IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i5p1142-1150.html
   My bibliography  Save this article

Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

Author

Listed:
  • de Souza, David R.
  • Tomé, Tânia

Abstract

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S → I → R → S (SIRS). The open process S → I → R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations.

Suggested Citation

  • de Souza, David R. & Tomé, Tânia, 2010. "Stochastic lattice gas model describing the dynamics of the SIRS epidemic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1142-1150.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:5:p:1142-1150
    DOI: 10.1016/j.physa.2009.10.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437109009091
    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.2009.10.039?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. 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).
    2. 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.
    3. Silva, Ana T.C. & Assis, Vladimir R.V. & Pinho, Suani T.R. & Tomé, Tânia & de Oliveira, Mário J., 2017. "Stochastic spatial structured model for vertically and horizontally transmitted infection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 131-138.
    4. Kumar, Aanjaneya & Grassberger, Peter & Dhar, Deepak, 2021. "Chase-Escape percolation on the 2D square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    5. Katori, Machiko & Katori, Makoto, 2021. "Continuum percolation and stochastic epidemic models on Poisson and Ginibre point processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    6. Pires, Marcelo A. & Crokidakis, Nuno, 2017. "Dynamics of epidemic spreading with vaccination: Impact of social pressure and engagement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 167-179.
    7. Jorritsma, Joost & Hulshof, Tim & Komjáthy, Júlia, 2020. "Not all interventions are equal for the height of the second peak," Chaos, Solitons & Fractals, Elsevier, vol. 139(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:389:y:2010:i:5:p:1142-1150. 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.