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Ergodic property, extinction and density function of a stochastic SIR epidemic model with nonlinear incidence and general stochastic perturbations

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  • Zhou, Baoquan
  • Han, Bingtao
  • Jiang, Daqing

Abstract

Focusing on the unpredictability of person-to-person contacts and the complexity of random variations in nature, this paper will formulate a stochastic SIR epidemic model with nonlinear incidence rate and general stochastic noises. First, we derive a stochastic critical value R0S related to the basic reproduction number R0. Via our new method in constructing suitable Lyapunov function types, we obtain the existence and uniqueness of an ergodic stationary distribution of the stochastic system if R0S>1. Next, via solving the corresponding Fokker-Planck equation, it is theoretically proved that the stochastic model has a log-normal probability density function when another critical value R0H>1. Then the exact expression of the density function is obtained. Moreover, we establish the sufficient condition R0C<1 for disease extinction. Finally, several numerical simulations are provided to verify our analytical results. By comparison with other existing results, our developed theories and methods will be highlighted to end this paper.

Suggested Citation

  • Zhou, Baoquan & Han, Bingtao & Jiang, Daqing, 2021. "Ergodic property, extinction and density function of a stochastic SIR epidemic model with nonlinear incidence and general stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006925
    DOI: 10.1016/j.chaos.2021.111338
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    as
    1. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    2. Khan, Tahir & Khan, Amir & Zaman, Gul, 2018. "The extinction and persistence of the stochastic hepatitis B epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 123-128.
    3. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    4. Zhang, Xinhong & Shi, Zhenfeng & Wang, Yuanyuan, 2019. "Dynamics of a stochastic avian–human influenza epidemic model with mutation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    5. Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    6. Caraballo, Tomás & Fatini, Mohamed El & Khalifi, Mohamed El & Gerlach, Richard & Pettersson, Roger, 2020. "Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. Bernardo Spagnolo & Davide Valenti, 2008. "Volatility Effects on the Escape Time in Financial Market Models," Papers 0810.1625, arXiv.org.
    8. Zhou, Baoquan & Zhang, Xinhong & Jiang, Daqing, 2020. "Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    9. Yan Wang & Daqing Jiang, 2017. "Stationary Distribution and Extinction of a Stochastic Viral Infection Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-13, October.
    10. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    11. Liu, Qun & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 140-147.
    12. Wang, Fengyan & Wang, Xiaoyi & Zhang, Shuwen & Ding, Changming, 2014. "On pulse vaccine strategy in a periodic stochastic SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 127-135.
    13. Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    14. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 199-210.
    15. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    16. Roy, Manojit & Holt, Robert D., 2008. "Effects of predation on host–pathogen dynamics in SIR models," Theoretical Population Biology, Elsevier, vol. 73(3), pages 319-331.
    17. Spagnolo, B. & La Barbera, A., 2002. "Role of the noise on the transient dynamics of an ecosystem of interacting species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 114-124.
    18. Liu, Qun & Chen, Qingmei & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 115-125.
    19. Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    20. Wei Hu, 2018. "A New Stability Criterion for Neutral Stochastic Delay Differential Equations with Markovian Switching," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, October.
    21. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

    1. Shuang Li, 2024. "SIR Epidemic Model with General Nonlinear Incidence Rate and Lévy Jumps," Mathematics, MDPI, vol. 12(2), pages 1-21, January.
    2. Liu, Qun & Jiang, Daqing, 2023. "Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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