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Epidemic Thresholds

  1. Frank Ball

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a07022

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Ball, F. 2005. Epidemic Thresholds. Encyclopedia of Biostatistics. 3.

Author Information

  1. University of Nottingham, Nottingham, UK

Publication History

  1. Published Online: 15 JUL 2005


This article gives an overview of the threshold behavior of epidemic models, focusing primarily on stochastic closed population models. A key parameter is the reproduction number R0 of an epidemic. For a broad range of models, branching process theory is used to show that an epidemic initiated by a trace of infection in a large population can take off only if R0 is larger than one. These models assume either a homogeneous population or a stratified population in which all the subpopulations are large. Models for the spread of an epidemic among a population partitioned into a large number of small households, or among a spatially configured population, are also considered. In both of these cases R0 no longer provides a good indicator as to whether an epidemic can take off. The article closes with a brief discussion of the threshold and long-term behaviors of open population models, which incorporate demographic effects.


  • epidemic model;
  • threshold theorem;
  • branching process;
  • reproduction number;
  • critical vaccination coverage;
  • structured populations;
  • closed and open populations;
  • endemic behavior