Network Reconstruction Problem for an Epidemic Reaction-Diffusion

TL;DR

This paper investigates the network reconstruction problem in epidemic reaction-diffusion models, analyzing how diffusion rate and network topology affect the ability to reconstruct and predict epidemic dynamics, with theoretical and experimental insights.

Contribution

It provides new theoretical results on the identifiability of network structures and explores the impact of diffusion and sampling rate on reconstruction and prediction.

Findings

Reconstruction is identifiable for almost every network.

Faster diffusion complicates network reconstruction.

Higher sampling rates improve reconstruction accuracy.

Abstract

We study the network reconstruction problem for an epidemic reaction-diffusion. These models are an extension of deterministic, compartmental models to a graph setting, where the reactions within the nodes are coupled by a diffusion. We study the influence of the diffusion rate, and the network topology, on the reconstruction and prediction problems, both from a theoretical and experimental standpoint.Results first show that for almost every network, the reconstruction problem is identifiable. Then, we show that the faster the diffusion, the harder the reconstruction, but that increasing the sampling rate may help in this respect.Second, we demonstrate that it is possible to classify symmetrical networks generating the same trajectories, and that the prediction problem can still be solved satisfyingly, even when the network topology makes exact reconstruction difficult.