The rise of hiv/aids in the 1980s created an urgent need to uncover how the epidemic was spreading. What features of the disease were driving transmission? The month before Diana visited Middlesex Hospital, Robert May and Roy Anderson had published a paper that broke down the reproduction number for hiv.[46] They noted that R was influenced by a number of different things. First, it depends on how long a person is infectious: the shorter an infection is, the less time there is to give it to someone else. As well as the duration of infection, R will depend on how many people someone interacts with while infectious. If they have a lot of contact with others, it will provide plenty of opportunities for the infection to spread. Finally, it depends on the probability that the infection is passed on during each of these encounters, assuming the other person is susceptible.
R therefore depends on four factors: the duration of time a person is infectious; the average number of opportunities they have to spread the infection each day they’re infectious; the probability an opportunity results in transmission; and the average susceptibility of the population. I like to call these the ‘DOTS’ for short. Joining them together gives us the value of the reproduction number:
R = Duration × Opportunities × Transmission probability × Susceptibility
Breaking the reproduction number down into these DOTS components, we can see how different aspects of transmission trade off against each other. This can help us work out the best way to control an epidemic, because some aspects of the reproduction number will be easier to change than others. For example, widespread sexual abstinence would reduce the number of opportunities for hiv transmission, but it’s not an appealing or practical option for most people. Health agencies have therefore focused on getting people to use condoms, which reduce the probability of transmission during sex. In recent years, there has also been a lot of success with so-called pre-exposure prophylaxis (PrEP), whereby hiv-negative people take anti-hiv drugs to reduce their susceptibility to the infection.[47]
The type of transmission opportunities we’re interested in will depend on the infection. For influenza or smallpox, transmission can occur during face-to-face conversations, while infections like hiv and gonorrhea are spread mostly through sexual encounters. The trade-off in the DOTS means that if someone is infectious for twice as long, in transmission terms it’s equivalent to them making twice as many contacts. In the past, smallpox and hiv have at times both had an R of around 5.[48] However, people are generally infectious with smallpox for a shorter period, which means that there must be more opportunities to spread infection per day, or a higher transmission probability during each opportunity, to compensate.
The reproduction number has become a crucial part of modern outbreak research, but there’s another feature of contagion we also need to consider. Because R looks at the average level of transmission, it doesn’t capture some of the unusual events that can occur during outbreaks. One such event happened in March 1972, when a Serbian teacher arrived at Belgrade’s main hospital with an unusual mix of symptoms. He’d been given penicillin at his local medical centre to treat a rash, but severe haemorrhaging had followed. Dozens of students and staff in the hospital gathered to see what they presumed was a strange reaction to the drug. But it was no allergy. After the man’s brother also fell ill, staff realised what the real problem was, and what they had exposed themselves to. The man had been infected with smallpox, and there would be 38 more cases – all traceable to him – before the infections in Belgrade subsided.[49]
Although smallpox wouldn’t be eradicated globally until 1980, it was already gone from Europe, with no cases reported in Serbia since 1930. The teacher had likely caught the disease from a local clergyman who’d recently returned from Iraq. Several similar flare-ups had happened in Europe during the 1960s and 1970s, most of them travel-related. In 1961, a girl returned from Karachi, Pakistan to Bradford, England, bringing the smallpox virus with her and unwittingly infecting ten other people. An outbreak in Meschede, Germany, in 1969 also started with a visitor to Karachi. This time it was a German electrician who’d travelled there; he would pass the infection on to seventeen others.[50] However, these events weren’t typical: most cases who returned to Europe didn’t infect anyone.
In a susceptible population, smallpox has a reproduction number of around 4–6. This represents the number of secondary cases we’d expect to see, but it’s still just an average value: in reality there can be a lot of variation between individuals and outbreaks. Although the reproduction number provides a useful summary of overall transmission, it doesn’t tell us how much of this transmission comes from a handful of what epidemiologists call ‘superspreading’ events.
A common misconception about disease outbreaks is that they grow steadily generation-by-generation, with each case infecting a similar number of people. If an infection spreads from person-to-person, creating a chain of cases, we refer to it as ‘propagated transmission’. However, propagated outbreaks don’t necessarily follow the clockwork pattern of the reproduction number, growing by the exact same amount each generation. In 1997, a group of epidemiologists proposed the ‘20/80 rule’ to describe disease transmission. For diseases like hiv and malaria they’d found that 20 per cent of cases were responsible for around 80 per cent of transmission.[51] But like most biological rules, there were some exceptions to the 20/80 rule of transmission. The researchers had focused on sexually transmitted infections (STIs) and mosquito-borne infections. Other outbreaks didn’t always follow this pattern. After the 2003 sars epidemic – which had involved several instances of mass infection – there was renewed interest in the notion of superspreading. For sars, it seemed to be particularly important: 20 per cent of cases caused almost 90 per cent of transmission. In contrast, diseases like plague have fewer superspreading events, with the top 20 per cent of cases responsible for
