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We propose a new approximation framework that unifies and generalizes anumber of existing mean-field approximation methods for the SIS epidemic modelon complex networks. We derive the framework, which we call the UniversalMean-Field Framework (UMFF), as a set of approximations of the exact MarkovianSIS equations. Our main novelty is that we describe the mean-fieldapproximations from the perspective of the isoperimetric problem, an insightwhich results in bounds on the UMFF approximation error. These new boundsprovide insight in the accuracy of existing mean-field methods, such as thewidely-used N-Intertwined Mean-Field Approximation (NIMFA) and HeterogeneousMean-Field method (HMF). Additionally, the geometric perspective of theisoperimetric problem enables the UMFF approximation accuracy to be related tothe regularity notions of Szemer\'edi's regularity lemma, which yields aprediction about the behavior of the SIS process on large graphs.

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