Decorated cospans are a general framework for composing open networks
and mapping them to dynamical systems. We explain this framework and
illustrate it with the example of stock and flow diagrams. These
diagrams are widely used in epidemiology to model the dynamics of
populations. Although tools already exist for building these diagrams
and simulating the systems they describe, we have created a new
software package called StockFlow which uses decorated cospans to
overcome some limitations of existing software. Our approach cleanly
separates the syntax of stock and flow diagrams from the semantics
they can be assigned. We have implemented a semantics where stock and
flow diagrams are mapped to ordinary differential equations, although
others are possible. We illustrate this with code in StockFlow that
implements a simplified version of a COVID-19 model used in Canada.
This is joint work with Xiaoyan Li, Sophie Libkind, Nathaniel Osgood
and Evan Patterson.