Modeling epidemics on adaptively evolving networks: a data-mining perspective

TL;DR

This paper presents a data-driven method using Diffusion Maps to identify key observables in epidemic models on adaptive networks, aiding the development of reduced models for complex epidemic dynamics.

Contribution

It introduces a novel application of Diffusion Maps for extracting informative statistics from epidemic network data, facilitating coarse-grained modeling.

Findings

Successfully identified key observables in simulated epidemic data.

Demonstrated the approach on a complex epidemic model with dynamic networks.

Discussed potential extensions and limitations of the method.

Abstract

The exploration of epidemic dynamics on dynamically evolving ("adaptive") networks poses nontrivial challenges to the modeler, such as the determination of a small number of informative statistics of the detailed network state (that is, a few "good observables") that usefully summarize the overall (macroscopic, systems level) behavior. Trying to obtain reduced, small size, accurate models in terms of these few statistical observables - that is, coarse-graining the full network epidemic model to a small but useful macroscopic one - is even more daunting. Here we describe a data-based approach to solving the first challenge: the detection of a few informative collective observables of the detailed epidemic dynamics. This will be accomplished through Diffusion Maps, a recently developed data-mining technique. We illustrate the approach through simulations of a simple mathematical model of epidemics on a network: a model known to exhibit complex temporal dynamics. We will discuss potential extensions of the approach, as well as possible shortcomings.