IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v142y2021ics0960077920309115.html
   My bibliography  Save this article

Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth

Author

Listed:
  • Han, Bingtao
  • Jiang, Daqing
  • Zhou, Baoquan
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

Focusing on the results of Rajasekar (2020) and the continuous dynamics of stochastic differential equation (SDE) developed by Mao (1997), a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth is investigated in this paper. First, we propose and prove that the unique solution of stochastic model is globally positive. By constructing some suitable Lyapunov functions, the sufficient condition R0h>1 is obtained for the unique stationary distribution which has ergodicity property. Next, by solving the corresponding Fokker-Planck equation, we derive the approximate probability density function around the quasi-endemic equilibrium of the stochastic system. The above stationary distribution and density function can reveal all statistical properties of the disease persistence. In addition, by comparison with other existing articles, our developed theoretical results and some numerical simulations are introduced at the end of this paper.

Suggested Citation

  • Han, Bingtao & Jiang, Daqing & Zhou, Baoquan & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920309115
    DOI: 10.1016/j.chaos.2020.110519
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920309115
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110519?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. Liu, Qun & Jiang, Daqing & Shi, Ningzhong, 2018. "Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 310-325.
    2. Yakui Xue & Tiantian Li, 2013. "Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, November.
    3. 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).
    4. Liu, Qun & Jiang, Daqing, 2019. "Stationary distribution of a stochastic staged progression HIV model with imperfect vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    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. 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. Rajasekar, S.P. & Pitchaimani, M., 2020. "Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    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. Li, Jinhui & Teng, Zhidong & Wang, Guangqing & Zhang, Long & Hu, Cheng, 2017. "Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatment," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 63-71.
    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. Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    2. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Rao, Feng & Kang, Yun, 2023. "Dynamics of a stochastic prey–predator system with prey refuge, predation fear and its carry-over effects," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. 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.

    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. 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.
    2. Han, Bingtao & Zhou, Baoquan & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary solution, extinction and density function for a high-dimensional stochastic SEI epidemic model with general distributed delay," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    3. 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).
    4. 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).
    5. 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).
    6. Zhao, Yu & Zhang, Liping & Yuan, Sanling, 2018. "The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 248-260.
    7. Huyi Wang & Ge Zhang & Tao Chen & Zhiming Li, 2023. "Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence," Mathematics, MDPI, vol. 11(7), pages 1-17, April.
    8. 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).
    9. 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.
    10. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    11. Liu, Qun & Jiang, Daqing, 2020. "Dynamical behavior of a higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    12. 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).
    13. 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.
    14. 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).
    15. Ángel G. C. Pérez & Eric Avila-Vales & Gerardo Emilio García-Almeida, 2019. "Bifurcation Analysis of an SIR Model with Logistic Growth, Nonlinear Incidence, and Saturated Treatment," Complexity, Hindawi, vol. 2019, pages 1-21, July.
    16. Liu, Yue & Sun, Huaping & Zhang, Jijian & Taghizadeh-Hesary, Farhad, 2020. "Detection of volatility regime-switching for crude oil price modeling and forecasting," Resources Policy, Elsevier, vol. 69(C).
    17. Wang, Jinling & Jiang, Haijun & Ma, Tianlong & Hu, Cheng, 2019. "Global dynamics of the multi-lingual SIR rumor spreading model with cross-transmitted mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 148-157.
    18. Wang, Qi & Xiang, Kainan & Zhu, Chunhui & Zou, Lang, 2023. "Stochastic SEIR epidemic models with virus mutation and logistic growth of susceptible populations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 289-309.
    19. Liu, Yan & Mei, Jingling & Li, Wenxue, 2018. "Stochastic stabilization problem of complex networks without strong connectedness," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 304-315.
    20. 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).

    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:chsofr:v:142:y:2021:i:c:s0960077920309115. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.