  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.
