Coronavirus symptoms overlap heavily with those of colds and flu
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).