by Tom Chivers
Thursday, 23
September 2021
Explainer
10:29

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).

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Norman Powers
Norman Powers
1 year ago

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%.

It amazes me anyone can look at this stat and not be suspicious about it. Social distancing appears to have had no impact at all on COVID. At least it seems that way from trying to spot sharp artificial drops in case curves, which is what you’d expect sudden and well observed policy changes to trigger (which social distancing was, at the beginning).
But here we’re being asked to believe that despite this apparent failure, social distancing, which was working in June 2020 but is quite obviously as dead as a dodo now, has eliminated flu entirely?
This feels like a pretty major violation of Occam’s Razor. The simplest explanation is not that the absolutely minimal social distancing being practiced in the UK has 100% wiped out one virus whilst having no observable impact on another. The simplest explanation is that what we’re being told about testing precision isn’t accurate.

Last edited 1 year ago by Norman Powers
Alan Thorpe
Alan Thorpe
1 year ago
Reply to  Norman Powers

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.

Michael Miles
Michael Miles
1 year ago
Reply to  Norman Powers

I agree. That is one huge anomaly that is at the root of the continuation of the “COVID” pandemic. What is COVID disease specifically? It’s a disease with non-specific symptoms that overlap with other corona viruses and influenza symptoms, that is diagnosed with an imperfect test, based on a problematic genomic definition.

Norman Powers
Norman Powers
1 year ago
Reply to  Michael Miles

Interesting – what’s problematic about the genomic definition?
I’ve seen many glaring problems in COVID science over the past 18 months but the microbiology of the virus itself seemed to be something scientists have a pretty good grip on. Like, I see no reason to doubt the accuracy of the RNA sequences found on UniProt. And I’ve read about how PCR tests work and understand why scientists think they are very precise. I’ll freely admit to having no mechanistic explanation at all for how PCR testing could confuse flu and SARS-CoV-2, despite the many other problems PCR testing obviously has (like the insistence COVID testing has no false positives, a position based on circular logic, not actual measurements). My suspicion is based purely on the internal inconsistencies in the alternative explanations for what’s happened to flu.
But I’m not a microbiologist and the apparent robustness of this type of science may simply be a lack of familiarity relative to the dodgy stats and programming being practiced in other fields like epidemiology. So, what’s wrong with the genetics of it?

Last edited 1 year ago by Norman Powers
rodney foy
rodney foy
1 year ago
Reply to  Norman Powers

I like the way you are attacking the figures, which is the right approach. Some people seem to make their mind up, then simply reject everything that doesn’t match.

It is suspicious that earlier social distancing managed to virtually eradicate the flu virus. Could it be because sars-cov-2 (especially Delta) is much more transmissible ?

Norman Powers
Norman Powers
1 year ago
Reply to  rodney foy

Well, is it much more transmissible? All claims about “transmissibility” (read: modelled chance of Alice infecting Bob during a randomized encounter) seem to be rooted in trying to work backwards from the case curves, in particular, the claim that Delta is “more transmissible” was based on the usual dodgy abuses of stats – comparing delta in its initial days when it was growing quickly to alpha at the same time, instead of comparing the growth phases of both viruses to each other.
But let’s put that to one side.
The Great Flu Disappearance is really quite the staggering mystery and the more you think about it, the more mysterious it gets. I reject claims that it’s to do with social distancing because I saw none of that on my recent trip to the UK. I was on busy trains where few were wearing masks, etc. Not much observable difference to pre-COVID times. If this practically invisible amount of social distancing can kill off flu completely then that would represent by far the most astounding epidemiological discovery ever, and raise the question of why it was never noticed before given the enormous effect sizes, and we’ve been bothering trying to create flu vaccines all this time.
But test confusion is also not an entirely satisfying explanation. It would require a few things to be happening for which there’s no evidence or even contradictory evidence:

  1. COVID tests would have to flag flu as COVID with ~100% reliability. Possible, but, PCR validation tests involve submitting non-SARS-CoV-2 viruses to labs and ensuring they don’t say yes.
  2. Flu tests would have to in fact always be preceded by COVID tests, that is, there could be no pure flu tests being done anywhere, and a COVID+Flu positive would have to be interpreted as a COVID positive (or the flu test is simply never done). Otherwise – assuming flu tests haven’t inexplicably broken – at some least some tests would return positive. To reach zero you’d need a 100% buggy COVID test to eclipse flu tests 100% of the time, and for nobody to have noticed that they went for a flu test and were told they had COVID.

