title: Critical properties of a superdiffusive epidemic process.
abstract: 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.
authors.affiliation: Departamento de Física, Universidade Federal do Rio Grande do Norte, 59072-970, Natal, Rio Grande do Norte, Brazil.
authors.forename: M B
authors.initials: MB
authors.lastname: da Silva
authors.forename: A
authors.initials: A
authors.lastname: Macedo-Filho
authors.forename: E L
authors.initials: EL
authors.lastname: Albuquerque
authors.forename: M
authors.initials: M
authors.lastname: Serva
authors.forename: M L
authors.initials: ML
authors.lastname: Lyra
authors.forename: U L
authors.initials: UL
authors.lastname: Fulco
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D004058:Diffusion; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D018562:Disease Transmission, Infectious / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D015233:Models, Statistical