@article{fdi:010046096,
  title = {{E}ffects of a disease affecting a predator on the dynamics of a predator-prey system},
  author = {{A}uger, {P}ierre and {M}c{H}ich, {R}. and {C}howdhury, {T}. and {S}allet, {G}. and {T}chuente, {M}. and {C}hattopadhyay, {J}.},
  editor = {},
  language = {{ENG}},
  abstract = {{W}e study the effects of a disease affecting a predator on the dynamics of a predator-prey system. {W}e couple an {SIRS} model applied to the predator population, to a {L}otka-{V}olterra model. {T}he {SIRS} model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. {T}he {L}otka-{V}olterra model describes the predator-prey interactions. {W}e consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. {W}e use the classical "aggregation method" in order to obtain a reduced equivalent model. {W}e show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. {I}n this latter case, the predator population tends either to a "disease-free" or to a "disease-endemic" state. {M}oreover, the total predator density in the disease-endemic state is greater than the predator density in the "disease-free" equilibrium ({DFE}).},
  keywords = {{L}otka-{V}olterra model ; {P}redator-prey model ; {I}nfected predators ; {T}ime scales ; {A}ggregation of variables ; {S}tability ; {SIRS} model},
  booktitle = {},
  journal = {{J}ournal of {T}heoretical {B}iology},
  volume = {258},
  numero = {3},
  pages = {344--351},
  ISSN = {0022-5193},
  year = {2009},
  DOI = {10.1016/j.jtbi.2008.10.030},
  URL = {https://www.documentation.ird.fr/hor/fdi:010046096},
}