Hierarchical and Upstream-Downstream Composition of Stock and Flow Models
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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.
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