Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 527610, 17 pages
Review Article

The Failure of 𝑅 0

1Department of Mathematics, Pennsylvania State University, University Park, State College, PA 16802, USA
2School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
3Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Avenue, Ottawa ON, Canada K1N 6N5

Received 30 January 2011; Revised 18 May 2011; Accepted 18 May 2011

Academic Editor: Haitao Chu

Copyright © 2011 Jing Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.