Dynamics and stochastic sensitivity technique of a stochastic SIRS epidemic model

Jiabing Huang; Jierui Du; Haiye Liang; Jiabing Huang; Jierui Du; Haiye Liang

doi:10.3934/math.2026278

AIMS Mathematics

2026, Volume 11, Issue 3: 6720-6743. doi: 10.3934/math.2026278

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Research article

Dynamics and stochastic sensitivity technique of a stochastic SIRS epidemic model

1.
School of Mathematics and Statistics, Guilin University of Technology, Guilin, Guangxi, 541004, China
2.
Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guilin, Guangxi, 541004, China

Received: 31 January 2026 Revised: 03 March 2026 Accepted: 06 March 2026 Published: 16 March 2026
MSC : 92D30, 92D25, 60H10, 34D20, 37A30

The article investigates a stochastic SIRS epidemic model by perturbing the natural death rate. A stochastic threshold $ R_{s} $ that determines the dynamics of the model is given. More concretely, if $ R_{s} < 1 $, then the disease will die out; if $ R_{s} > 1 $, then the model exhibits an ergodic stationary distribution. Furthermore, a Gaussian approximation of the stationary distribution is given using the stochastic sensitivity technique. For the visual description of the distribution, a confidence ellipsoid is presented by the visualization geometric method of confidence domains. The confidence ellipsoid is helpful for us to estimate the equilibrium region of the stochastic model. Moreover, several numerical analyses are presented to verify the results.
- SIRS model,
- stochastic threshold,
- ergodic stationary distribution,
- stochastic sensitivity technique,
- confidence ellipsoid
Citation: Jiabing Huang, Jierui Du, Haiye Liang. Dynamics and stochastic sensitivity technique of a stochastic SIRS epidemic model[J]. AIMS Mathematics, 2026, 11(3): 6720-6743. doi: 10.3934/math.2026278

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Abstract

The article investigates a stochastic SIRS epidemic model by perturbing the natural death rate. A stochastic threshold $ R_{s} $ that determines the dynamics of the model is given. More concretely, if $ R_{s} < 1 $, then the disease will die out; if $ R_{s} > 1 $, then the model exhibits an ergodic stationary distribution. Furthermore, a Gaussian approximation of the stationary distribution is given using the stochastic sensitivity technique. For the visual description of the distribution, a confidence ellipsoid is presented by the visualization geometric method of confidence domains. The confidence ellipsoid is helpful for us to estimate the equilibrium region of the stochastic model. Moreover, several numerical analyses are presented to verify the results.

References

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