Dynamics of a stochastic epidemic model with quarantine and non-monotone incidence

Tingting Wang; Shulin Sun; Tingting Wang; Shulin Sun

doi:10.3934/math.2023669

AIMS Mathematics

2023, Volume 8, Issue 6: 13241-13256. doi: 10.3934/math.2023669

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Research article

Dynamics of a stochastic epidemic model with quarantine and non-monotone incidence

Tingting Wang ^,,
Shulin Sun ^,

School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, Shanxi, China

Received: 09 December 2022 Revised: 03 March 2023 Accepted: 08 March 2023 Published: 03 April 2023
MSC : 34D30, 60H10, 92D25

In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts.
- stochastic model,
- non-monotone incidence,
- Itô's formula,
- Lyapunov function,
- basic reproduction number,
- extinction,
- stationary distribution
Citation: Tingting Wang, Shulin Sun. Dynamics of a stochastic epidemic model with quarantine and non-monotone incidence[J]. AIMS Mathematics, 2023, 8(6): 13241-13256. doi: 10.3934/math.2023669

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Abstract

In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts.

References

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