Understanding how ‘overdispersion’ works is key to controlling Covid
In February, when Covid-19 was just beginning to spread around the world, a single infected individual exposed as many as 1,100 people in Daegu, South Korea, possibly infecting hundreds. This “superspreading event” sparked a cluster of transmission that eventually grew to more than 5,000 cases in a country recognised as having one of the most effective Covid-19 control programmes to date.
At first glance, this seems wildly inconsistent with what we know about how efficiently Sars-CoV-2 (the virus that causes Covid-19) transmits. The average number of infections caused by someone infected with Sars-CoV-2 – a value known as R – is thought to be between two and five if there is no immunity in the population. How, then, could this one individual, known as “patient 31” by health officials, infect so many?
Though exceptional, the South Korea cluster is just one of many large transmission events that have occurred during the pandemic. We’ve repeatedlyseen clusters of 10, 20, or even 50 cases caused by a single individual – far greater than would be indicated by R. This is because R is only an average, and this average masks an interesting phenomenon that has been the subject of growing public interest in recent weeks. It’s known in scientific circles as “overdispersion”. But what exactly is it, and how can an understanding of it translate into action?
Simply put, overdispersion means that a minority of infected individuals are responsible for an unexpectedly high percentage of transmission. Overdispersion is often reported as the proportion of infected individuals who cause 80% of transmission. For Sars-CoV-2, this value may be 10% or lower. So, while on average a group of 10 infected individuals might cause 25 secondary infections, just one of those originally infected might infect 20 people, while the remaining nine combine to infect only five.
In part, overdispersion in disease transmission mirrors overdispersion in patterns of social contact: a typical day for most of us might result in only a few contacts, but on some days we may see hundreds of people. For some, such high-contact days are the norm. Patient 31 attended large indoor services at the Shincheonji Church of Jesus and travelled throughout central Daegu in the week prior to her diagnosis, providing thousands more opportunities to transmit the virus than if she had been at home with her family.
Biological and environmental factors are important for overdispersion, too. Most people infected with Sars
CoV-2 will start to transmit the virus before they feel ill. For some this asymptomatic period can last days, while the infected individual continues their regular activities, unknowingly spreading disease. Certain activities, such as singing or shouting, and poorly ventilated, indoor spaces may also facilitate transmission.
Overdispersion was important in helping to understand some puzzling aspects of the start of the pandemic. In early February, many countries had registered multiple confirmed Covid-19 cases but had no evidence of substantial community spread. This seemed inconsistent with evidence for the transmissibility of Sars-CoV-2 from Wuhan, China. This apparent discrepancy could, however, be explained by overdispersion: most countries had so far been spared the kind of high-transmission events that can jump-start an outbreak. For example, in New Zealand, as many as 80% of the infected individuals who entered the country transmitted to only one other person or to no one at all. In this way, overdispersion can slow the spread of the virus to new locations, as most introductions fail to spark an epidemic .
The other side of these failed introductions, though, is that when transmission does take off, it can do so explosively. South Korea registered more than 1,900 cases within 10 days of identifying patient 31, mostly among the Shincheonji Church cluster, having identified only six cases in the 10 days before that.
Controlling this sort of explosive growth can be daunting; but overdispersion can work in our favour if we can identify and target the areas with high risk of superspreading. One way to do this is cluster investigations, or “backwards contact tracing”, which have been a key feature of the thus far successful response in Japan.
This strategy relies on the fact that we are more likely to first identify one of the many people infected in a superspreading event than the individual who triggered the event. Tracing chains of transmission back to their
source allows investigators to identify, and intervene on, people and settings responsible for a disproportionate amount of transmission. Through these investigations, officials in Japan decided early to implement recommendations against and restrictions on gatherings in crowded, enclosed spaces, which may have an outsized effect on transmission because of the likelihood of superspreading in such contexts.
Overdispersion, though, is unpredictable. We cannot know where the next superspreading event will occur, and often we cannot fully explain why an event occurred at all. Cluster investigations are effective when conducted quickly and thoroughly, but an outbreak can quickly spiral out of control if just one cluster goes undetected or uncontrolled. And most clusters won’t look like the Shincheonji cluster, but instead may be outbreaks of 10 or 15 cases, driven by household transmission or small gatherings. These smaller clusters are less likely to be detected and targeted for intervention, particularly when resources are scarce.
The unpredictability of superspreading has another important consequence. Some have argued that the high levels of overdispersion mean we may soon have adequate levels of immunity to stop spread without further control. This argument relies on a theoretical consequence of overdispersion, that highly connected individuals will become infected, and then immune, quickly at the start of an outbreak. Because those most likely to transmit are quickly removed from the pool of potential cases, transmission slows after just a small fraction of the population is infected.
This argument, though, only holds if it is always the same people who make up the highly connected, highrisk population. If a previously low-risk individual can become high-risk (say, as many return to work or school after months of social distancing), or superspreading events are truly random, there will be no benefit of overdispersion for achieving “herd immunity”. We also know that reinfection is at least possible, further complicating reliance on “herd immunity” as a response strategy.
Overdispersion is not unique to Sars-CoV-2, but it is shaping the current pandemic in important ways, and can both aid and impede control. To the extent that places such as Japan have successfully targeted the sources of high transmission, overdispersion has granted them an efficiency and focus in their control efforts. Cluster investigations, extensive test and trace programmes, and restrictions on the places and activities most conducive to superspreading may be particularly effective for controlling transmission with high levels of overdispersion.
Yet South Korea’s experience shows us how quickly a seemingly controlled outbreak can reignite with just a few unlucky incidents. As we confront new stages of the Covid-19 pandemic over the coming months and years, overdispersion can help us better understand why the disease behaves as it does and sharpen our efforts at control.
• Kyra Grantz is a doctoral student in infectious disease epidemiology and biostatistics at the Johns Hopkins Bloomberg School of Public Health. Justin Lessler is an associate professor of epidemiology at the Johns Hopkins Bloomberg School of Public Health