Asymptotic behavior of the solutions for a stochastic SIRS model with information intervention

Tingting Ding; Tongqian Zhang; Tingting Ding; Tongqian Zhang

doi:10.3934/mbe.2022327

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 6940-6961. doi: 10.3934/mbe.2022327

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Asymptotic behavior of the solutions for a stochastic SIRS model with information intervention

Tingting Ding ,
Tongqian Zhang ^,

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Academic Editor: Sanling Yuan

Received: 09 April 2022 Revised: 26 April 2022 Accepted: 04 May 2022 Published: 09 May 2022

In this paper, a stochastic SIRS epidemic model with information intervention is considered. By constructing an appropriate Lyapunov function, the asymptotic behavior of the solutions for the proposed model around the equilibria of the deterministic model is investigated. We show the average in time of the second moment of the solutions of the stochastic system is bounded for a relatively small noise. Furthermore, we find that information interaction response rate plays an active role in disease control, and as the intensity of the response increases, the number of infected population decreases, which is beneficial for disease control.
- information intervention,
- SIRS model,
- stochastic perturbation,
- asymptotic behavior
Citation: Tingting Ding, Tongqian Zhang. Asymptotic behavior of the solutions for a stochastic SIRS model with information intervention[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6940-6961. doi: 10.3934/mbe.2022327

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Abstract

In this paper, a stochastic SIRS epidemic model with information intervention is considered. By constructing an appropriate Lyapunov function, the asymptotic behavior of the solutions for the proposed model around the equilibria of the deterministic model is investigated. We show the average in time of the second moment of the solutions of the stochastic system is bounded for a relatively small noise. Furthermore, we find that information interaction response rate plays an active role in disease control, and as the intensity of the response increases, the number of infected population decreases, which is beneficial for disease control.

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