Interdependency and hierarchy of exact epidemic models on networks

TL;DR

This paper explores the relationships and hierarchies among various exact epidemic models on networks, providing a unified motif-based framework and deriving general differential equations for epidemic dynamics.

Contribution

It introduces a motif-based perspective linking different SIS models, derives exact differential equations from master equations, and compares model performance on various network structures.

Findings

Models can be derived from one another or extended to do so.

A general result for exact differential equations for motifs is established.

Model performance varies with network structure.

Abstract

Over the years numerous models of SIS (susceptible - infected - susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general motif-based models. We illustrate how the different models can be derived from one another and, where this is not possible, discuss extensions to established models that enables this derivation. We also derive a general result for the exact differential equations for the expected number of an arbitrary motif directly from the Kolmogorov/master equations and conclude with a comparison of the performance of the different closed systems of equations on networks of varying structure.