A final size relation for epidemic models

Julien Arino, Fred Brauer, P. Van Den Driessche, James Watmough, Jianhong Wu

Research output: Contribution to journalArticlepeer-review

100 Scopus citations


A final size relation is derived for a general class of epidemic models, including models with multiple susceptible classes. The derivation depends on an explicit formula for the basic reproduction number of a general class of disease transmission models, which is extended to calculate the basic reproduction number in models with vertical transmission. Applications are given to specific models for influenza and SARS.

Original languageEnglish (US)
Pages (from-to)159-175
Number of pages17
JournalMathematical Biosciences and Engineering
Issue number2
StatePublished - Apr 2007
Externally publishedYes


  • Basic reproduction number
  • Epidemic models
  • Final size relation
  • Vertical transmission

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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