The threshold of stochastic SIS epidemic model with saturated incidence rate

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• 作者：Qixing Han (1) (2)
  Daqing Jiang (2)
  Shan Lin (3)
  Chengjun Yuan (4)
  
  1. School of Mathematics ; Changchun Normal University ; Changchun ; 130032 ; China
  2. College of Science ; China University of Petroleum (East China) ; Qingdao ; 266580 ; China
  3. School of Mathematics and Statistics ; Northeast Normal University ; Changchun ; 130024 ; China
  4. School of Mathematics and Computer ; Harbin University ; Harbin ; 150086 ; China
  
• 关键词：stochastic SIS model ; saturated incidence rate ; It么鈥檚 formula ; extinction ; ergodic property
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,125 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

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.