Unified mean-field framework for susceptible-infected-susceptible epidemics on networks, based on graph partitioning and the isoperimetric inequality
K. Devriendt (TU Delft - Network Architectures and Services)
P. Van Mieghem (TU Delft - Network Architectures and Services)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
We propose an approximation framework that unifies and generalizes a number of existing mean-field approximation methods for the susceptible-infected-susceptible (SIS) epidemic model on complex networks. We derive the framework, which we call the unified 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, 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 N-intertwined mean-field approximation and heterogeneous mean-field method, which are contained by UMFF. Additionally, the isoperimetric inequality relates the UMFF approximation accuracy to the regularity notions of Szemerédi's regularity lemma.