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Schurz, H. (2001) Moment Attractivity, Stability and Contractivity Exponents of Stochastic Dynamical Systems. Discrete and Continuous Dynamical Systems— Series A, 7, 487-515. https://doi.org/10.3934/dcds.2001.7.487

has been cited by the following article:

• TITLE: Asymptotic Behavior and Stability of Stochastic SIR Model with Variable Diffusion Rates

  AUTHORS: Xianhua Xie, Li Ma, Jingfei Xu

  KEYWORDS: SIR Model, Regularity, Lyapunov Function, Stochastic Asymptotic Stability

  JOURNAL NAME: Applied Mathematics, Vol.8 No.8, August 7, 2017

  ABSTRACT: In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.