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 DA and DB over a distance distributed according to a power-law probability P ( ) ∝ 1/ μ . For μ 3 the propagation is equivalent to diffusion, while μ < 3 corresponds to L ́ evy flights. In the DA > DB 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) DA > DB 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