A new way of investigating the asymptotic behaviour of a stochastic SIS system with multiplicative noise. (January 2019)

• Record Type: Journal Article
• Authors: Chang, Zhengbo; Meng, Xinzhu; Zhang, Tonghua
• Is Part Of: Applied mathematics letters. Volume 87(2019)
• Page Start: 80
• Page End: 86
• Publication Date: 2019-01
• Subjects: Stochastic SIS model -- Ornstein–Uhlenbeck process -- Compact random absorbing set; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.07.014
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we investigate a nonlinear stochastic SIS epidemic system with multiplicative noise. First, we transform the Itô's integral into an equivalent Stratonovich integral. Then, by using the solution of Langevin equation and Ornstein–Uhlenbeck process, we prove that the system generates a random dynamical system which has a tempered compact random absorbing set, implying the condition for the extinction of the disease. Finally, the discussion and numerical simulation are given to demonstrate the obtained result.