期刊
MATHEMATICAL BIOSCIENCES AND ENGINEERING
卷 19, 期 10, 页码 10618-10636出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2022496
关键词
epidemic model; stochastic; Brownian motion; extinction; persistence; numerical simulation
资金
- Natural Science Foundation of Xinjiang Uygur Autonomous Region [2021D01B35]
- Natural Science Foundation of Colleges and Universities in Xinjiang Uygur Autonomous Region [XJEDU2021Y048]
- Doctoral Initiation Fund of Xinjiang Institute of Engineering [2020xgy012302]
A stochastic SIRS epidemic model with vaccination is discussed in this paper. A new stochastic threshold R-0(s) is determined. It is found that when the noise is very low (R-0(s) < 1), the disease becomes extinct, and if R-0(s) > 1, the disease persists. Furthermore, the solution of the stochastic model is shown to oscillate around the endemic equilibrium point, with the intensity of the fluctuation proportional to the intensity of the white noise. Computer simulations are used to support these findings.
A stochastic SIRS epidemic model with vaccination is discussed. A new stochastic threshold R-0(s) is determined. When the noise is very low (R-0(s) < 1), the disease becomes extinct, and if R-0(s) > 1, the disease persists. Furthermore, we show that the solution of the stochastic model oscillates around the endemic equilibrium point and the intensity of the fluctuation is proportional to the intensity of the white noise. Computer simulations are used to support our findings.
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