by Tom Chivers
Thursday, 23
September 2021

If you have a cough, what are the odds it’s Covid?

Coronavirus symptoms overlap heavily with those of colds and flu
by Tom Chivers
Time for a PCR. Credit: Getty

I had a cold last week. It was mild, but I felt a bit off and had a cough for a day or so.

Nowadays, of course, a cold isn’t just a cold. The symptoms of Covid, especially in vaccinated people, overlap heavily with those of colds and flu. And I really didn’t want to be spreading Covid around. So: how likely was it that it was Covid? These calculations are necessarily all very rough, but let’s see where we end up.

A starting point might be the prevalence in the population. The most recent ONS infection survey estimated that about 1.3% of people in England had detectable virus; numbers may have gone down a bit since then, but let’s use it.

The US CDC says the average adult gets two to three colds a year, more if you have school-age kids (as I do). Assuming Britons are roughly comparable, and colds last a week, then on average about 6% of Britons have colds at any given time.

There are two problems. First, cold and flu numbers are very low because of social distancing measures. At this time in 2019, when people were tested in hospital, 1.7% had flu. Now it’s 0.0%. Earlier this year, GPs reported that colds were down by four-fifths.

Second, we’re comparing who tests positive for Covid on a PCR test with who has cold symptoms. With Covid, at least, you will test positive for a long time after you’ve fully recovered – perhaps four or even eight times longer. Let’s say four.

If we assume that the 6% of Brits who usually have a cold is indeed down by four-fifths to 1.2%, we can multiply that by four to get the PCR positivity rate so we can compare it to the Covid survey. So 4.8%.

If we agree that I definitely had something, then the chance I had Covid given that I had cold symptoms was (1.3/(1.3+4.8))*100, or about 21%. That’s high: greater than the chance of rolling a 1 on a six-sided die, something I do all the time. I’d be very nervous about, say, going to the pub with that chance of having the virus.

But don’t worry. For seven days, I tested every day with a lateral flow test. Critics say they’re only about 60% sensitive, meaning they miss about 40% of positive cases. Take that as true, and also remember that the tests aren’t independent, so let’s call it 50% sensitive. If that’s roughly fair, then chances of getting seven false negatives in a row would be about one in 128. If we take our 21% and multiply it by 1/128, you get about a 0.16% chance that I had Covid.

Oh, and I did a PCR. And that was negative too. PCRs aren’t perfect either, but I’m an old hand, so I’d imagine I do them pretty well. Let’s say, conservatively, that it was 65% sensitive. That’d bring me down to about a 0.06% chance of having Covid, about one in 2,000. I think I can say that, after testing, I am less likely to have Covid than a randomly selected Briton, even though I had symptoms.

These numbers are spuriously precise: I obviously can’t really say I have a 0.06% chance, or whatever. It’s just a Fermi estimate. The point is the ballpark figures. Having a cough or a cold doesn’t mean you have Covid, but it means there’s a reasonable chance, not unlike rolling a one. But if you do a few tests and test negative, your chances drop very quickly. What you consider a safe level is up to you, but after a few LFTs I no longer think I’m a risk (except of giving someone a cold).

Join the discussion

  • and the PCR lab test can tell the diff between colds/flu/virus exactly how?
    The inventor of the PCR lab test says it cannot; are you smarter than the inventor of the machine?

    Dr. Fauci says that above a cycle of about 25 the PCR lab test is worthless, yet the FDA recommends running the test at 40 cycles, and labs are running the cycles as high as 50!

    Are you smarter than Dr. Fauci and the FDA and the labs running the test at arbitrary cycles?

    Do you believe your own lying eyes?

    Do you believe that believing in a bigger lie is easier than believing in a little lie?
    (hint for the clueless: answer is yes)

  • This is the Rationalist approach in the absence of good evidence. Humans are poor at assessing risk, and this gives you a feel for the risks and mitigations. It’s not meant to be accurate, but it’s good enough to guide our behaviour, and is better than guessing.

    As part of an Engineering team, we have to do this kind of analysis all the time, or we’d never progress. Sometimes the outcome is that we need more measurements, and have to build test pieces, or better computer models, but these are not always possible

  • There is a report in the Cochrane Library on Physical Interventions to interrupt the spread of respiratory viruses. They found masks to have little effect and hand washing a modest effect. They criticise the quality of the trials and data but say physical interventions can be effective. It isn’t clear how they think this can be achieved.

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