Why is it easier to predict the epidemic curve than to reconstruct the underlying contact network?

TL;DR

This paper demonstrates that predicting epidemic curves is more robust than reconstructing the underlying contact network, providing a rigorous mathematical explanation and explicit formulas based on graph regularity principles.

Contribution

It offers a rigorous derivation explaining why epidemic curve prediction is easier than network reconstruction, utilizing Szemerédi's weak regularity lemma.

Findings

Prediction of epidemic curves is robust for large networks.

Network reconstruction is ill-conditioned and less reliable.

An explicit formula for the underlying network is provided when reconstruction is feasible.

Abstract

We study the deterministic Susceptible-Infected-Susceptible (SIS) epidemic model on weighted graphs. In their numerical study [10] van Mieghem et al. have shown that it is possible to learn an estimated network from a finite time sample of the trajectories of the dynamics that in turn can give an accurate prediction beyond the sample time range, even though the estimated network might be qualitatively far from the ground truth. We give a mathematically rigorous derivation for this phenomenon, notably that for large networks, prediction of the epidemic curves is robust, while reconstructing the underlying network is ill-conditioned. Furthermore, we also provide an explicit formula for the underlying network when reconstruction is possible. At the heart of the explanation, we rely on Szemer\'edi's weak regularity lemma.