@article{fdi:010054339,
  title = {{T}he model of {K}ermack and {M}c{K}endrick for the plague epidemic in {B}ombay and the type reproduction number with seasonality},
  author = {{B}aca{\¨e}r, {N}icolas},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he figure showing how the model of {K}ermack and {M}c{K}endrick fits the data from the 1906 plague epidemic in {B}ombay is the most reproduced figure in books discussing mathematical epidemiology. {I}n this paper we show that the assumption of constant parameters in the model leads to quite unrealistic numerical values for these parameters. {M}oreover the reports published at the time show that plague epidemics in {B}ombay occurred in fact with a remarkable seasonal pattern every year since 1897 and at least until 1911. {S}o the 1906 epidemic is clearly not a good example of epidemic stopping because the number of susceptible humans has decreased under a threshold, as suggested by {K}ermack and {M}c{K}endrick, but an example of epidemic driven by seasonality. {W}e present a seasonal model for the plague in {B}ombay and compute the type reproduction numbers associated with rats and fleas, thereby extending to periodic models the notion introduced by {R}oberts and {H}eesterbeek.},
  keywords = {{P}lague ; {E}pidemic model ; {S}easonality ; {T}ype reproduction number ; {INDE}},
  booktitle = {},
  journal = {{J}ournal of {M}athematical {B}iology},
  volume = {64},
  numero = {3},
  pages = {403--422},
  ISSN = {0303-6812},
  year = {2012},
  DOI = {10.1007/s00285-011-0417-5},
  URL = {https://www.documentation.ird.fr/hor/fdi:010054339},
}