Network Reconstruction Problem for an Epidemic Reaction-Diffusion

Abstract

We study the network reconstruction problem for an epidemic reactiondiffusion. 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.

Flow Redirection for Epidemic Reaction-DIffusion Control

“…Quick diffusion loss. Conversely, the third loss, QuickDiffLoss for "Quick Diffusion Loss", is the limit, when τ → 0, of the basic reproduction number (see Beaufort et al (2021) for a proof in the special case of a SIR reaction, but the same reasoning applies to SEIR). It is defined by, for every parameter θ,…”