  The growing complexity of decision-making in public health and health care
has motivated an increasing use of mathematical modeling. An important line of
health modeling is based on stock & flow diagrams. Such modeling elevates
transparency across the interdisciplinary teams responsible for most impactful
models, but existing tools suffer from a number of shortcomings when used at
scale. Recent research has sought to address such limitations by establishing a
categorical foundation for stock & flow modeling, including the capacity to
compose a pair of models through identification of common stocks and sum
variables. This work supplements such efforts by contributing two new forms of
composition for stock & flow diagrams. We first describe a hierarchical means
of diagram composition, in which a single existing stock is replaced by a
diagram featuring compatible flow structure. Our composition method offers
extra flexibility by allowing a single flow in the stock being replaced to
split into several flows totalling to the same overall flow rate. Secondly, to
address the common need of docking a stock & flow diagram with another
"upstream" diagram depicting antecedent factors, we contribute a composition
approach that allows a flow out of an upstream stock in one diagram to be
connected to a downstream stock in another diagram. Both of these approaches
are enabled by performing colimit decomposition of stock & flow diagrams into
single-stock corollas and unit flows.
