@article{fdi:010078898,
  title = {{D}eux modeles de population dans un environnement periodique lent ou rapide},
  author = {{B}aca{\¨e}r, {N}icolas},
  editor = {},
  language = {{ENG}},
  abstract = {{T}wo problems in population dynamics are addressed in a slow or rapid periodic environment. {W}e first obtain a {T}aylor expansion for the probability of non-extinction of a supercriticial linear birth-and-death process with periodic coefficients when the period is large or small. {I}f the birth rate is lower than the mortality for part of the period and the period tends to infinity, then the probability of non-extinction tends to a discontinuous limit related to a "canard" in a slow-fast system. {S}econdly, a nonlinear {S}-{I}-{R} epidemic model is studied when the contact rate fluctuates rapidly. {T}he final size of the epidemic is close to that obtained by replacing the contact rate with its average. {A}n approximation of the correction can be calculated analytically when the basic reproduction number of the epidemic is close to 1. {T}he correction term, which can be either positive or negative, is proportional to both the period of oscillations and the initial fraction of infected people.},
  keywords = {{P}eriodic environment ; {B}irth-and-death process ; {S}-{I}-{R} epidemic ; {A}veraging},
  booktitle = {},
  journal = {{J}ournal of {M}athematical {B}iology},
  volume = {80},
  numero = {4},
  pages = {1021--1037},
  ISSN = {0303-6812},
  year = {2020},
  DOI = {10.1007/s00285-019-01447-z},
  URL = {https://www.documentation.ird.fr/hor/fdi:010078898},
}