IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v434y2015icp25-35.html
   My bibliography  Save this article

SIR model on a dynamical network and the endemic state of an infectious disease

Author

Listed:
  • Dottori, M.
  • Fabricius, G.

Abstract

In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on dynamical networks that involve local and global contacts among individuals and analysed the influence of the network properties on the characterization of the quasi-stationary state. We computed probability density functions (PDF) for infected fraction of individuals and found that they are well fitted by gamma functions, excepted the tails of the distributions that are q-exponentials. We also computed the fluctuation power spectra of infective time series for different networks. We found that network effects can be partially absorbed by rescaling the rate of infective contacts of the model. An explicit relation between the effective transmission rate of the disease and the correlation of susceptible individuals with their infective nearest neighbours was obtained. This relation quantifies the known screening of infective individuals observed in these networks. We finally discuss the goodness and limitations of the SIR model with homogeneous mixing and parameters taken from epidemiological data to describe the dynamic behaviour observed in the networks studied.

Suggested Citation

  • Dottori, M. & Fabricius, G., 2015. "SIR model on a dynamical network and the endemic state of an infectious disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 25-35.
    • Handle: RePEc:eee:phsmap:v:434:y:2015:i:c:p:25-35
    DOI: 10.1016/j.physa.2015.04.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115003660
    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.2015.04.007?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.

    Citations

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


    Cited by:

    1. Alexander Karaivanov, 2020. "A social network model of COVID-19," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-33, October.
    2. Fabricius, Gabriel & Maltz, Alberto, 2020. "Exploring the threshold of epidemic spreading for a stochastic SIR model with local and global contacts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Lu, Xuefei & Borgonovo, Emanuele, 2023. "Global sensitivity analysis in epidemiological modeling," European Journal of Operational Research, Elsevier, vol. 304(1), pages 9-24.
    4. Maltz, Alberto & Fabricius, Gabriel, 2016. "SIR model with local and global infective contacts: A deterministic approach and applications," Theoretical Population Biology, Elsevier, vol. 112(C), pages 70-79.
    5. Wang, Dan & Cheng, Shun-Jun, 2016. "A two-stage broadcast message propagation model in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1286-1293.

    More about this item

    Keywords

    SIR; Network; Stochastic; Pertussis;
    All these keywords.

    Statistics

    Access and download statistics

    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:434:y:2015:i:c:p:25-35. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.