As a veterinary epidemiologist, I study how viruses spread between animals and animal populations. The principles of viral transmission are much the same in humans (indeed, many scientists work on both). The concept of a second wave in public health is often linked to factors outside of human control. This might include the birth of infants who are susceptible to a particular disease causing the wavelike patterns we see in childhood illnesses, or environmental factors that influence the seasonality of influenza. But for Covid-19, the anticipation of a second wave has more to do with actions within our control.
Shifts in social behaviour create more opportunities for human contact. In China, the entry of people with coronavirus across the Russian border is one example where easing restrictions resulted in new cases of the virus. Meanwhile in Germany, outbreaks of coronavirus linked to abattoirs where employees live in poor housing conditions is a reminder that the R number can also increase when vulnerable individuals are exposed to the virus for the first time.
The potential rise in R after lockdown measures are relaxed is something that epidemiologists are well aware of. If the government delivers an effective testing and contact-tracing strategy that can bring the virus under control by the time lockdown measures are lifted for everyone, new cases of Covid-19 would theoretically be little cause for concern – as health authorities would have measures in place to identify and curb incipient outbreaks.
What’s of greater concern to epidemiologists are indications that the R number is rising uncontrollably, or in a way that increases the exposure of the most vulnerable or puts health systems under great strain. In other words, what’s as important as the R number is the total number of cases across a population that an increase in R would cause. While the increase in Germany’s R number is concerning, this would be far more alarming were it to occur in the UK, where there are currently many more cases of coronavirus.
Regional differences in the value of R are also important. Easing the lockdown in areas with greater health resources, fewer Covid-19 cases and where more people have already had the virus, may be practical compared with another part of the country where outcomes of an increasing R would be more severe. Differences in the R number among particular risk groups, such as care home residents, are also likely to be more meaningful than the value of R for the country as a whole. Again, we’ll need a widespread programme of testing and tracing to determine these risks, and enable health authorities to rapidly contain incipient outbreaks.
Intuitively, we know that if contact between people with Covid-19 and those susceptible to infection increases, the R number is likely to rise. But this doesn’t happen in a straightforward way. A 10% increase in contact doesn’t necessarily mean a 10% increase in R, or a 10% increase in overall risk of catching the virus. Understanding how contact between people affects transmission, whether it be transmission of hate messages via a malicious bot on the internet or transmission of a virus from an infected person, is a pivotal concept in the field of “network science”.
For Covid-19, a single contact can endanger an otherwise isolated community. Once an infection is introduced, the results can be disastrous. In network science, this pattern is described as a “small-world” effect. The concept originated from the idea that individuals with apparently little in common often have connections they are unaware of. What this means for public health is that even if only a handful of people have the potential to expose other communities to disease risk, in communities that are geographically distant or isolated, the impact of those few people on the spread of a virus can be significant. In the case of coronavirus, many areas in the UK have only experienced small outbreaks so far, creating fewer opportunities for the effects of “herd immunity” to curb the risk of a future outbreak.
To understand why mass gatherings are so important for infection, we can use a second concept borrowed from network science, that of “scale-free networks”. This is when some individuals in a network have a disproportionate number of contacts compared with the average. Gatherings are one context in which a single individual who is infected with Covid-19 could have many more contacts with other people than average. Emerging scientific research suggests that some individuals may be responsible for infecting many more people than others. One crucial question, which scientists haven’t yet answered, is whether these patterns are driven by more contact or differences in infectiousness.
Mass gatherings become more significant if such events occur frequently, with at least some of the same individuals returning repeatedly to the same place. This is often the case for scheduled football matches or religious services, both of which occur weekly – an interval conveniently similar to the time it takes a person infected with coronavirus to become infectious to others. Gatherings both increase the opportunities to become infected and increase the chances of infecting other people. If a few people who are infected with coronavirus come into contact with many others, the risk of a rapid spread can become uncontrollable. And some events present both kinds of risk: drawing in many people from great distances, and holding them together in close contact for an extended period.
Lowering our chance of a second wave will require minimising the impact of both of these factors. This means restricting large gatherings, especially where individuals might repeat these over the course of a single infection, and restricting movements over long distances, or those with a higher probability of putting vulnerable groups at risk. Crucially, it also means having in place a testing and tracing strategy that allows health authorities to identify new cases of Covid-19. These concepts are intuitive, but what network science tells us is that the risk associated with even a small change in patterns of human contact can be substantial.
• Rowland Kao is the Sir Timothy O’Shea Professor of Veterinary Epidemiology and Data Science at the University of Edinburgh, and is working with Public Health Scotland on coronavirus modelling.