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Genealogy with seasonality, the basic reproduction number, and the influenza pandemic

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Abstract

The basic reproduction number R 0 has been used in population biology, especially in epidemiology, for several decades. But a suitable definition in the case of models with periodic coefficients was given only in recent years. The definition involves the spectral radius of an integral operator. As in the study of structured epidemic models in a constant environment, there is a need to emphasize the biological meaning of this spectral radius. In this paper we show that R 0 for periodic models is still an asymptotic per generation growth rate. We also emphasize the difference between this theoretical R 0 for periodic models and the “reproduction number” obtained by fitting an exponential to the beginning of an epidemic curve. This difference has been overlooked in recent studies of the H1N1 influenza pandemic.

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Authors and Affiliations

  1. Research group UMMISCO, IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143, Bondy, France

    Nicolas Bacaër

  2. Laboratoire de Mathématiques et Dynamique des Populations, Université Cadi Ayyad, Marrakech, Morocco

    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. Genealogy with seasonality, the basic reproduction number, and the influenza pandemic. J. Math. Biol. 62, 741–762 (2011). https://doi.org/10.1007/s00285-010-0354-8

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  • DOI: https://doi.org/10.1007/s00285-010-0354-8

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