What is the reproduction number and why is it always two weeks old?

The reproduction number (R) is the number of people who are infected, on average, by one person with COVID-19. This number shows how fast the virus is spreading.

The number of transmissions remains more or less constant when the value of R is 1. This means 1 person with coronavirus only infects 1 other person. This is illustrated in the figure below.

Exponential growth

If the value of R is greater than 1, the number of people getting infected is increasing. For instance, if R is 1.06, then 100 people with coronavirus infect 106 others.

If R is 2, the number of people being infected doubles with each ‘generation’ of transmission. It starts with 1 person infecting 2 others. These 2 people infect 4 others. And these 4 people infect 8 others. This is called exponential growth and this is what it looks like:

So, when the reproduction number is greater than 1 the number of people infected increases faster and faster. When you plot the number of infections in a graph, you can see the line rising more and more steeply. This is the graph when the value of R is 2:

So, when R is 2, it takes only 10 steps (10 ‘generations’ of transmission) to go from 1 infected person to more than 1,000 infected people.

Getting the reproduction number below 1

If the value of R is less than 1, the number of people getting infected is falling.

For example, if there are 8 people with coronavirus and the value of R is 0.5, then they will infect 4 people. These 4 people will infect 2 others. And these 2 people will infect only 1 other person. This is what it looks like:

Clearly, it’s important to get the value of R below 1 so that the number of people getting infected declines.

Value of R is reliable after 14 days

The National Institute for Public Health and the Environment (RIVM) calculates the reproduction number. You may have wondered why the most up-to-date value of R is always two weeks old.

In the Netherlands, the time between a person getting infected and then transmitting the virus to somebody else is usually 4 days. Once people are infected, it usually takes 2 to 14 days before they develop symptoms, although some people never do. This is called the incubation period. The average time it takes for the virus to be transmitted between two people depends on the infectious period, the incubation period and people’s behaviour. And there is usually some time between people developing symptoms and getting tested. And between a sample testing positive and this result being passed on to RIVM.

This means RIVM does not have a complete and reliable picture of the number of infections that have taken place until around 14 days have passed. So it’s impossible for RIVM to give a reliable estimate of the value of R for today.