Network Reconstruction and Prediction of Epidemic Outbreaks for General Group-Based Compartmental Epidemic Models

The underlying core of most epidemic models is the graph that specifies the contacts between healthy and infected individuals. However, in the majority of applications, the contact network is unknown. To understand and predict an epidemic outbreak nonetheless, network reconstruction methods aim to estimate the contact network from viral state observations. This work considers general compartmental epidemic models (GEMF) in discrete time, which describe the viral spread between groups of individuals. The reconstruction of the network translates into a set of linear equations that is severely ill-conditioned. Counterintuitively, we show that the contact network cannot be reconstructed from one epidemic outbreak with any finite machine precision, although an accurate prediction of the epidemic outbreak is possible.