Superspreaders: The problem with forecasting the beginnings of epidemics hafsteinn Follow Mar 27 · 5 min read

As the Covid-19 epidemic is turning into a pandemic, some serious effort has been invested in forecasting how the disease will progress. This blog post concerns the reliability of such predictions, especially at the beginning of the disease, when little data is available. This post also serves as a warning of how hard it can be to control a highly infectious disease without extreme measures.

I come from Iceland, a country with a small population (~350k), and small changes in the number of infected can make a big difference for our health care system. Therefore, we need to be aware of the tremendous influence only a single individual can have on the spread of the disease.

Models can, in many cases, be useful. I do not want to criticize their practicality as it can be helpful to know the expected course of a disease. But given that we have lives at stake, we should focus on the worst realistic outcome to make decisions. Personally, I would feel better if we had too many ventilators than just enough. When news agencies report model results, I believe it is responsible to report on the worst realistic outcome. Such reports can possibly encourage members of the public to stay at home and follow orders from the government.

But back to the question, why is there so much uncertainty about an epidemic’s progress in the beginning? Many attempts have been made to describe the evolution of epidemics with models. In many cases, a model is intended to describe average behavior for a large number of individuals. Therefore, such methods generally ignore the variability that accompanies the onset of the epidemic when assumptions of having sufficiently many infected individuals do not hold. When a few are infected, it is simply impossible to trust that the number of new infections is within some given narrow limits as a single individual wreak havoc.

In this short review, I would particularly like to discuss superspreaders. In some epidemics, a small group of individuals is responsible for almost all infections. They are the so-called superspreaders. It is easy to imagine that a sick person who shakes many hands could infect far more than anyone who chooses to stay at home. Some people cannot spread the disease as their symptoms are too insignificant to transmit it. In contrast, others become quickly so sick that they do not have the opportunity to infect many. For example, it could be said that the pandemic in South Korea has become much worse because one superspreader came early into the picture.

One reason we have superspreaders is how connected we are. A great deal of research has been done on how people connect. It generally states that the network of our connections is scale-free. For this review, it means in short that most people have relatively few connections, but some have an enormous number. If everyone had only a few connections, it would be easier to predict the progress of an epidemic. However, the few individuals who are the most connected carry the potential to transmit a great deal more than the average person.

Let us consider a simple example. Suppose ten people are initially infected. When an individual becomes infected, 3–7 days pass until he becomes ill. At that point, he infects everyone else who is connected to him and they then become sick 3–7 days later and so on. At this point it is essential to determine how many infections each individual causes, the so-called R0 value. Assume that R0 is 2.2. Let us start by looking at how this process develops over 30 days if we don’t have superspreaders. We assume that each individual can infect up to six others, the probability distribution can be seen below.

The probability distribution of how many infections each infected person spreads without the influence of superspreaders.

This is a random process and it is useful to simulate it many times to see how it behaves. An individual is only considered to be infected on the day he or she develops symptoms. Ten infected people start the epidemic on day 0 and they have to wait for 3–7 days for symptoms to appear. The blue line shows the average over 200 trials.

Total number of infected individuals when we do not allow superspreaders to participate.

This pandemic is behaving well in the sense that we do not see great fluctuations. The worst result is only twice as bad as the average result.

Now, consider what happens when we allow superspreaders to participate. As before, R0 is fixed to 2.2 but in this scenario each person can infect up to 100 others. The probability distribution can be seen below. It may be noted that an individual is not likely to infect 100 others. For example, the probability that someone infects 20 or more others is only about 2.5% in this distribution.

The probability distribution of how many infections each infected person spreads with the influence of superspreaders.

A simulation of an epidemic with this distribution shows a very different picture compared to the one we studied without superspreaders.

Total number of infected individuals when we do allow superspreaders to participate.

The blue line showing the mean is similar to the one before without superspreaders. However, the total number of infected is about six times higher in the worst case. On the other hand, there are also considerably many scenarios where the total number of infected persons is much lower.

What can we learn from this? For example, the assumptions that the prediction models are based on can have a significant effect, the average behaviour of epidemics does not need to reflect the worst outcomes especially since superspreaders can make a big difference. Small countries are much more vulnerable to superspreaders and should base decisions on results from models with a healthy amount of skepticism.

The actions of the Icelandic government to date are meant to increase social distancing. In this way, the R0 coefficient of the epidemic can be lowered and thus the epidemic slowed down. With this review, however, I would like to emphasise how important it is to minimise the effects of superspreaders. If companies have some employees who potentially meet hundreds of other people a day, they should work at home if possible. If that is not possible they should seek out a way to limit their impact like for example testing them regularly if that is possible.

I hope this short post demonstrates also how important it is to stay at home if symptoms arise. Don’t be a superspreader if you can prevent it.