The failure of R0

Comput Math Methods Med. 2011:2011:527610. doi: 10.1155/2011/527610. Epub 2011 Aug 16.

Abstract

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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Review

MeSH terms

  • Basic Reproduction Number / statistics & numerical data*
  • Bluetongue / epidemiology
  • Bluetongue / transmission
  • Cholera / epidemiology
  • Cholera / transmission
  • Dengue / epidemiology
  • Dengue / transmission
  • Disease Outbreaks / statistics & numerical data*
  • Female
  • HIV Infections / epidemiology
  • HIV Infections / transmission
  • Humans
  • Influenza, Human / epidemiology
  • Influenza, Human / transmission
  • Malaria / epidemiology
  • Malaria / transmission
  • Male
  • Models, Biological*
  • Rift Valley Fever / epidemiology
  • Rift Valley Fever / transmission
  • West Nile Fever / epidemiology
  • West Nile Fever / transmission