  For mathematical and experimental ease, models with time varying parameters
are often simplified to assume constant parameters. However, this
simplification can potentially lead to identifiability issues (lack of
uniqueness of parameter estimates). Methods have been developed to
algebraically and numerically determine the identifiability of a model, as well
as resolve identifiability issues. This specific type of simplification
presents an alternate opportunity to instead use this information to resolve
the unidentifiability. Given that re-parameterizing, collecting more data, and
adding inputs can be potentially costly or impractical, this could present new
alternatives.
  We present a method for resolving unidentifiability in a system by
introducing a new data stream correlated with a parameter of interest. First,
we demonstrate how and when non-constant input data can be introduced into any
rational function ODE system without worsening the model identifiability. Then,
we prove when these input functions improve structural and potentially also
practical identifiability for a given model and relevant data.
  By utilizing pre-existing data streams, these methods can potentially reduce
experimental costs, while still answering key questions. By connecting
mathematical proofs to application, our framework removes guesswork from when,
where, and how researchers can best introduce new data to improve model
outcomes.
