@article{fdi:010053487,
  title = {{G}enealogy with seasonality, the basic reproduction number, and the influenza pandemic},
  author = {{B}aca{\¨e}r, {N}icolas and {D}ads, {E}. {A}.},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he basic reproduction number {R} (0) has been used in population biology, especially in epidemiology, for several decades. {B}ut a suitable definition in the case of models with periodic coefficients was given only in recent years. {T}he definition involves the spectral radius of an integral operator. {A}s in the study of structured epidemic models in a constant environment, there is a need to emphasize the biological meaning of this spectral radius. {I}n this paper we show that {R} (0) for periodic models is still an asymptotic per generation growth rate. {W}e 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. {T}his difference has been overlooked in recent studies of the {H}1{N}1 influenza pandemic.},
  keywords = {{B}asic reproduction number ; {S}easonality ; {E}pidemics ; {H}1{N}1 influenza},
  booktitle = {},
  journal = {{J}ournal of {M}athematical {B}iology},
  volume = {62},
  numero = {5},
  pages = {741--762},
  ISSN = {0303-6812},
  year = {2011},
  DOI = {10.1007/s00285-010-0354-8},
  URL = {https://www.documentation.ird.fr/hor/fdi:010053487},
}