1. On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model.
- Author
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Fu, Xiaoming
- Subjects
- *
INVARIANT measures , *BASIC reproduction number , *GLOBAL analysis (Mathematics) , *DIFFUSION coefficients , *STOCHASTIC models - Abstract
In this paper, we consider a stochastic epidemic model with time delay and general incidence rate. We first prove the existence and uniqueness of the global positive solution. By using the Krylov–Bogoliubov method, we obtain the existence of invariant measures. Furthermore, we study a special case where the incidence rate is bilinear with distributed time delay. When the basic reproduction number R 0 < 1 , the analysis of the asymptotic behavior around the disease-free equilibrium E 0 is provided while when R 0 > 1 , we prove that the invariant measure is unique and ergodic. The numerical simulations also validate our analytical results. • The well-posedness of a stochastic delayed SIRS model with general incidence rate is studied. • Establish a general condition on the drift and diffusion coefficients for the existence of invariant measures. • The asymptotic behavior around the disease-free equilibrium is studied. • Obtain a sufficient condition for the uniqueness and the ergodicity of the invariant measure. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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