IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v387y2008i14p3555-3562.html
   My bibliography  Save this article

Multi-phase epidemic model by a Markov chain

Author

Listed:
  • Buccellato, Stefania Maria
  • Tornatore, Elisabetta

Abstract

In this paper we propose a continuous-time Markov chain to describe the spread of an infective and non-mortal disease into a community numerically limited and subjected to an external infection. We make a numerical simulation that shows tendencies for recurring epidemic outbreaks and for fade-out or extinction of the infection.

Suggested Citation

  • Buccellato, Stefania Maria & Tornatore, Elisabetta, 2008. "Multi-phase epidemic model by a Markov chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3555-3562.
  • Handle: RePEc:eee:phsmap:v:387:y:2008:i:14:p:3555-3562
    DOI: 10.1016/j.physa.2008.01.115
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437108001283
    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.2008.01.115?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. 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.
    Full references (including those not matched with items on IDEAS)

    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. Li, Shuang & Xiong, Jie, 2024. "SIR epidemic model with non-Lipschitz stochastic perturbations," Statistics & Probability Letters, Elsevier, vol. 210(C).
    2. William Brock & Anastasios Xepapadeas, 2020. "The Economy, Climate Change and Infectious Diseases: Links and Policy Implications," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 811-824, August.
    3. Zhiming Li & Zhidong Teng, 2019. "Analysis of uncertain SIS epidemic model with nonlinear incidence and demography," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 475-491, December.
    4. 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.
    5. 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.
    6. 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.
    7. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    8. 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.
    9. Guo, Yingjia, 2017. "Stochastic regime switching SIR model driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 1-11.
    10. 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.
    11. Bobryk, R.V., 2021. "Stability analysis of a SIR epidemic model with random parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    12. Zhou, Yanli & Zhang, Weiguo, 2016. "Threshold of a stochastic SIR epidemic model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 204-216.
    13. 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.
    14. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Su, Huishuang & Li, Xue, 2020. "Dynamic behaviors of a two-group stochastic SIRS epidemic model with standard incidence rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    15. El Fatini, Mohamed & El Khalifi, Mohamed & Gerlach, Richard & Laaribi, Aziz & Taki, Regragui, 2019. "Stationary distribution and threshold dynamics of a stochastic SIRS model with a general incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    16. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 816-826.
    17. Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.
    18. Pan, Tao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Extinction and periodic solutions for an impulsive SIR model with incidence rate stochastically perturbed," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 385-397.
    19. 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).
    20. Settati, A. & Lahrouz, A. & Assadouq, A. & El Fatini, M. & El Jarroudi, M. & Wang, K., 2020. "The impact of nonlinear relapse and reinfection to derive a stochastic threshold for SIRI epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 137(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:387:y:2008:i:14:p:3555-3562. 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.