Epidemic spreading with long-range infections and incubation times

Abstract

The non-equilibrium phase transition in models for epidemic spreading with long-range infections in combination with incubation times is investigated by field-theoretical and numerical methods. Here the spreading process is modelled by spatio-temporal Levy flights, i.e., it is assumed that both spreading distance and incubation time decay algebraically. Depending on the infection rate one observes a phase transition from a fluctuating active phase into an absorbing phase, where the infection becomes extinct. This transition between spreading and extinction is characterized by continuously varying critical exponents, extending from a mean-field regime to a phase described by the universality class of directed percolation. We compute the critical exponents in the vicinity of the upper critical dimension by a field-theoretic renormalization group calculation and verify the results in one spatial dimension by extensive numerical simulations.

arXiv comment20 pages, 7 figures

References in corpus (9)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Langevin equations for continuous time Lévy flights
• Universal scaling behavior of non-equilibrium phase transitions
• Wilson renormalization of a reaction-diffusion process
• Levy-flight spreading of epidemic processes leading to percolating clusters
• Levy Flights in External Force Fields: From Models to Equations
• Levy Flights in Inhomogeneous Media
• A model for anomalous directed percolation

Cited by in corpus (11)

• Non-equilibrium Phase Transitions with Long-Range Interactions
• Long-range epidemic spreading with immunization
• Contact processes with long-range interactions
• Long-range epidemic spreading in a random environment
• Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models
• Nonequilibrium phase transition in a spreading process on a timeline
• Phase-transitions of the random bond Potts chain with long-range interactions
• Fractional Klein-Gordon Equation on AdS${}_{2+1}$
• Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Persistence discontinuity in disordered contact processes with long-range interactions