IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v540y2020ics0378437119319478.html
   My bibliography  Save this article

Threshold behavior in a stochastic SIR epidemic model with Logistic birth

Author

Listed:
  • Liu, Qun
  • Jiang, Daqing

Abstract

In this paper, we consider a stochastic SIR epidemic model with Logistic birth. By using the stochastic Lyapunov function method, we show that the stochastic basic reproduction number R0S can be used to determine the threshold dynamics of the stochastic system. If R0S>1, we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model. While if R0S<1, under some extra conditions, we obtain sufficient conditions for extinction of the disease. Finally, some examples and numerical simulations are provided to illustrate the theoretical results.

Suggested Citation

  • Liu, Qun & Jiang, Daqing, 2020. "Threshold behavior in a stochastic SIR epidemic model with Logistic birth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119319478
    DOI: 10.1016/j.physa.2019.123488
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119319478
    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.2019.123488?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. 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.
    2. 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.
    3. Guo, Wenjuan & Cai, Yongli & Zhang, Qimin & Wang, Weiming, 2018. "Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2220-2236.
    4. Xu, Chaoqun & Yuan, Sanling & Zhang, Tonghua, 2018. "Sensitivity analysis and feedback control of noise-induced extinction for competition chemostat model with mutualism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 891-902.
    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. 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.
    7. 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.
    8. 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.
    9. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    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. Doménech-Carbó, Antonio & Doménech-Casasús, Clara, 2021. "The evolution of COVID-19: A discontinuous approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    2. Satoh, Daisuke & Uchida, Masato, 2021. "Riccati equation as topology-based model of computer worms and discrete SIR model with constant infectious period," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(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. Wang, Lei & Wang, Kai & Jiang, Daqing & Hayat, Tasawar, 2018. "Nontrivial periodic solution for a stochastic brucellosis model with application to Xinjiang, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 522-537.
    2. Yang, Bo, 2018. "A stochastic Feline immunodeficiency virus model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 448-458.
    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. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    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. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    7. 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).
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. Acuña-Zegarra, Manuel Adrian & Díaz-Infante, Saúl, 2018. "Stochastic asymptotic analysis of a multi-host model with vector transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 243-260.
    13. Wang, Yan & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2018. "Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 276-292.
    14. Lv, Xuejin & Meng, Xinzhu & Wang, Xinzeng, 2018. "Extinction and stationary distribution of an impulsive stochastic chemostat model with nonlinear perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 273-279.
    15. 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.
    16. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Threshold behavior in two types of stochastic three strains influenza virus models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    17. Liu, Yan & Zhang, Di & Su, Huan & Feng, Jiqiang, 2019. "Stationary distribution for stochastic coupled systems with regime switching and feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    18. Liu, Qun & Jiang, Daqing & He, Xiuli & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 273-287.
    19. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 614-625.
    20. Tuerxun, Nafeisha & Wen, Buyu & Teng, Zhidong, 2021. "The stationary distribution in a class of stochastic SIRS epidemic models with non-monotonic incidence and degenerate diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 888-912.

    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:540:y:2020:i:c:s0378437119319478. 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.