  Ordinary differential equations (ODE) models have a wide variety of
applications in the fields of mathematics, statistics, and the sciences. Though
they are widely used, these models are sometimes viewed as inflexible with
respect to the incorporation of time delays. The Generalized Linear Chain Trick
(GLCT) serves as a way for modelers to incorporate much more flexible delay or
dwell time distribution assumptions than the usual exponential and Erlang
distributions. In this paper we demonstrate how the GLCT can be used to
generate new ODE models by generalizing or approximating existing models to
yield much more general ODEs with phase-type distributed delays or dwell times.
