems to engender in the public - from subtle influence like the difficulty I have trying to buy hand-soap that isn't antibacterial to the very overt - all the medical students due to come to our team shortly after swine flu broke in 2009 pulled out, citing concerns over personal safety.  People think that my job poses some great risk of personal illness - in fact I'm probably at lower occupational risk than pretty much every other specialty (I don't do procedures on people - and I know when and how to wear personal protective equipment!).  

The piece in question was an opinion piece and I'm sure the feeling in question was a genuine one. But publishing nonsense in the name of science is bad for everyone, regardless of the issue or your opinions on it.  

A good friend of mine is quite a fan of pointing out how poorly scientists communicate the implications of their research to the public.  But it's really important to remember that there are two parts to "science journalism".  Science without journalism may not get through to the public but journalism without science can misinform, mislead and create panic.

By all means, stay away from visiting at hospitals if you're unwell.  Cough into your elbow and wash your hands.  But if you start sneezing on your way back to the car park, don't flagellate yourself for being a "deadly weapon" - because it's just bullshit.