An expanded schematic for compartmental systems

Abstract

A major advantage of the usual diagrammatic representation for linear, time-invariant compartmental models is that there is a one-to-one correspondence between the model and the set of linear, constant-coefficient differential equations it represents. This means the investigator can get insight into the system the model is describing by studying the connectivity of the model without worrying about the differential equations. No such general schematic exists for the general compartmental model, i.e. compartmental models described by equations that are nonlinear. In the present work, a schematic for such models in given. This schematic has the following advantages: (1) consistency with the rules of graph theory, and (2) reduction to the usual representation for linear, constant-coefficient systems. Thus the understanding of the system enjoyed in the simpler case is retained with the suggested schematics. Examples of how the rules apply are given.