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

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  • 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
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    Citations

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    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. 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).
    3. 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).
    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. 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.
    6. 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).
    7. 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.

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