Many people are surprised to hear of Covid cases after vaccination, but vaccines do not completely protect against the virus.
Two weeks after the second dose, the current vaccines are about 60 to 80 per cent effective, meaning there are still going to be people who catch the disease.
This is why people still get flu every year, despite vaccination being widespread – flu vaccines actually tend to be less effective than those we have for Covid.
Most people who catch Covid will have much milder symptoms after being vaccinated than they would have had otherwise, and this is borne out by the low numbers of admissions to hospital in Scotland, compared to very high case rates.
This doesn't mean there is no risk of getting sick, and Mr Marr labelled his infection “very nasty”.
The Delta variant has also slightly increased the chances of people catching Covid after vaccination.
The vaccines are still very effective, but there is a marked difference compared to the Alpha variant.
In a recent study, researchers at Edinburgh University found the Pfizer vaccine was 79 per cent effective against the Delta variant compared to 92 per cent for the Alpha strain.
For the AstraZeneca vaccine, these figures were 60 and 73 per cent respectively.
The researchers also noted that second doses were particularly important with the Delta variant.
The Pfizer vaccine offers just 12 per cent protection in the first month after a first dose, and just 30 per cent after a month. In the two weeks after a second dose this is 66 per cent, and it rises to 79 two weeks after the second dose.
Figures are similar for the AstraZeneca vaccine.
Mr Marr asked Sir Peter Horby, who chairs the government’s New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), about his infection.
Professor Horby said: “It’s really important for people to realise that, as we increase the vaccination rates and most older people are vaccinated, we will see breakthrough infections.
“That does not mean that the vaccines don’t work – breakthroughs were expected.
“What we want to do is to prevent hospitalisations and deaths, and the vaccines do that very effectively.”