Universal mean-field framework for SIS epidemics on networks, based on graph partitioning and the isoperimetric inequality

Abstract

We propose a new approximation framework that unifies and generalizes a number of existing mean-field approximation methods for the SIS epidemic model on complex networks. We derive the framework, which we call the Universal Mean-Field Framework (UMFF), as a set of approximations of the exact Markovian SIS equations. Our main novelty is that we describe the mean-field approximations from the perspective of the isoperimetric problem, an insight which results in bounds on the UMFF approximation error. These new bounds provide insight in the accuracy of existing mean-field methods, such as the widely-used N-Intertwined Mean-Field Approximation (NIMFA) and Heterogeneous Mean-Field method (HMF). Additionally, the geometric perspective of the isoperimetric problem enables the UMFF approximation accuracy to be related to the regularity notions of Szemerédi's regularity lemma, which yields a prediction about the behavior of the SIS process on large graphs.

References in corpus (9)

• Epidemic spreading in scale-free networks
• Epidemic processes in complex networks
• Hyperbolic Geometry of Complex Networks
• Thresholds for epidemic spreading in networks
• Epidemic spreading in correlated complex networks
• Unification of theoretical approaches for epidemic spreading on complex networks
• Self-similarity of complex networks and hidden metric spaces
• Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks
• Epidemic Outbreaks in Networks with Equitable or Almost-Equitable Partitions

Cited by in corpus (8)

• Clustering for epidemics on networks: a geometric approach
• Non-linear network dynamics with consensus-dissensus bifurcation
• Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time
• A unified framework of epidemic spreading prediction by empirical mode decomposition based ensemble learning techniques
• Transition from time-variant to static networks: timescale separation in NIMFA SIS epidemics
• Accuracy criterion for mean field approximations of Markov processes on hypergraphs
• Weights Adaptation Optimization of Heterogeneous Epidemic Spreading Networks: A Constrained Cooperative Coevolution Strategy
• Statistical inference for unknown parameters of stochastic SIS epidemics on complete graphs