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Exact solution of the dynamic epidemic model on the Bethe lattice

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  • Vandewalle, N.
  • Ausloos, M.

Abstract

The dynamic epidemic model considers the spreading of a cluster in a medium containing a fraction x of mobile particles which are pushed by the propagation front. This model is analytically studied on the Bethe lattice for any branching rate z. We give the exact solution xc = (z2 − 1)/z2 for the percolation threshold. This is in contrast with the xc = (z − 1)/z result for static particles. Moreover, we calculate the critical exponents γ = 1 and ν = 1 characterizing respectively the divergence of the cluster mass and the correlation length at xc. These exponents are found to be the same as for the case of static particles, i.e. for random percolation on the Bethe lattice.

Suggested Citation

  • Vandewalle, N. & Ausloos, M., 1996. "Exact solution of the dynamic epidemic model on the Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(1), pages 1-10.
    • Handle: RePEc:eee:phsmap:v:230:y:1996:i:1:p:1-10
    DOI: 10.1016/0378-4371(96)00103-3
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    References listed on IDEAS

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    1. Aharony, Joseph & Saunders, Anthony & Swary, Itzhak, 1988. "The effects of DIDMCA on bank stockholders' returns and risk," Journal of Banking & Finance, Elsevier, vol. 12(3), pages 317-331, September.
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    Cited by:

    1. Vitanov, Nikolay K. & Vitanov, Kaloyan N., 2018. "Discrete-time model for a motion of substance in a channel of a network with application to channels of human migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 635-650.
    2. Ausloos, M. & Mróz, I. & Pȩkalski, A. & Vandewalle, N., 1998. "Lattice gas model of gradual evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 248(1), pages 155-164.
    3. Vandewalle, N. & Ausloos, M., 1997. "The boundary of “life” for a self-organized critical evolution: the role of the interaction range," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 494-502.

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