Threshold dynamics of a stochastic general SIRS epidemic model with migration

Zhongwei Cao; Jian Zhang; Huishuang Su; Li Zu; Zhongwei Cao; Jian Zhang; Huishuang Su; Li Zu

doi:10.3934/mbe.2023497

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 11212-11237. doi: 10.3934/mbe.2023497

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Threshold dynamics of a stochastic general SIRS epidemic model with migration

1.
Logistics Industry Economy and Intelligent Logistics Laboratory, Jilin University of Finance and Economics, Changchun 130117, China
2.
Department of Basic Teaching and Research, Changchun Finance College, Changchun 130028, China
3.
Yatai School of Business Management, Jilin University of Finance and Economics, Changchun 130117, China
4.
College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China

Academic Editor: Xichao Duan

Received: 02 December 2022 Revised: 27 March 2023 Accepted: 14 April 2023 Published: 25 April 2023

In this study, a stochastic SIRS epidemic model that features constant immigration and general incidence rate is investigated. Our findings show that the dynamical behaviors of the stochastic system can be predicted using the stochastic threshold $ R_0^S $. If $ R_0^S < 1 $, the disease will become extinct with certainty, given additional conditions. Conversely, if $ R_0^S > 1 $, the disease has the potential to persist. Moreover, the necessary conditions for the existence of the stationary distribution of positive solution in the event of disease persistence is determined. Our theoretical findings are validated through numerical simulations.
- immigration,
- general incidence rate,
- SIRS epidemic model,
- threshold dynamics,
- ergodicity
Citation: Zhongwei Cao, Jian Zhang, Huishuang Su, Li Zu. Threshold dynamics of a stochastic general SIRS epidemic model with migration[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 11212-11237. doi: 10.3934/mbe.2023497

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Abstract

In this study, a stochastic SIRS epidemic model that features constant immigration and general incidence rate is investigated. Our findings show that the dynamical behaviors of the stochastic system can be predicted using the stochastic threshold $ R_0^S $. If $ R_0^S < 1 $, the disease will become extinct with certainty, given additional conditions. Conversely, if $ R_0^S > 1 $, the disease has the potential to persist. Moreover, the necessary conditions for the existence of the stationary distribution of positive solution in the event of disease persistence is determined. Our theoretical findings are validated through numerical simulations.

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