Abstract
The non-equilibrium phase transition in models for epidemic spreading with long-range infectionsin combination with incubation times is investigated by field-theoretical and numerical methods.In this class of models the infection is assumed to spread isotropically over long distancesr whose probability distribution decays algebraically asP(r)∼r−d−σ,where d is the spatial dimension. Moreover, a freshly infected individual can infect otherindividuals only after a certain incubation time, modelled here as a waiting timeΔt, which is distributedprobabilistically as P(Δt)∼(Δt)−1−κ. Tuning the balance between spreading and spontaneous recovery one observes acontinuous phase transition from a fluctuating active phase into an absorbingphase, where the infection becomes extinct. Depending on the parametersσ and κ this transition between spreading and extinction is characterized by continuously varyingcritical exponents, extending from a mean field regime to a phase described by theuniversality class of directed percolation. Specifying the phase diagram in terms ofσ and κ we compute the critical exponents in the vicinity of the upper critical dimensiondc = σ(3−κ−1) by a field-theoretic renormalization group calculation and verify the results in one spatialdimension by extensive numerical simulations.
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have