IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v545y2020ics037843711931622x.html
   My bibliography  Save this article

Extinction and stationary distribution of an epidemic model with partial vaccination and nonlinear incidence rate

Author

Listed:
  • Wei, Fengying
  • Chen, Lihong

Abstract

A stochastic susceptible–infected–vaccinated model with a general incidence rate and varying population size is considered in this paper. By means of constructing a suitable Lyapunov function, the sufficient conditions for the extinction are derived. Further, some conditions that guarantee the existence of a unique stationary distribution is obtained. The main results are illustrated by computer simulations.

Suggested Citation

  • Wei, Fengying & Chen, Lihong, 2020. "Extinction and stationary distribution of an epidemic model with partial vaccination and nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s037843711931622x
    DOI: 10.1016/j.physa.2019.122852
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711931622X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.122852?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Lihong & Wei, Fengying, 2017. "Persistence and distribution of a stochastic susceptible–infected–removed epidemic model with varying population size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 386-397.
    2. Wei, Fengying & Liu, Jiamin, 2017. "Long-time behavior of a stochastic epidemic model with varying population size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 146-153.
    3. Zhao, Yanan & Jiang, Daqing & O’Regan, Donal, 2013. "The extinction and persistence of the stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4916-4927.
    4. 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.
    5. 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.
    6. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    7. 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.
    8. Qixing Han & Daqing Jiang & Chengjun Yuan, 2013. "Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
    9. Zhao, Dianli & Zhang, Tiansi & Yuan, Sanling, 2016. "The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 372-379.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Fangfang & Wei, Fengying, 2022. "An epidemic model with Beddington–DeAngelis functional response and environmental fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Xiao-Bing & Huo, Hai-Feng & Xiang, Hong & Shi, Qihong & Li, Dungang, 2017. "The threshold of a stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 362-374.
    2. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
    3. Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.
    4. Chang, Zhengbo & Meng, Xinzhu & Lu, Xiao, 2017. "Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 103-116.
    5. 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.
    6. Rifhat, Ramziya & Wang, Lei & Teng, Zhidong, 2017. "Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 176-190.
    7. Li, Yan & Ye, Ming & Zhang, Qimin, 2019. "Strong convergence of the partially truncated Euler–Maruyama scheme for a stochastic age-structured SIR epidemic model," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    8. 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).
    9. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li, 2019. "Dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 894-907.
    10. 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.
    11. Jia, Pingqi & Wang, Chao & Zhang, Gaoyu & Ma, Jianfeng, 2019. "A rumor spreading model based on two propagation channels in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 342-353.
    12. Wanduku, Divine, 2017. "Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 49-76.
    13. Liu, Yue, 2022. "Extinction, persistence and density function analysis of a stochastic two-strain disease model with drug resistance mutation," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    14. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Wei, Xiang, 2017. "A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 198-208.
    15. Hattaf, Khalid & Mahrouf, Marouane & Adnani, Jihad & Yousfi, Noura, 2018. "Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 591-600.
    16. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    17. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Liu, Liya & Hu, Jingwei, 2020. "Analysis of a hybrid switching SVIR epidemic model with vaccination and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    18. Zhao, Dianli & Zhang, Tiansi & Yuan, Sanling, 2016. "The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 372-379.
    19. Sun, Shulin & Zhang, Xiaofeng, 2018. "Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 38-56.
    20. Zhang, Xiao-Bing & Chang, Suqin & Shi, Qihong & Huo, Hai-Feng, 2018. "Qualitative study of a stochastic SIS epidemic model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 805-817.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s037843711931622x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.