The reproduction number expresses the average number of people infected by someone who is infectious, but that average can mask large differences. Indeed, the probability of infection depends on a complex interplay between the properties of the virus itself and of the infected person (his or her biological characteristics and behavior), as well as on environmental conditions, such as humidity, temperature, ventilation, etc.

What if most people do not infect anyone at all and a few individuals infect a lot of people? Super-spreaders can greatly influence the overall course of an epidemic. Indeed, one super-spreading event can cause a large outbreak even if Rt is smaller than one.

So who are these super-spreaders and how can we account for this phenomenon in our models? How dramatic are super-spreading events in the context of a pandemic?

Super-spreaders: Who are they and what do they do?

Superspreaders are often supershedders: they release more viral particles than others. They breathe or cough more droplets and aerosols with virus particles in them; either because they have a high load of viral particles, or because they are built a little differently--larger nostrils, cavities or ducts, so they automatically disperse more droplets while talking.

Another important factor is the number of contacts. The more people you see, the more likely you are to infect many of them. Even the biggest supershedder can't infect anyone if they stay in isolation.

Several studies have tried to measure how important supershedding was during the pandemic. A study of the COVID-19 outbreak in Shenzen, China, reported that about 9% of cases were responsible for 80% of all viral transmission. Another study with a focus on Hong Kong found 19% of cases were responsible for 80% of local infections. Similarly, a study of outbreaks outside China concluded that 80% of infections were caused by about 10% of infected individuals, all of which suggests that if we can prevent super spreading, for example by canceling major events, we can already contain the pandemic to a significant extent.

An extra layer of complexity

Our models aim to calculate how fast the virus will spread and to who. Super-spreaders make this a bit more complex both technically and conceptually. If the proportion of infected people causing 80% of infections is small, this means that the vast majority of infected people do not transmit the virus and in other words, that an epidemic will stall if there is no superspreading, for example by not organizing large gatherings. However, if the group of people who cause 80% of infections is large, this means that more infectious people contribute to the viral spread. In other words, the virus spreads to a large extent through day-to-day contacts at work, at school or at home, for example. The relative contribution of super-spreading events to the overall viral spread will also play a role in the speed of viral transmission. More infections on a more limited scale may slow doubling times compared to fewer infection events on a larger scale.

The relationship between the mean, in this case the reproduction number, and the actual variation in the study population can be expressed mathematically in several ways. Typically, in the context of infection models, a given distribution with discrete outcomes (0, 1, 2, 3, 4... etc.) is used. Therefore, one infected person will infect a specific number of persons: 0, 1, 2, 3 persons, etc., depending on the number of high-risk contacts. Most individuals will infect only a limited number of people. In a few, the super-spreaders, this figure will be high. In statistics, we speak of overdispersion when there is more variation than expected based on the underlying model and if this is the case, it can greatly distort the outcome of the calculations.

To find out which distribution is best suited to express the variation in the number of infections per infected person, we did a number of simulations using different statistical distributions. When there is no variation in infection rates it makes little difference which distribution you use, but the more overdispersion there is, the more difficult it becomes to estimate the mean and variation correctly. We also used COVID-19 infection data from different countries to compare the outcome using different distributions. This showed that the classically used distribution often underestimates the number of persons causing only one infection. In this way, the importance of super-spreaders may actually be overestimated.

Again, it remains difficult to make correct estimates based on the available information. Usually, the data are only available on a small scale, for a well-defined region or for a short period of time, and thus perhaps the number of exceptional super-spreading events is underestimated. On the other hand, contact tracing data are biased for large outbreaks because infections are often easier to link together in that context. Because this is always an estimate, it is important to keep comparing different distributions to see how super-spreaders might be distorting the actual results.

There are also calls for mathematical models to distinguish between supershedders, who infect more people because they are intrinsically more infectious, and specifically those super-spreaders who infect more people because they have more high-risk contacts. Depending on the properties of the virus, the variation of both may also differ, further complicating correct modeling.

We used our individual-based model for the spread of SARS-CoV-2 in Belgium to get a better picture of this interplay. In our model, each individual in society has a unique set of characteristics, from age to health and behavior, and we can include variation in infectivity. We compared the role of superspreading due to higher intrinsic infectiousness versus superspreading due to riskier behavior, both for a period without strict measures and for a period with social distancing measures.

The effect of the two different types of super-spreading appeared to be different. Wide variation in shedding meant less frequent large outbreaks. Indeed, in this scenario, when most people infect (almost) no one, supershedders must encounter and be able to infect other supershedders to keep the epidemic going. Not all infected supershedders will also have many contacts and thus necessarily become true super-spreaders. Peaks thus become smaller. Group immunity would also be achieved more quickly.

On the other hand, when there is a large difference in contact-related infectivity, outbreaks become more frequent and explosive. In such case, super-spreaders, because of their large number of high-risk contacts, are more likely to get infected themselves and subsequently infect others. Spikes will be more frequent and higher, and it will take a lot longer to build up group immunity. When supershedding is mainly caused by a large number of high-risk contacts, the likelihood of resurgence after a lockdown is also higher than when it is mainly a matter of supershedding.

In all likelihood, during the corona crisis, a combination of both heterogeneity in intrinsic infectivity and heterogeneity in the number of contacts--along with a host of other factors--played a role in superdiffusion events. Changing measures and new variants also influence the relative contribution of different forms of superspreading. So it remains important to continually recalibrate models using current figures, including with respect to the role of superspreaders. This is what we are trying to do, for example, by incorporating the role of the environment into our models.