On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model
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 R0 < 1, the analysis of the asymptotic behavior around the disease-free equilibrium E0 is provided while when R0 > 1, we prove that the invariant measure is unique and ergodic. The numerical simulations also validate our analytical results.
- Publication:
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Physica A Statistical Mechanics and its Applications
- Pub Date:
- June 2019
- DOI:
- 10.1016/j.physa.2019.04.181
- arXiv:
- arXiv:1806.08696
- Bibcode:
- 2019PhyA..523.1008F
- Keywords:
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- Stochastic delayed SIRS model;
- General incidence rate;
- Invariant measure;
- Asymptotic behavior;
- Mathematics - Dynamical Systems
- E-Print:
- This article is a total of 20 pages and contains 5 figures