Critical properties of a superdiffusive epidemic process.

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.