Answering FAQs: Part 1

What is the reproduction number? What about future risks?

Anthony B. Masters


To help the Royal Statistical Society, I wrote answers to frequently asked questions about COVID-19.

The main constraint was a limit of 400 words. These are the original version of the articles. The posts were later improved by other authors.

What is R and how is it determined?

What is the reproduction number (R)?

The reproduction number is the average number of direct infections from one case. This is over the whole time while people are infectious.

If the reproduction number is 2, we expect 100 infected people to infect 200 more people. If the reproduction number is 0.5, the average group of 100 infected people infects 50 more.

The reproduction number can change over time. If people reduce contacts, the virus has fewer transmissions.

The basic reproduction number (R₀) is for when the population has no immunity. This is not a biological constant. The same virus may spread in different populations at different paces. By itself, this number does not determine how fast a virus spreads. Initial ‘seed’ cases and infectious periods are important.

The virus passes on in each generation. (Image: Stanford University/James Holland Jones)

Suppose people can recover, conferring immunity. Over time, more infected people will recover, die, or get vaccinated. The effective reproduction number is for the remaining susceptible population.

Reproduction numbers are averages.

One person could pass on the virus to 100 people, and 99 others do not pass it on. In that population, the average new infections is 1. If every infected person infects one more, that would be the same reproduction number. The implications for health policy differ.

How is the reproduction number determined?

Researchers estimate this number, through mathematical models.

Model inputs could include:

  • Data on confirmed infections, hospital admissions, critical care, and deaths.
  • Social contact surveys, with self-reported data on contacts.
  • Household infection surveys, which can study current prevalence of…



Anthony B. Masters

This blog looks at the use of statistics in Britain and beyond. It is written by RSS Statistical Ambassador and Chartered Statistician @anthonybmasters.