The basic reproduction number in epidemic models with periodic demographics

Curtis L. Wesley, Linda J.S. Allen

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

Patterns of contact in social behaviour and seasonality due to environmental influences often affect the spread and persistence of diseases. Models of epidemics with seasonality and patterns in the contact rate include time-periodic coefficients, making the systems nonautonomous. No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models. However, for some epidemic models with periodic coefficients and constant population size, the time-averaged basic reproduction number has been shown to be a threshold for disease extinction. We extend these results by showing that the time-averaged basic reproduction number is a threshold for disease extinction when the population demographics are periodic. The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains.

Original languageEnglish
Pages (from-to)116-129
Number of pages14
JournalJournal of Biological Dynamics
Volume3
Issue number2-3
DOIs
StatePublished - 2009

Keywords

  • Basic reproduction number
  • Differential equations
  • Epidemic models
  • Periodic coefficients

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