On some topological properties of a strongly connected compartmental system with application to the identifiability problem

Abstract In this paper some structural properties of a strongly connected compartmental system are illustrated. In particular a suitable set of “cycles” and “paths” associated to the compartmental graph is constructed, such that an application exists between the parameter space and the space of sycles and paths, whose suitable restriction is a bijection. It is shown that this set contains the minimum number of functions necessary to uniquely identify the parametrization vector, and its relevance in identifiability analysis is illustrated.