EDMD methods for analysis and prediction of bilinear compartmental models

Abstract

In this paper, we consider bilinear compartmental models. Using the Koopman operator in connection with the Extended Dynamic Mode Decomposition (EDMD), we try to obtain a linear approximation of the original system in a vector space whose dimension is bigger than the original state space. This approach is based on the choice of a dictionary of observables. In the case of bilinear compartmental models there is a natural choice of observables. We present this choice and we examine the efficiency of the method. Especially, we focus on the SIR model which is used to describe the transmission of a disease through some population.