Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks

Abstract

We present a quenched mean-field (QMF) theory for the dynamics of the susceptible-infected-susceptible (SIS) epidemic model on complex networks where dynamical correlations between connected vertices are taken into account by means of a pair approximation. We present analytical expressions of the epidemic thresholds in the star and wheel graphs and in random regular networks. For random networks with a power law degree distribution, the thresholds are numerically determined via an eigenvalue problem. The pair and one-vertex QMF theories yield the same scaling for the thresholds as functions of the network size. However, comparisons with quasi-stationary simulations of the SIS dynamics on large networks show that the former is quantitatively much more accurate than the latter. Our results demonstrate the central role played by dynamical correlations on the epidemic spreading and introduce an efficient way to theoretically access the thresholds of very large networks that can be extended to dynamical processes in general.

6 pages, 6 figures

References in corpus (5)

• Critical phenomena in complex networks
• Thresholds for epidemic spreading in networks
• Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Quasi-stationary analysis of the contact process on annealed scale-free networks

Cited by in corpus (43)

• Epidemic processes in complex networks
• Unification of theoretical approaches for epidemic spreading on complex networks
• Fundamentals of spreading processes in single and multilayer complex networks
• Abrupt phase transition of epidemic spreading in simplicial complexes
• Effective approach to epidemic containment using link equations in complex networks
• Multistability, intermittency and hybrid transitions in social contagion models on hypergraphs
• Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks
• Heterogeneous pair-approximation for the contact process on complex networks
• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Collective versus hub activation of epidemic phases on networks
• Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks
• Metastable Localization of Diseases in Complex Networks
• Non-Markovian recovery makes complex networks more resilient against large-scale failures
• Optimal Allocation of Resources for Suppressing Epidemic Spreading on Networks
• Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks
• Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks
• Spectral properties and the accuracy of mean-field approaches for epidemics on correlated networks
• Universal mean-field framework for SIS epidemics on networks, based on graph partitioning and the isoperimetric inequality
• From subcritical behavior to elusive transitions in rumor models
• An overview of epidemic models with phase transitions to absorbing states running on top of complex networks
• Non massive immunization to contain spreading on complex networks
• Epidemic Extinction Paths in Complex Networks
• Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks
• Cumulative Merging Percolation and the epidemic transition of the Susceptible-Infected-Susceptible model in networks
• High prevalence regimes in the pair quenched mean-field theory for the susceptible-infected-susceptible model on networks
• On the onset of synchronization of Kuramoto oscillators in scale-free networks
• Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
• Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks
• Approximating quasi-stationary behaviour in network-based SIS dynamics
• Rounding of abrupt phase transitions in brain networks
• Lumping of Degree-Based Mean Field and Pair Approximation Equations for Multi-State Contact Processes
• Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time
• Multistage onset of epidemics in heterogeneous networks
• Variational approximations for stochastic dynamics on graphs
• Critical drift in a neuro-inspired adaptive network
• Influence of individual nodes for continuous-time Susceptible-Infected-Susceptible dynamics on synthetic and real-world networks
• Correlation between transition probability and network structure in epidemic model
• Epidemic threshold and localization of the SIS model on directed complex networks
• Comparison of theoretical approaches for epidemic processes with waning immunity in complex networks
• Data-Driven Optimal Closures for Mean-Cluster Models: Beyond the Classical Pair Approximation
• Abrupt transition of the efficient vaccination strategy in a population with heterogeneous fatality rates
• Spreading processes in "post-epidemic" environments. II. Safety patterns on scale-free networks
• From random point processes to hierarchical Cavity Master Equations for the stochastic dynamics of disordered systems in Random Graphs: Ising models and epidemics