Long-range epidemic spreading in a random environment

Abstract

Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma }$. We study the dynamical behavior of the model at and below the epidemic threshold by a variant of the strong-disorder renormalization group method and by Monte Carlo simulations in one and two spatial dimensions. Starting from a single infected site, the average survival probability is found to decay as $P(t)\sim t^{-d/z}$ up to multiplicative logarithmic corrections. Below the epidemic threshold, a Griffiths phase emerges, where the dynamical exponent $z$ varies continuously with the control parameter and tends to $z_c=d+\sigma$ as the threshold is approached. At the threshold, the spatial extension of the infected cluster (in surviving trials) is found to grow as $R(t)\sim t^{1/z_c}$ with a multiplicative logarithmic correction, and the average number of infected sites in surviving trials is found to increase as $N_s(t)\sim (\ln t{)}^{\chi }$ with $\chi =2$ in one dimension.

12 pages, 6 figures

References in corpus (39)

• Universality classes in nonequilibrium lattice systems
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Strong disorder RG approach of random systems
• Griffiths phases on complex networks
• Strong disorder fixed point in absorbing state phase transitions
• Levy-flight spreading of epidemic processes leading to percolating clusters
• Absorbing state phase transitions with quenched disorder
• The boundary between long-range and short-range critical behavior
• Critical behavior and Griffiths effects in the disordered contact process
• Relations between Short Range and Long Range Ising models
• An Impurity Driven Phase Transition in the Antiferromagnetic Spin-1 Chain
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Phase transition of one dimensional bosons with strong disorder
• Infinite disorder scaling of random quantum magnets in three and higher dimensions
• A model for anomalous directed percolation
• Percolation Transition in the random antiferromagnetic spin-1 chain
• Superfluid-insulator transition of disordered bosons in one-dimension
• Criticality and quenched disorder: rare regions vs. Harris criterion
• Influence of long-range interactions on the critical behavior of the Ising model
• Non-equilibrium Phase Transitions with Long-Range Interactions
• Renormalization group study of random quantum magnets
• Phases of random antiferromagnetic spin-1 chains
• Disorder induced cross-over effects at quantum critical points
• Random transverse-field Ising chain with long-range interactions
• Rare region effects in the contact process on networks
• Two-dimensional SIR epidemics with long range infection
• Weakly disordered absorbing-state phase transitions
• SIR epidemics with long range infection in one dimension
• Directed Percolation with long-range interactions: modeling non-equilibrium wetting
• Long-range epidemic spreading with immunization
• Contact processes with long-range interactions
• Epidemic spreading with long-range infections and incubation times
• Strong disorder renormalization group study of S=1/2 Heisenberg antiferromagnet layers/bilayers with bond randomness, site dilution and dimer dilution
• The one-dimensional contact process: duality and renormalisation
• Contact process with long-range interactions: a study in the ensemble of constant particle number
• The contact process in heterogeneous and weakly-disordered systems
• Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process
• Infinite randomness critical behavior of the contact process on networks with long-range connections
• Infinite-disorder critical points of models with stretched exponential interactions

Cited by in corpus (15)

• Percolation on complex networks: Theory and application
• Strong Disorder RG approach - a short review of recent developments
• Long-range random transverse-field Ising model in three dimensions
• Measuring neuronal avalanches in disordered systems with absorbing states
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Strong Disorder Renewal Approach to DNA denaturation and wetting : typical and large deviation properties of the free energy
• Phase-transitions of the random bond Potts chain with long-range interactions
• Emergence of disconnected clusters in heterogeneous complex systems
• Dyson hierarchical quantum ferromagnetic Ising chain with pure or random transverse fields
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Multipartite Entanglement in the Random Ising Chain
• Persistence discontinuity in disordered contact processes with long-range interactions
• Renormalization theory of disordered contact processes with heavy-tailed dispersal
• Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal
• Local vs. long-range infection in unidimensional epidemics