Dynamics of a stochastic SIRS epidemic model with standard incidence and vaccination

Tingting Xue; Xiaolin Fan; Zhiguo Chang; Tingting Xue; Xiaolin Fan; Zhiguo Chang

doi:10.3934/mbe.2022496

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 10618-10636. doi: 10.3934/mbe.2022496

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Dynamics of a stochastic SIRS epidemic model with standard incidence and vaccination

1.
School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi, Xinjiang, China
2.
School of Safety Science, Xinjiang Institute of Engineering, Urumqi, Xinjiang, China

Academic Editor: Jesús Martín Vaquero

Received: 28 May 2022 Revised: 19 July 2022 Accepted: 20 July 2022 Published: 26 July 2022

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.
- epidemic model,
- stochastic,
- Brownian motion,
- extinction,
- persistence,
- numerical simulation
Citation: Tingting Xue, Xiaolin Fan, Zhiguo Chang. Dynamics of a stochastic SIRS epidemic model with standard incidence and vaccination[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10618-10636. doi: 10.3934/mbe.2022496

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Abstract

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.

References

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