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Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):062108. Epub 2013 Jun 6.

Critical properties of a superdiffusive epidemic process.

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Departamento de Física, Universidade Federal do Rio Grande do Norte, 59072-970, Natal, Rio Grande do Norte, Brazil.


We introduce a superdiffusive one-dimensional epidemic process model on which infection spreads through a contact process. Healthy (A) and infected (B) individuals can jump with distinct probabilities D(A) and D(B) over a distance ℓ distributed according to a power-law probability P(ℓ)[proportionality]1/ℓ(μ). For μ≥3 the propagation is equivalent to diffusion, while μ<3 corresponds to Lévy flights. In the D(A)>D(B) diffusion regime, field-theoretical results have suggested a first-order transition, a prediction not supported by several numerical studies. An extensive numerical study of the critical behavior in both the diffusive (μ≥3) and superdiffusive (μ<3) D(A)>D(B) regimes is also reported. We employed a finite-size scaling analysis to obtain the critical point as well as the static and dynamic critical exponents for several values of μ. All data support a second-order phase transition with continuously varying critical exponents which do not belong to the directed percolation universality class.

[Indexed for MEDLINE]

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