@article{fdi:010048307,
  title = {{O}n the final size of epidemics with seasonality},
  author = {{B}aca{\¨e}r, {N}icolas and {G}omes, {M}.{G}.{M}.},
  editor = {},
  language = {{ENG}},
  abstract = {{W}e first study an {SIR} system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. {U}nlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number {R}-0 or of the initial fraction of infected people. {M}oreover, large epidemics can happen even if {R}-0 < 1. {B}ut like in a constant environment, the final epidemic size tends to 0 when {R}-0 < 1 and the initial fraction of infected people tends to 0. {W}hen {R}-0 > 1, the final epidemic size is bigger than the fraction 1-1/{R}-0 of the initially nonimmune population. {I}n summary, the basic reproduction number {R}-0 keeps its classical threshold property but many other properties are no longer true in a seasonal environment. {T}hese theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases ({W}est-{N}ile, dengue, chikungunya) or air-borne diseases ({SARS}, pandemic influenza); all these diseases being influenced by seasonality.},
  keywords = {{B}asic reproduction number ; {S}easonality ; {F}inal epidemic size},
  booktitle = {},
  journal = {{B}ulletin of {M}athematical {B}iology},
  volume = {71},
  numero = {8},
  pages = {1954--1966},
  ISSN = {0092-8240},
  year = {2009},
  DOI = {10.1007/s11538-009-9433-7},
  URL = {https://www.documentation.ird.fr/hor/fdi:010048307},
}