IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v615y2023ics0378437123001607.html
   My bibliography  Save this article

Stationary distribution, extinction and probability density function of a stochastic SEIV epidemic model with general incidence and Ornstein–Uhlenbeck process

Author

Listed:
  • Su, Tan
  • Yang, Qing
  • Zhang, Xinhong
  • Jiang, Daqing

Abstract

Considering the great benefit of vaccination and the variability of environmental influence, a stochastic SEIV epidemic model with mean-reversion Ornstein–Uhlenbeck process and general incidence rate is investigated in this paper. First, it is theoretically proved that stochastic model has a unique global solution. Next, by constructing a series of suitable Lyapunov functions, we obtain a sufficient criterion R0s>1 for the existence of stationary distribution which means the disease will last for a long time. Then, the sufficient condition for the extinction of the infectious disease is also derived. Furthermore, an exact expression of probability density function near the quasi-endemic equilibrium is obtained by solving the corresponding four-dimensional matrix equation. Finally, some numerical simulations are carried out to illustrate the theoretical results.

Suggested Citation

  • Su, Tan & Yang, Qing & Zhang, Xinhong & Jiang, Daqing, 2023. "Stationary distribution, extinction and probability density function of a stochastic SEIV epidemic model with general incidence and Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    • Handle: RePEc:eee:phsmap:v:615:y:2023:i:c:s0378437123001607
    DOI: 10.1016/j.physa.2023.128605
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123001607
    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.2023.128605?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. 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. Zhang, Xiaofeng & Yuan, Rong, 2021. "A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    3. 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).
    4. 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.
    5. Zhang, Shengqiang & Yuan, Sanling & Zhang, Tonghua, 2022. "A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    6. Ayoubi, Tawfiqullah & Bao, Haibo, 2020. "Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    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. Zhang, Ge & Li, Zhiming & Din, Anwarud & Chen, Tao, 2024. "Dynamic analysis and optimal control of a stochastic COVID-19 model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 498-517.
    2. Lili Kong & Luping Li & Shugui Kang & Fu Chen, 2023. "Dynamic Behavior of a Stochastic Avian Influenza Model with Two Strains of Zoonotic Virus," Mathematics, MDPI, vol. 11(19), pages 1-21, October.

    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. Wang, Haile & Zuo, Wenjie & Jiang, Daqing, 2023. "Dynamical analysis of a stochastic epidemic HBV model with log-normal Ornstein–Uhlenbeck process and vertical transmission term," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Liu, Qun & Jiang, Daqing, 2023. "Analysis of a stochastic inshore–offshore hairtail fishery model with Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. 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).
    4. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    5. Han, Cheng & Wang, Yan & Jiang, Daqing, 2023. "Dynamics analysis of a stochastic HIV model with non-cytolytic cure and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    6. Han, Bingtao & Jiang, Daqing, 2023. "Coexistence and extinction for a stochastic vegetation-water model motivated by Black–Karasinski process," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    7. 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).
    8. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    9. Fehaid Salem Alshammari & Fahir Talay Akyildiz, 2023. "Epidemic Waves in a Stochastic SIRVI Epidemic Model Incorporating the Ornstein–Uhlenbeck Process," Mathematics, MDPI, vol. 11(18), pages 1-15, September.
    10. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    11. 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).
    12. Shi, Zhenfeng & Jiang, Daqing & Zhang, Xinhong & Alsaedi, Ahmed, 2022. "A stochastic SEIRS rabies model with population dispersal: Stationary distribution and probability density function," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    13. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    14. de la Cruz, H. & Jimenez, J. C, 2020. "Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    15. Selvan, T. Tamil & Kumar, M., 2023. "Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    16. Liu, Qun & Jiang, Daqing, 2020. "Stationary distribution of a stochastic cholera model with imperfect vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    17. Xu, Jiang & Chen, Tao & Wen, Xiangdan, 2021. "Analysis of a Bailey–Dietz model for vector-borne disease under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    18. Zhang, Xiaofeng & Yuan, Rong, 2021. "Forward attractor for stochastic chemostat model with multiplicative noise," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    19. Huo, Hai-Feng & Jing, Shuang-Lin & Wang, Xun-Yang & Xiang, Hong, 2020. "Modeling and analysis of a H1N1 model with relapse and effect of Twitter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    20. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of a stochastic cholera model between communities linked by migration," Applied Mathematics and Computation, Elsevier, vol. 373(C).

    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:615:y:2023:i:c:s0378437123001607. 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.