Identifiability of Linear Compartmental Models: The Impact of Removing Leaks and Edges

A mathematical model is identifiable if its parameters can be recovered from data. Here, we focus on a particular class of model, linear compartmental models, which are used to represent the transfer of substances in a system. We analyze what happens to identifiability when operations are performed on a model, specifically, adding or deleting a leak or an edge. We first consider the conjecture of Gross et al. that states that removing a leak from an identifiable model yields a model that is again identifiable. We prove a special case of this conjecture, and also show that the conjecture is equivalent to asserting that leak terms do not divide the so-called singular-locus equation. As for edge terms that do divide this equation, we conjecture that removing any one of these edges makes the model become unidentifiable,and then prove a case of this somewhat surprising conjecture.