The Failure ofR0

Abstract

The basic reproductive ratio,R0, 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: ifR0<1, the disease dies out, whereas ifR0>1, the disease persists.R0has 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,R0is flawed. Diseases can persist withR0<1, while diseases withR0>1can die out. We show that the same model of malaria gives many different values ofR0, depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values ofR0for a variety of diseases, and examine some of the alternatives that have been proposed. IfR0is 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.