@article{fdi:010061746,
  title = {{O}n the probability of extinction in a periodic environment},
  author = {{B}aca{\¨e}r, {N}icolas and {D}ads, {E}. {A}.},
  editor = {},
  language = {{ENG}},
  abstract = {{F}or a certain class of multi-type branching processes in a continuous-time periodic environment, we show that the extinction probability is equal to (resp. less than) 1 if the basic reproduction number is less than (resp. bigger than) 1. {T}he proof uses results concerning the asymptotic behavior of cooperative systems of differential equations. {I}n epidemiology the extinction probability may be used as a time-periodic measure of the epidemic risk. {A}s an example we consider a linearized {SEIR} epidemic model and data from the recent measles epidemic in {F}rance. {D}iscrete-time models with potential applications in conservation biology are also discussed.},
  keywords = {{B}ranching process ; {E}xtinction probability ; {B}asic reproduction number ; {S}easonality ; {E}pidemic ; {FRANCE}},
  booktitle = {},
  journal = {{J}ournal of {M}athematical {B}iology},
  volume = {68},
  numero = {3},
  pages = {533--548},
  ISSN = {0303-6812},
  year = {2014},
  DOI = {10.1007/s00285-012-0623-9},
  URL = {https://www.documentation.ird.fr/hor/fdi:010061746},
}