Open AccessExtinction and persistence of a stochastic SIRS model with nonlinear incidence rate and transfer from infectious to susceptible
Author(s) -
Qiuhua Zhang,
Kai Zhou
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1324/1/012016
Subject(s) - extinction (optical mineralogy) , persistence (discontinuity) , uniqueness , nonlinear system , mathematics , epidemic model , incidence (geometry) , statistical physics , econometrics , biology , physics , medicine , mathematical analysis , environmental health , engineering , geometry , geotechnical engineering , paleontology , population , quantum mechanics
In this paper, we propose a stochastic SIRS model with nonlinear incidence rate and transfer from infectious to susceptible. We first give the existence and uniqueness of the positive solution for this system. Moreover, the extinction of the disease and the persistence in the mean are established in the terms of a threshold value.