The discounted reproductive number for epidemiology

Timothy C. Rbluga, Jan Medlock, Alison Galvani

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The basic reproductive number, Ro, and the effective reproductive number, 72, are commonly used in mathematical epidemiology as summary statistics for the size and controllability of epidemics. However, these commonly used reproductive numbers can be misleading when applied to predict pathogen evolution because they do not incorporate the impact of the timing of events in the life-history cycle of the pathogen. To study evolution problems where the host population size is changing, measures like the ultimate proliferation rate must be used. A third measure of reproductive success, which combines properties of both the basic reproductive number and the ultimate proliferation rate, is the discounted reproductive number RdThe discounted reproductive number is a measure of reproductive success that is an individual's expected lifetime offspring production discounted by the background population growth rate. Here, we draw attention to the discounted reproductive number by providing an explicit definition and a systematic application framework. We describe how the discounted reproductive number overcomes the limitations of both the standard reproductive numbers and proliferation rates, and show that 72.d is closely connected to Fisher's reproductive values for different life-history stages.

Original languageEnglish (US)
Pages (from-to)377-393
Number of pages17
JournalMathematical Biosciences and Engineering
Volume6
Issue number2
DOIs
StatePublished - Apr 2009

All Science Journal Classification (ASJC) codes

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

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