The Failure of R (0)

The basic reproductive ratio, R (0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R (0) < 1, the disease dies out, whereas if R (0) > 1, the disease persists. R (0) has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R (0) is flawed. Diseases can persist with R (0) < 1, while diseases with R (0) > 1 can die out. We show that the same model of malaria gives many different values of R (0), depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R (0) for a variety of diseases, and examine some of the alternatives that have been proposed. If R (0) is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.