This scenario also seems kind of weird and unlikely, albeit it requires only government incompetence, so it seems more plausible than social distancing having miracle powers against flu.
The final explanation that tends to be presented is that flu and SARS-CoV-2 cannot co-exist in the body. One kicks out the other. This explanation is appealing but has its own problems:

  1. There’s no known scientific explanation for how this could work. It would have to be something like “the immune system, once primed by fighting COVID, can destroy flu so fast that it never gets a chance to make you sick, and this effect persists for months after having had COVID, and basically everyone has had it by now, in many cases without them noticing”.
  2. If COVID was able to kick flu out, then there should be some places where a flu wave starts, and then is suddenly cut off by a COVID wave. You’d be able to see the flu being beaten back by COVID in the graphs. We don’t see this. Instead we just see all-COVID-all-the-time, with flu never making an appearance.

In short, no explanation presented so far including my own makes any sense at all.

Last edited 1 year ago by Norman Powers
rodney foy
rodney foy
1 year ago
Reply to  Norman Powers

I just looked at a study in Nature on 19-Aug that R0 for delta is about 6.4. I read somewhere else that R0 for seasonal flu is about 1.3. I would need to be an epidemiologist to understand if these numbers are correct, but I tend to bow to people with years of experience

rodney foy
rodney foy
1 year ago
Reply to  rodney foy
Johann Strauss
Johann Strauss
1 year ago
Reply to  Norman Powers

I suspect the reason the flu has “so-called” disappeared is that it’s simply not being tested for. Recall that number of flu cases in the community is based entirely on modeling derived from hospitalized cases. So if you have flu-like symptoms right now, you are likely to get a covid test but not a flu one. Unless you require hospitalization, that flu-like illness would never appear in the statistics.
Then we also need to consider hospitalization. Let’s say you need to be hospitalized with flu-like symptoms. Right now, a CVID test would be done upon admittance to the ER but probably not a flu test. If you are admitted, it’s still probably counted as a COVID case, since, in the US at least, every COVID case brings money into the hospital, and there is no point doing an influenza test since the treatment (or lake thereof) is effectively the same: i.e. oxygen, fluids, perhaps antibiotics to prevent a secondary bacterial infection (but in the hospital unlikely to be given until such time as a secondary bacterial pneumonia actually develops), and steroids (iv dexamethasone). So from the hospital’s perspective any hospitalization with flu-like symptoms is probably assumed to be COVID whether it is or not, and whether the case is PCR positive or not.

Norman Powers
Norman Powers
1 year ago
Reply to  Johann Strauss

I looked at that already. It’s not so simple. There are dashboards in the USA that show the number of flu tests being done and their positivity rate. Tests done hasn’t changed much. There are people who say they regularly go for flu tests just because, and that they’re still doing so.
I agree that there must be some sort of eclipsing of flu tests going on like you say, but, it’s hard to square that with data saying flu tests are still happening.

Andrew D
Andrew D
1 year ago

To hell with your speculative pseudo-calculations. I also have a cold/flu/covid at the moment. Who knows which it is? I’ll just stay in bed with cups of hot lemon drink and honey, look at unherd and occasionally make an inane contribution. If I get seriously worse I’ll phone for an ambulance. One thing I won’t do is take a PCR test – never have, never will.

