Unified mean-field framework for susceptible-infected-susceptible epidemics on networks, based on graph partitioning and the isoperimetric inequality

Unified mean-field framework for susceptible-infected-susceptible epidemics on networks, based on graph partitioning and the isoperimetric inequality

Devriendt, K.L.T. (TU Delft Network Architectures and Services)
Van Mieghem, P.F.A. (TU Delft Network Architectures and Services)

2017

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.

http://resolver.tudelft.nl/uuid:18157513-a0ab-4680-93c6-f9bf76ce01d4

https://doi.org/10.1103/PhysRevE.96.052314

2470-0045

Physical Review E, 96 (5), 1-18

Institutional Repository

journal article

© 2017 K.L.T. Devriendt, P.F.A. Van Mieghem