Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation

Zhengwen Yin; Yuanshun Tan; Zhengwen Yin; Yuanshun Tan

doi:10.3934/math.20241597

AIMS Mathematics

2024, Volume 9, Issue 12: 33467-33492. doi: 10.3934/math.20241597

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Research article

Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation

Zhengwen Yin ,
Yuanshun Tan ^,

College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China

Received: 22 September 2024 Revised: 06 November 2024 Accepted: 18 November 2024 Published: 25 November 2024
MSC : 34F05, 60G10

In this paper, we investigated a stochastic SIRS epidemic infectious disease model that accounted for environmentally driven infection and incorporated multiparameter perturbations. In addition to establishing the existence and uniqueness of the global positive solution of the model, we derived the threshold conditions for the extinction and persistence of the disease using the comparison theorem and It$ \hat{o} $'s formula of stochastic differential equations. Subsequently, we obtained the asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the deterministic model corresponding to the stochastic model through stochastic stability theory. The results indicated that high-intensity noise perturbation can inhibit the spread of the disease, and the dynamic behavior of the disease transitioned from persistence to extinction as noise intensity increased. Our study also demonstrated that, compared to perturbations in the indirect infection rate, changes in noise intensity that affect the direct infection rate will have a more significant impact on disease transmission.
- SIRS epidemic model,
- environmental driven infections,
- threshold dynamics,
- multiparameter perturbation
Citation: Zhengwen Yin, Yuanshun Tan. Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation[J]. AIMS Mathematics, 2024, 9(12): 33467-33492. doi: 10.3934/math.20241597

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Abstract

In this paper, we investigated a stochastic SIRS epidemic infectious disease model that accounted for environmentally driven infection and incorporated multiparameter perturbations. In addition to establishing the existence and uniqueness of the global positive solution of the model, we derived the threshold conditions for the extinction and persistence of the disease using the comparison theorem and It$ \hat{o} $'s formula of stochastic differential equations. Subsequently, we obtained the asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the deterministic model corresponding to the stochastic model through stochastic stability theory. The results indicated that high-intensity noise perturbation can inhibit the spread of the disease, and the dynamic behavior of the disease transitioned from persistence to extinction as noise intensity increased. Our study also demonstrated that, compared to perturbations in the indirect infection rate, changes in noise intensity that affect the direct infection rate will have a more significant impact on disease transmission.

References

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