Alan Thorpe
Alan Thorpe
1 year ago
Reply to  Andrew D

Exactly my view. Tom talks about everything but misses the point that common sense used to prevail. Covid has apparently resulted in all journalists having no common sense.

rodney foy
rodney foy
1 year ago
Reply to  Andrew D

I just watched this from Tim Spector on this very subject https://youtu.be/kTTMMmZfHmQ

robert stowells
robert stowells
1 year ago
Reply to  Andrew D

I believe that I caught COVID back around January/February 2020 just when Italy was beginning to develop as a centre of COVID outbreak and was experiencing those national debt issues (surely not related?). I was surprised to be coming down with flu when I had had the flu jab but did not make the connection that what I was experiencing was COVID. I do not follow the news very much. I would describe it as moderate to severe flu (I have had worse but the symptoms did appear to be different to what I normally experience). The symptoms were a constant misery (but no more than that), sweating, some aches, and a dry cough all of which persisted for about 12 days. I did my job working very long hours each day but everything was an effort and I abandoned myself to bed each night.  So, in hindsight, I did catch something back in early 2020 which was different to my normal experience of flu and so probably COVID particularly as I had had the flu jab.
One of the things that concerned me regarding the reporting of deaths during the COVID development was just how many deaths that were written down as due to COVID were done so as the result of reliable tests. As one comment has stated there is money for hospitals in COVID.

Last edited 1 year ago by robert stowells
George Glashan
George Glashan
1 year ago

If we assume

If we agree

Take that as true

so let’s call it 50% 

so I’d imagine 

I think I can say

I obviously can’t really say I have a 0.05% chance

What you consider a safe level is up to you, but after a few LFTs I no longer think I’m a risk

Congratulations on marking your own homework in a way which proves you are correct, with rigour like that have SAGE been intouch to offer you a job yet?
In future how about:
we dont assume
we dont agree
Let not Take that as true
Let’s not call it 50% 
How about evidence instead of imagination

rodney foy
rodney foy
1 year ago
Reply to  George Glashan

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

George Glashan
George Glashan
1 year ago
Reply to  rodney foy

I understand what Rationalism is, this is not that, this is magical thinking for people who flatter themselves as scientific thinkers. Its a litany to The Science.

Last edited 1 year ago by George Glashan
Norman Powers
Norman Powers
1 year ago
Reply to  rodney foy

People seem to be objecting to the very idea of back of the envelope calculations. Perhaps it’s the result of government presenting such calculations as more reliable than they really are.
Nonetheless, as someone who is also an engineer let me agree with you 100%. Some of the numbers in this article may be wrong. The conclusions may be totally wrong. Nonetheless, is reasoning through the numbers better or worse than just making something up / repeating something that sounds good and then asserting it to be obviously correct, which is the usual approach journalists take? To me it’s clearly better. We can still disagree (and below I take aim at one specific thing), but the idea of trying to get the basic gist of something by using numbers isn’t wrong – unless you incorrectly handle uncertainty, which is a typical problem found in epidemiology.

George Glashan
George Glashan
1 year ago
Reply to  Norman Powers

Thank you Rodney and Norman for your comments. My objection to the article is when you strip away the scientific set dressing every phrase i highlighted above can be replaced with the words … I guess… and the guess work concludes that the most beneficial outcome, not having covid was the one arrived at.
i dont care for his guesses, if we are just guessing i can make my own guesses, maybe i guess its a 100% certainty he had covid or 0%, its all just guessing.
Equally the …I guess… can be substituted for …i pray…, which i think is closer to the mark, the above article is more like a secular prayer to The Science, miraculously his divine revelation at the end of the prayer is he doesn’t have covid. Halleluiah!.

Last edited 1 year ago by George Glashan
rodney foy
rodney foy
1 year ago
Reply to  George Glashan

I see where you’re coming from. Can we place any credence on the numbers?

He has used vague words quite often. I suspect that he has given it a lot of thought, but I need to go back and understand his sources.

