  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 Szemer\'edi's regularity lemma, which yields a
prediction about the behavior of the SIS process on large graphs.
