The threshold of stochastic SIS epidemic model with saturated incidence rate

Advances in Difference Equations

Shan Lin¹  Daqing Jiang¹  Chengjun Yuan²  Qixing Han³ 

[1] College of Science, China University of Petroleum (East China), Qingdao, China;School of Mathematics and Statistics, Northeast Normal University, Changchun, China;School of Mathematics, Changchun Normal University, Changchun, China

关键词: stochastic SIS model;    saturated incidence rate;    Itô’s formula;    extinction;    ergodic property;   

DOI  :  10.1186/s13662-015-0355-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper considers a stochastic SIS model with saturated incidence rate. We investigate the existence and uniqueness of the positive solution to the system, and we show the condition for the infectious individuals to be extinct. Moreover, we prove that the system has the ergodic property and derive the expression for its invariant density. The simulation results are illustrated finally.

【 授权许可】

CC BY