I wonder by how much they would need to be wrong to come to a different conclusion

Alka Hughes-Hallett
Alka Hughes-Hallett
1 year ago
Reply to  George Glashan

How awful is this piece? Is anyone in Unherd taking notice? I can never read much of TC articles , always abandon after a couple of lines . Lost in conjecture, and over confusing with numbers, devoid of logic.

Caroline Watson
Caroline Watson
1 year ago

That’s because it is a cold virus. And ‘flu’ isn’t a disease, it’s a colloquial term from mediaeval Italian meaning the influence of the planets; that being what they believed caused winter fevers.
if it looks like a duck…….
The end of this hysterical nonsense is long overdue.

Gordon Black
Gordon Black
1 year ago

This article took me back 65 years to a schooldays limerick:-
A mathematician named Hall
had a hexahedronical b###
The cube of its weight plus its volume times eight
was two-thirds of four-fifths of f### all.

Fran Martinez
Fran Martinez
1 year ago

The real question is: Who cares?

robert stowells
robert stowells
11 months ago
Reply to  Fran Martinez

I do but only because it is such a big issue to Governments and people have accepted lockdown so I challenge it for my own sanity and my contribution to sanity.

Last edited 11 months ago by robert stowells
Julian Farrows
Julian Farrows
1 year ago

The dangers of COVID have been so extremely exaggerated that I’ve lost a lot of trust in the medical profession. I used to trust doctors, even though I knew there were some bad ones around. There are a few speaking up about government excesses with lockdowns and vaccine passports, but they are either lumped in with the conspiracy theorists, or have lost their licenses. We are told to follow ‘the science’, but this seems to only apply when it matches a certain political agenda.
We are going the way of Ancient Rome.

Lloyd Byler
Lloyd Byler
1 year ago

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)

Norman Powers
Norman Powers
1 year ago
Reply to  Lloyd Byler

Did Mullis really say PCR tests can’t distinguish between flu viruses and other viruses? If so, can you give a precise quote where he says that? I know he said many other things about PCR tests that are relevant, but inability to distinguish at all between influenza and SARS-CoV-2 RNA would be very surprising given he won the Nobel prize specifically because PCR (done correctly in lab conditions i.e. not what COVID testing centres do) is supposed to be very precise and sensitive.

Johann Strauss
Johann Strauss
1 year ago
Reply to  Norman Powers

The issue really relates to number of cycles used in the PCR test. Anything over 25 cycles, and certainly over 30 cycles is completely worthless and loaded with false positives as a result of accumulation of replication errors.

Adam Bartlett
Adam Bartlett
1 year ago

I like this article. I see quite a few fellow unherd subscribers seem to be “never tell me the odds” Han Solo fans.

Neven Curlin
Neven Curlin
1 year ago

Thank you for this insight into hypochondria.

Johann Strauss
Johann Strauss
1 year ago

While the numbers and logic seem reasonable, Chivers is actually missing a very basic element. Your chances of having COVID depend entirely upon what you’ve been doing and what you’ve been exposed to. For example, if you have used public transportation and especially the tube when it’s crowded, if you have frequented crowded, poorly ventilated indoor spaces (such as pubs and nightclubs, and even many restaurants), if you have attended very large indoor gatherings (including cocktail parties that so many politicians go to), if you have spoken face-to-face with an active COVID patient for 20 min or more, the probability of having COVID goes up massively. If, on the other hand, you don’t do those things, the probability of having COVID is very very small indeed.

Martin Smith
Martin Smith
1 year ago

Don’t Covid and influenza give you a fever whereas a cold doesn’t? That’s my rule of thumb anyway.

rodney foy
rodney foy
1 year ago
Reply to  Martin Smith

The Zoe Covid study says that fever is no longer a common symptom of Covid

Martin Smith
Martin Smith
1 year ago
Reply to  rodney foy

Thanks. I’ve now checked. Only if you are vaccinated is a fever no longer a feature. For us unvaccinated scum it is still on the list.

Last edited 1 year ago by Martin Smith
rodney foy
rodney foy
1 year ago
Reply to  Martin Smith

Yes, thanks for the clarification