Calculation of R0 for age-of-infection models

Christine K. Yang, Fred Brauer

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We consider age-of-infection epidemic models to describe multiple-stage epidemic models, including treatment. We derive an expression for the basic reproduction number Ro in terms of the distributions of periods of stay in the various compartments. We find that, in the model without treatment, Ro depends only on the mean periods in compartments, and not on the form of the distributions. In treatment models, Ro depends on the form of the distributions of stay in infective compartments from which members are removed for treatment, but the dependence for treatment compartments is only on the mean stay in the compartments. The results give a considerable simplification in the calculation of the basic reproduction number.

Original languageEnglish (US)
Pages (from-to)585-599
Number of pages15
JournalMathematical Biosciences and Engineering
Issue number3
StatePublished - Jul 2008
Externally publishedYes


  • Age-of-infection models
  • Basic reproduction number
  • Epidemic models
  • Treatment models

ASJC Scopus subject areas

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


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