Covid-19 has made A&E departments very quiet. I worked in the one at St Thomas’s Hospital when it was called Casualty. Undressing a homeless patient once caused the centrifugal escape from his clothes of a shimmering sheen of lice, hundreds of them. Sister Cas was called. She rolled up her sleeves and said: ‘This reminds me of Dunkirk!’

Most lousy people have only a handful. The best quantitative study of lousiness was done by Alexander Peacock, an RAMC entomologist, in the trenches on the Western Front in the First World War. He found that 95 per cent of the soldiers were infested, more than 60 per cent with 20 lice or fewer, but 2.8 per cent – he called them ‘horrible examples’ – had more than 350 on their trousers and shirts. This pattern of distribution, in which most of a human population’s parasites are concentrated in only a few individuals, is very common. Statisticians call it ‘overdispersion’.

At the beginning of the 20th century, Cornish tin miners suffered from hookworm, which causes anaemia. Most had only a few worms but some had hundreds. One of the superwormy miners had probably been infected in India and returned home when the gold price fell. Deep in the mine, crapping in a corner was universal. The excreted worm larvae, which had hatched and thrived because the mines were as warm as the tropics, would have fed on the faeces, got onto ladder rungs via shit on boots, penetrated the skin of hands and arms, travelled to the lungs, up the windpipe and down the oesophagus to settle in the intestines.

Another imported infection, E.coli O157, also shows overdispersion, not in people but in its natural hosts, ruminant animals. In a herd of cattle that carry it, most only excrete small bacterial numbers, but a few supershedders excrete millions. They help to keep the infection going in the herd, and are dangerous for humans because the likelihood of meat from their carcasses being contaminated in the slaughterhouse is great.

Nasty coronaviruses go in for overdispersion in a big way. Superspreading events are common. In the case of SARS, a doctor from Guangzhou, who had been treating patients with atypical pneumonia, stayed at the Metropole Hotel in Hong Kong on 21 February 2003. He was unwell and admitted to hospital on 22 February, where he died. Seven people staying on the same floor of the hotel contracted SARS: three from Singapore, one from Vietnam, two from Canada and one from Hong Kong. Their returning home triggered outbreaks with 70 cases in Singapore, 59 in Hanoi, 16 in Toronto and more than 100 in Hong Kong. In a different event in Beijing, a patient contracted SARS in hospital and infected many close contacts, including her husband, sons, daughters and son-in-law, and set up a chain of infections in healthcare workers and hospital visitors. This superspreading event led to a total of 77 cases.

Even bigger outbreaks have been caused by Covid-19, such as the 2500 cases associated with the international gathering of the Christian Open Door Church at Mulhouse in France from 17 to 24 February, and the 5212 confirmed cases linked to the late February meeting of the Shincheonji Church in South Korea. Evangelical meetings are not quiet affairs, and it is noteworthy how many other Covid-19 outbreaks have been associated with heavy breathing and singing, including the infection of 33 of the 61 attendees at a choir practice in Skagit County, Washington State on 10 March; the second biggest outbreak in New Zealand (96 cases) that affected the Marist College, a girls school, possibly associated with a fiafia night; and another one in New Zealand at a St Patricks Day celebration (77 cases) where the participants were encouraged to get ‘shamrocked’.

The ‘Nike haka’ performed at the company’s international conference in Edinburgh on 26-27 February may have played an important role in virus transmission that led to Scotland’s first outbreak of 25 cases, an event that we know about only because of the work of investigative journalists. In contrast, Covid-19 information from New Zealand is comprehensive: 41 per cent of the 1504 confirmed and probable cases occurred in 16 clusters of 13 or more cases.

Public health staff in New Zealand identified Covid-19 outbreaks using traditional methods, including contact tracing. In the UK this stopped on 12 March, and no reports of formal public health investigations of the chain of transmission of infection have been published. It is not even evident whether any have been done. It is very clear, however, that outbreaks have been very common in care homes, and it is reasonable to conclude that Covid-19 overdispersion has been happening in the UK to the same degree as everywhere else.

Covid-19 press conferences use the R0 number as a key indicator of success in controlling the virus. The overdispersion parameter k isn’t mentioned. The smaller it is, the more the cases cluster, and the bigger the clusters. Without doubt k is small for Covid-19. The good news is this means many cases have contracted their infections from a minority of infectious individuals, superspreader events are still important, and finding and controlling them by test and trace may well send R tumbling down.