Stability of stochastic SIRS epidemic models with saturated incidence rates and delay. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Zhong, Xiaoyun; Guo, Shangjiang; Peng, Minfang
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 1(2017)
• Page Start: 1
• Page End: 26
• Publication Date: 2017-01-02
• Subjects: Stochastic SIRS model -- delay -- Its formula -- stability in probability -- Euler–Maruyama method; 34F05 -- 37H10 -- 60H10 -- 92D25 -- 92D30; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2016.1244644
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this article, we consider stochastic susceptible-infected-removed-susceptible (SIRS) epidemic models with saturated incidence rates and delay. We investigate the stochastic stability in probability of the disease-free and endemic equilibria for the stochastic dynamic model with variability in the natural death rate, and the stochastic stability in probability of the endemic equilibrium for the dynamic model when the variability in the environment is proportional to a deviation between the state of the system and the endemic equilibrium. The numerical experiments are provided to support our theoretical results.