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Droplet finite-size scaling theory of asynchronous SIR model on quenched scale-free networks

Author

Listed:
  • Alencar, D.S.M.
  • Alves, T.F.A.
  • Ferreira, R.S.
  • Lima, F.W.S.
  • Alves, G.A.
  • Macedo-Filho, A.

Abstract

We present a finite-size scaling theory of the asynchronous susceptible–infected–removed model on scale-free networks, which models epidemic outbreaks and gives a non-vanishing critical threshold. The susceptible–infected–removed model can be mapped in a bond percolation process, as stressed by P. Grassberger, allowing us to compare the critical behavior of site and bond universality classes on networks. We employ a droplet heterogeneous mean-field theory, adding the effect of an external field defined as the initial number of infected individuals. One can choose the external field scaling as N−1, where N is the number of network nodes, and compare theoretical results with simulations on the uncorrelated model and Barabasi–Albert networks. The system presents a percolating phase transition where the critical behavior obeys the mean-field universality class, as we show theoretically and by extensive simulations.

Suggested Citation

  • Alencar, D.S.M. & Alves, T.F.A. & Ferreira, R.S. & Lima, F.W.S. & Alves, G.A. & Macedo-Filho, A., 2023. "Droplet finite-size scaling theory of asynchronous SIR model on quenched scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    • Handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s037843712300657x
    DOI: 10.1016/j.physa.2023.129102
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
    2. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
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