What is R0?

We hear about the reproductive number or R0 from various sources, notably the UKs Chief Scientific Officer, and often in the media.But do you know what it means? Here is a (reasonably) simple explanation.

Firstly, it may help to understand the term when you know that it comes from population studies, where knowing the mean number of children in a family unit will allow for an estimate of how quickly the population will grow (or shrink). The higher the reproductive number, the greater the population growth. In that setting, it is genuinely a reproductive index.

When applied to infectious diseases, R0 aims to define the expected number of new cases directly generated by one index case in a population where all individuals are susceptible to infection. If R0 is less than 1, then the disease will stop spreading. If it is greater than 1, then it will spread wider and wider.

But R0 is not a real number. The value of R0 is derived from the application of mathematical models to the situation. Many assumptions are built into the model. For example, how long the person remains infectious: the longer they are infectious, the higher R0 will be. Clearly, in a densely populated area, R0 will increase, because one infected individual has more opportunity to come into contact with unaffected individuals. The measures that people take may affect how many people are infected from a single case – protective equipment, hand washing, distancing etc. If a lot of people in a population are immune, then R0 will fall, because it is defined by the spread in a susceptible population, and the susceptible population is smaller. This is the concept of herd immunity. The mathematical model makes the basic assumption that we are all the same, but some people are certain to be more susceptible than others.

Mathematicians make these, and other assumptions, based on incomplete data, especially with regard to Covid testing – we simply have no idea how many infected people are in the community, or how many are immune. In fact, we cannot answer most of the questions that allow for an accurate estimate of R0. In short, R0 is not evidence-based, except to a very small degree.

Even Wikipedia tells us that the use of R0 is severely limited. So when the Chief Scientific Officer tells you that R0 is now less than 1, take it with a large pinch of salt.

*The author was a consultant in the NHS. Is an elected Fellow of the Royal College of Physicians and the Royal Society of Medicine. He has a Masters in Soc and Pol Sci. He is not however, an expert in Public Health.*