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

Author

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  • 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
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    Citations

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    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. 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.
    4. 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.
    5. Lu, Xuefei & Borgonovo, Emanuele, 2023. "Global sensitivity analysis in epidemiological modeling," European Journal of Operational Research, Elsevier, vol. 304(1), pages 9-24.

    More about this item

    Keywords

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

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