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On the biological interpretation of a definition for the parameter R 0 in periodic population models

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Abstract

An adaptation of the definition of the basic reproduction number R 0 to time-periodic seasonal models was suggested a few years ago. However, its biological interpretation remained unclear. The present paper shows that in demography, this R 0 is the asymptotic ratio of total births in two successive generations of the family tree. In epidemiology, it is the asymptotic ratio of total infections in two successive generations of the infection tree. This result is compared with other recent work.

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Authors and Affiliations

  1. Institut de Recherche pour le Développement (IRD), UMI 209, Bondy, France

    Nicolas Bacaër

  2. Université Pierre et Marie Curie, UMI 209, Paris, France

    Nicolas Bacaër

  3. Département de Mathématiques, Université Cadi Ayyad, Marrakech, Maroc

    El Hadi Ait Dads

Authors
  1. Nicolas Bacaër
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  2. El Hadi Ait Dads
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Correspondence to Nicolas Bacaër.

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Bacaër, N., Ait Dads, E.H. On the biological interpretation of a definition for the parameter R 0 in periodic population models. J. Math. Biol. 65, 601–621 (2012). https://doi.org/10.1007/s00285-011-0479-4

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  • DOI: https://doi.org/10.1007/s00285-011-0479-4

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