Annealed and Mean-Field formulations of Disease Dynamics on Static and Adaptive Networks

TL;DR

This paper introduces an annealed network approach to model disease spread, providing a unified framework that improves accuracy over traditional methods and applies to both static and adaptive networks.

Contribution

It presents a novel annealed formulation for disease dynamics on networks, unifying static and adaptive cases and enhancing predictive accuracy over existing mean-field models.

Findings

Accurately reproduces numerical simulation results

Improves upon traditional heterogeneous mean-field models

Provides a new formulation for epidemic dynamics

Abstract

We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network ensemble, and allows to solve the dynamical evolution of the whole network ensemble all at once. Our results accurately reproduce those obtained by extensive numerical simulations showing a large improvement with respect to the usual heterogeneous mean-field formulation. Moreover, by means of the annealed formulation we derive a new heterogeneous mean-field formulation that correctly reproduces the epidemic dynamics.