Analysis of a stochastic SIB cholera model with saturation recovery rate and Ornstein-Uhlenbeck process

Buyu Wen; Bing Liu; Qianqian Cui; Buyu Wen; Bing Liu; Qianqian Cui

doi:10.3934/mbe.2023517

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 11644-11655. doi: 10.3934/mbe.2023517

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Research article

Analysis of a stochastic SIB cholera model with saturation recovery rate and Ornstein-Uhlenbeck process

1.
School of Information Engineering, Liaodong University, Dandong 118003, Liaoning, China
2.
School of Mathematics and Information Science, Anshan Normal University, Anshan 114007, Liaoning, China
3.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China

Received: 26 March 2023 Revised: 17 April 2023 Accepted: 23 April 2023 Published: 06 May 2023

In this paper, a stochastic SIB(Susceptible-Infected-Vibrios) cholera model with saturation recovery rate and Ornstein-Uhlenbeck process is investigated. It is proved that there is a unique global solution for any initial value of the model. Furthermore, the sufficient criterion of the stationary distribution of the model is obtained by constructing a suitable Lyapunov function, and the expression of probability density function is calculated by the same condition. The correctness of the theoretical results is verified by numerical simulation, and the specific expression of the marginal probability density function is obtained.
- stochastic SIB cholera model,
- saturation recovery rate,
- Ornstein-Uhlenbeck process,
- stationary distribution,
- density function
Citation: Buyu Wen, Bing Liu, Qianqian Cui. Analysis of a stochastic SIB cholera model with saturation recovery rate and Ornstein-Uhlenbeck process[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 11644-11655. doi: 10.3934/mbe.2023517

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Abstract

In this paper, a stochastic SIB(Susceptible-Infected-Vibrios) cholera model with saturation recovery rate and Ornstein-Uhlenbeck process is investigated. It is proved that there is a unique global solution for any initial value of the model. Furthermore, the sufficient criterion of the stationary distribution of the model is obtained by constructing a suitable Lyapunov function, and the expression of probability density function is calculated by the same condition. The correctness of the theoretical results is verified by numerical simulation, and the specific expression of the marginal probability density function is obtained.

References

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