@article{PAR00013355,
  title = {{D}ynamical behavior of a stochastic {SIRS} epidemic model},
  author = {{H}ieu, {N}. {T}. and {D}u, {N}. {H}. and {A}uger, {P}ierre and {D}ane, {N}. {H}.},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this paper we study the {K}ernack - {M}ac {K}endrick model under telegraph noise. {T}he telegraph noise switches at random between two {SIRS} models. {W}e give out conditions for the persistence of the disease and the stability of a disease free equilibrium. {W}e show that the asymptotic behavior highly depends on the value of a threshold lambda which is calculated from the intensities of switching between environmental states, the total size of the population as well as the parameters of both {SIRS} systems. {A}ccording to the value of lambda, the system can globally tend towards an endemic state or a disease free state. {T}he aim of this work is also to describe completely the omega-limit set of all positive solutions to the model. {M}oreover, the attraction of the omega-limit set and the stationary distribution of solutions will be shown.},
  keywords = {{E}pidemiology ; {SIRS} model ; {T}elegraph noise ; {S}tationary distribution},
  booktitle = {},
  journal = {{M}athematical {M}odelling of {N}atural {P}henomena},
  volume = {10},
  numero = {2},
  pages = {56--73},
  ISSN = {0973-5348},
  year = {2015},
  DOI = {10.1051/mmnp/201510205},
  URL = {https://www.documentation.ird.fr/hor/{PAR}00013355},
}