%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Hieu, N. T.
%A Du, N. H.
%A Auger, Pierre
%A Dane, N. H.
%T Dynamical behavior of a stochastic SIRS epidemic model
%D 2015
%L PAR00013355
%G ENG
%J Mathematical Modelling of Natural Phenomena
%@ 0973-5348
%K Epidemiology ; SIRS model ; Telegraph noise ; Stationary distribution
%M ISI:000355362000005
%N 2
%P 56-73
%R 10.1051/mmnp/201510205
%U https://www.documentation.ird.fr/hor/PAR00013355
%V 10
%W Horizon (IRD)
%X In this paper we study the Kernack - Mac Kendrick model under telegraph noise. The telegraph noise switches at random between two SIRS models. We give out conditions for the persistence of the disease and the stability of a disease free equilibrium. We 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. According to the value of lambda, the system can globally tend towards an endemic state or a disease free state. The aim of this work is also to describe completely the omega-limit set of all positive solutions to the model. Moreover, the attraction of the omega-limit set and the stationary distribution of solutions will be shown.
%$ 020 ; 050