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Stability analysis of a SIR epidemic model with random parametric perturbations

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  • Bobryk, R.V.

Abstract

This paper is concerned with a SIR model for the spread of an epidemic amongst a population of individuals with random additive perturbations of the transmission rate. Recently, many papers are devoted to the case of the Gaussian white noise perturbation. However, this model violates the condition of positivity of the transmission rate. In the paper we consider three models of the random perturbation which do not change this condition. The two of them are the telegraphic noise, trichotomous noise and the third is the bounded noise. Explicit conditions of the amost sure asymptotic stability of disease-free equilibrium state are obtained in the case of the first two models. An efficient numerical procedure is proposed for the construction of stability charts in the case of bounded noise. The effect of random perturbations on the stability behavior of disease-free equilibrium is discussed. Some transient mean-square properties of the SIR stochastic epidemic model are also presented.

Suggested Citation

  • Bobryk, R.V., 2021. "Stability analysis of a SIR epidemic model with random parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309437
    DOI: 10.1016/j.chaos.2020.110552
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    References listed on IDEAS

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    1. Wu, Jiancheng & Li, Xuan & Liu, Xianbin, 2017. "On the pth moment stability of the binary airfoil induced by bounded noise," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 109-120.
    2. d’Onofrio, Alberto & Caravagna, Giulio & de Franciscis, Sebastiano, 2018. "Bounded noise induced first-order phase transitions in a baseline non-spatial model of gene transcription," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2056-2068.
    3. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
    4. Siewe, M. Siewe & Kenfack, W. Fokou & Kofane, T.C., 2019. "Probabilistic response of an electromagnetic transducer with nonlinear magnetic coupling under bounded noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 26-35.
    5. Lu, Ruoxin & Wei, Fengying, 2019. "Persistence and extinction for an age-structured stochastic SVIR epidemic model with generalized nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 572-587.
    6. Ji, Chunyan & Jiang, Daqing & Shi, Ningzhong, 2011. "Multigroup SIR epidemic model with stochastic perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1747-1762.
    7. Liu, Qun & Chen, Qingmei, 2015. "Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 140-153.
    8. Ping Han & Zhengbo Chang & Xinzhu Meng, 2020. "Asymptotic Dynamics of a Stochastic SIR Epidemic System Affected by Mixed Nonlinear Incidence Rates," Complexity, Hindawi, vol. 2020, pages 1-17, May.
    9. Jin, Yanfei & Wang, Heqiang, 2020. "Noise-induced dynamics in a Josephson junction driven by trichotomous noises," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    10. Cheng, Guanghui & Liu, Weidan & Gui, Rong & Yao, Yuangen, 2020. "Sine-Wiener bounded noise-induced logical stochastic resonance in a two-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    11. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    12. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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