Journal of Mathematical Biology

, Volume 65, Issue 4, pp 601–621 | Cite as

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

  • Nicolas Bacaër
  • El Hadi Ait Dads


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.


Demography Epidemiology Generations Basic reproduction number Seasonality 

Mathematics Subject Classification (2000)

92D25 92D30 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut de Recherche pour le Développement (IRD), UMI 209BondyFrance
  2. 2.Université Pierre et Marie Curie, UMI 209ParisFrance
  3. 3.Département de MathématiquesUniversité Cadi AyyadMarrakechMaroc

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